540b971355
* spot/gen/formulas.hh, spot/gen/formulas.cc (genltl): Rename as... (ltl_pattern): This. (ltl_pattern_max): New function. * bin/genltl.cc: Adjust names, and simplify using ltl_pattern_max(). * python/spot/gen.i (ltl_patterns): New function. * tests/python/gen.py: Test it. * tests/python/gen.ipynb: New file to document the spot.gen package. * tests/Makefile.am, doc/org/tut.org: Add gen.ipynb.
1233 lines
38 KiB
C++
1233 lines
38 KiB
C++
// -*- coding: utf-8 -*-
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// Copyright (C) 2012-2017 Laboratoire de Recherche et Developpement
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// de l'EPITA (LRDE).
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//
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// This file is part of Spot, a model checking library.
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//
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// Spot is free software; you can redistribute it and/or modify it
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// under the terms of the GNU General Public License as published by
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// the Free Software Foundation; either version 3 of the License, or
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// (at your option) any later version.
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//
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// Spot is distributed in the hope that it will be useful, but WITHOUT
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// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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// License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <http://www.gnu.org/licenses/>.
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#include <cmath>
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#include <spot/gen/formulas.hh>
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#include <spot/tl/exclusive.hh>
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#include <spot/tl/relabel.hh>
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#include <spot/tl/parse.hh>
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#define G_(x) formula::G(x)
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#define F_(x) formula::F(x)
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#define X_(x) formula::X(x)
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#define Not_(x) formula::Not(x)
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#define Implies_(x, y) formula::Implies((x), (y))
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#define Equiv_(x, y) formula::Equiv((x), (y))
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#define And_(x, y) formula::And({(x), (y)})
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#define Or_(x, y) formula::Or({(x), (y)})
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#define U_(x, y) formula::U((x), (y))
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namespace spot
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{
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namespace gen
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{
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namespace
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{
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// F(p_1 & F(p_2 & F(p_3 & ... F(p_n))))
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static formula
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E_n(std::string name, int n)
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{
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if (n <= 0)
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return formula::tt();
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formula result = nullptr;
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for (; n > 0; --n)
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{
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std::ostringstream p;
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p << name << n;
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formula f = formula::ap(p.str());
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if (result)
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result = And_(f, result);
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else
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result = f;
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result = F_(result);
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}
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return result;
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}
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// p & X(p & X(p & ... X(p)))
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static formula
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phi_n(std::string name, int n,
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op oper = op::And)
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{
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if (n <= 0)
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return formula::tt();
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formula result = nullptr;
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formula p = formula::ap(name);
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for (; n > 0; --n)
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{
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if (result)
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result = formula::multop(oper, {p, X_(result)});
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else
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result = p;
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}
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return result;
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}
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static formula
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N_n(std::string name, int n)
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{
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return formula::F(phi_n(name, n));
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}
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// p & X(p) & XX(p) & XXX(p) & ... X^n(p)
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static formula
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phi_prime_n(std::string name, int n,
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op oper = op::And)
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{
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if (n <= 0)
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return formula::tt();
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formula result = nullptr;
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formula p = formula::ap(name);
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for (; n > 0; --n)
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{
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if (result)
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{
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p = X_(p);
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result = formula::multop(oper, {result, p});
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}
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else
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{
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result = p;
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}
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}
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return result;
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}
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static formula
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N_prime_n(std::string name, int n)
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{
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return F_(phi_prime_n(name, n));
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}
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// GF(p_1) & GF(p_2) & ... & GF(p_n) if conj == true
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// GF(p_1) | GF(p_2) | ... | GF(p_n) if conj == false
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static formula
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GF_n(std::string name, int n, bool conj = true)
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{
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if (n <= 0)
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return conj ? formula::tt() : formula::ff();
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formula result = nullptr;
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op o = conj ? op::And : op::Or;
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for (int i = 1; i <= n; ++i)
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{
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std::ostringstream p;
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p << name << i;
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formula f = G_(F_(formula::ap(p.str())));
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if (result)
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result = formula::multop(o, {f, result});
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else
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result = f;
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}
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return result;
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}
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// FG(p_1) | FG(p_2) | ... | FG(p_n) if conj == false
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// FG(p_1) & FG(p_2) & ... & FG(p_n) if conj == true
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static formula
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FG_n(std::string name, int n, bool conj = false)
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{
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if (n <= 0)
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return conj ? formula::tt() : formula::ff();
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formula result = nullptr;
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op o = conj ? op::And : op::Or;
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for (int i = 1; i <= n; ++i)
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{
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std::ostringstream p;
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p << name << i;
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formula f = F_(G_(formula::ap(p.str())));
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if (result)
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result = formula::multop(o, {f, result});
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else
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result = f;
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}
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return result;
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}
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// (((p1 OP p2) OP p3)...OP pn) if right_assoc == false
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// (p1 OP (p2 OP (p3 OP (... pn) if right_assoc == true
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static formula
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bin_n(std::string name, int n, op o, bool right_assoc = false)
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{
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if (n <= 0)
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n = 1;
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formula result = nullptr;
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for (int i = 1; i <= n; ++i)
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{
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std::ostringstream p;
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p << name << (right_assoc ? (n + 1 - i) : i);
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formula f = formula::ap(p.str());
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if (!result)
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result = f;
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else if (right_assoc)
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result = formula::binop(o, f, result);
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else
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result = formula::binop(o, result, f);
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}
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return result;
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}
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// (GF(p1)|FG(p2))&(GF(p2)|FG(p3))&...&(GF(pn)|FG(p{n+1}))"
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static formula
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R_n(std::string name, int n)
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{
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if (n <= 0)
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return formula::tt();
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formula pi;
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{
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std::ostringstream p;
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p << name << 1;
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pi = formula::ap(p.str());
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}
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formula result = nullptr;
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for (int i = 1; i <= n; ++i)
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{
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formula gf = G_(F_(pi));
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std::ostringstream p;
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p << name << i + 1;
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pi = formula::ap(p.str());
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formula fg = F_(G_(pi));
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formula f = Or_(gf, fg);
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if (result)
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result = And_(f, result);
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else
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result = f;
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}
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return result;
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}
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// (F(p1)|G(p2))&(F(p2)|G(p3))&...&(F(pn)|G(p{n+1}))"
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static formula
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Q_n(std::string name, int n)
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{
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if (n <= 0)
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return formula::tt();
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formula pi;
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{
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std::ostringstream p;
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p << name << 1;
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pi = formula::ap(p.str());
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}
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formula result = nullptr;
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for (int i = 1; i <= n; ++i)
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{
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formula f = F_(pi);
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std::ostringstream p;
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p << name << i + 1;
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pi = formula::ap(p.str());
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formula g = G_(pi);
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f = Or_(f, g);
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if (result)
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result = And_(f, result);
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else
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result = f;
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}
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return result;
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}
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// OP(p1) | OP(p2) | ... | OP(Pn) if conj == false
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// OP(p1) & OP(p2) & ... & OP(Pn) if conj == true
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static formula
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combunop_n(std::string name, int n, op o, bool conj = false)
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{
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if (n <= 0)
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return conj ? formula::tt() : formula::ff();
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formula result = nullptr;
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op cop = conj ? op::And : op::Or;
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for (int i = 1; i <= n; ++i)
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{
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std::ostringstream p;
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p << name << i;
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formula f = formula::unop(o, formula::ap(p.str()));
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if (result)
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result = formula::multop(cop, {f, result});
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else
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result = f;
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}
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return result;
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}
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// !((GF(p1)&GF(p2)&...&GF(pn))->G(q -> F(r)))
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// From "Fast LTL to Büchi Automata Translation" [gastin.01.cav]
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static formula
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fair_response(std::string p, std::string q, std::string r, int n)
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{
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formula fair = GF_n(p, n);
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formula resp = G_(Implies_(formula::ap(q), F_(formula::ap(r))));
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return Not_(Implies_(fair, resp));
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}
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// Builds X(X(...X(p))) with n occurrences of X.
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static formula
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X_n(formula p, int n)
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{
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assert(n >= 0);
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formula res = p;
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while (n--)
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res = X_(res);
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return res;
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}
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// Based on LTLcounter.pl from Kristin Rozier.
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// http://shemesh.larc.nasa.gov/people/kyr/benchmarking_scripts/
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static formula
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ltl_counter(std::string bit, std::string marker, int n, bool linear)
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{
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formula b = formula::ap(bit);
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formula neg_b = Not_(b);
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formula m = formula::ap(marker);
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formula neg_m = Not_(m);
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std::vector<formula> res(4);
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// The marker starts with "1", followed by n-1 "0", then "1" again,
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// n-1 "0", etc.
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if (!linear)
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{
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// G(m -> X(!m)&XX(!m)&XXX(m)) [if n = 3]
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std::vector<formula> v(n);
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for (int i = 0; i + 1 < n; ++i)
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v[i] = X_n(neg_m, i + 1);
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v[n - 1] = X_n(m, n);
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res[0] = And_(m, G_(Implies_(m, formula::And(std::move(v)))));
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}
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else
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{
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// G(m -> X(!m & X(!m X(m)))) [if n = 3]
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formula p = m;
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for (int i = n - 1; i > 0; --i)
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p = And_(neg_m, X_(p));
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res[0] = And_(m, G_(Implies_(m, X_(p))));
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}
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// All bits are initially zero.
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if (!linear)
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{
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// !b & X(!b) & XX(!b) [if n = 3]
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std::vector<formula> v2(n);
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for (int i = 0; i < n; ++i)
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v2[i] = X_n(neg_b, i);
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res[1] = formula::And(std::move(v2));
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}
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else
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{
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// !b & X(!b & X(!b)) [if n = 3]
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formula p = neg_b;
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for (int i = n - 1; i > 0; --i)
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p = And_(neg_b, X_(p));
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res[1] = p;
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}
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#define AndX_(x, y) (linear ? X_(And_((x), (y))) : And_(X_(x), X_(y)))
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// If the least significant bit is 0, it will be 1 at the next time,
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// and other bits stay the same.
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formula Xnm1_b = X_n(b, n - 1);
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formula Xn_b = X_(Xnm1_b);
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res[2] = G_(Implies_(And_(m, neg_b),
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AndX_(Xnm1_b,
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U_(And_(Not_(m), Equiv_(b, Xn_b)), m))));
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// From the least significant bit to the first 0, all the bits
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// are flipped on the next value. Remaining bits are identical.
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formula Xnm1_negb = X_n(neg_b, n - 1);
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formula Xn_negb = X_(Xnm1_negb);
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res[3] =
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G_(Implies_(And_(m, b),
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AndX_(Xnm1_negb,
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U_(And_(And_(b, neg_m), Xn_negb),
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Or_(m, And_(And_(neg_m, neg_b),
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AndX_(Xnm1_b,
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U_(And_(neg_m,
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Equiv_(b, Xn_b)),
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m))))))));
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return formula::And(std::move(res));
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}
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static formula
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ltl_counter_carry(std::string bit, std::string marker,
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std::string carry, int n, bool linear)
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{
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formula b = formula::ap(bit);
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formula neg_b = Not_(b);
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formula m = formula::ap(marker);
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formula neg_m = Not_(m);
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formula c = formula::ap(carry);
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formula neg_c = Not_(c);
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std::vector<formula> res(6);
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// The marker starts with "1", followed by n-1 "0", then "1" again,
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// n-1 "0", etc.
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if (!linear)
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{
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// G(m -> X(!m)&XX(!m)&XXX(m)) [if n = 3]
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std::vector<formula> v(n);
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for (int i = 0; i + 1 < n; ++i)
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v[i] = X_n(neg_m, i + 1);
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v[n - 1] = X_n(m, n);
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res[0] = And_(m, G_(Implies_(m, formula::And(std::move(v)))));
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}
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else
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{
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// G(m -> X(!m & X(!m X(m)))) [if n = 3]
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formula p = m;
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for (int i = n - 1; i > 0; --i)
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p = And_(neg_m, X_(p));
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res[0] = And_(m, G_(Implies_(m, X_(p))));
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}
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// All bits are initially zero.
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if (!linear)
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{
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// !b & X(!b) & XX(!b) [if n = 3]
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std::vector<formula> v2(n);
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for (int i = 0; i < n; ++i)
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v2[i] = X_n(neg_b, i);
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res[1] = formula::And(std::move(v2));
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}
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else
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{
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// !b & X(!b & X(!b)) [if n = 3]
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formula p = neg_b;
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for (int i = n - 1; i > 0; --i)
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p = And_(neg_b, X_(p));
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res[1] = p;
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}
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formula Xn_b = X_n(b, n);
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formula Xn_negb = X_n(neg_b, n);
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// If m is 1 and b is 0 then c is 0 and n steps later b is 1.
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res[2] = G_(Implies_(And_(m, neg_b), And_(neg_c, Xn_b)));
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// If m is 1 and b is 1 then c is 1 and n steps later b is 0.
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res[3] = G_(Implies_(And_(m, b), And_(c, Xn_negb)));
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if (!linear)
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{
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// If there's no carry, then all of the bits stay the same
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// n steps later.
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res[4] = G_(Implies_(And_(neg_c, X_(neg_m)),
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And_(X_(Not_(c)), Equiv_(X_(b), X_(Xn_b)))));
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// If there's a carry, then add one: flip the bits of b and
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// adjust the carry.
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res[5] = G_(Implies_(c, And_(Implies_(X_(neg_b),
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And_(X_(neg_c), X_(Xn_b))),
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Implies_(X_(b),
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And_(X_(c), X_(Xn_negb))))));
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}
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else
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{
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// If there's no carry, then all of the bits stay the same
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// n steps later.
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res[4] = G_(Implies_(And_(neg_c, X_(neg_m)),
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X_(And_(Not_(c), Equiv_(b, Xn_b)))));
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// If there's a carry, then add one: flip the bits of b and
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// adjust the carry.
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res[5] = G_(Implies_(c, X_(And_(Implies_(neg_b, And_(neg_c, Xn_b)),
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Implies_(b, And_(c, Xn_negb))))));
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}
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return formula::And(std::move(res));
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}
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static formula
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tv_f1(std::string p, std::string q, int n)
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{
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return G_(Implies_(formula::ap(p), phi_prime_n(q, n, op::Or)));
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}
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static formula
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tv_f2(std::string p, std::string q, int n)
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{
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return G_(Implies_(formula::ap(p), phi_n(q, n, op::Or)));
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}
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static formula
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tv_g1(std::string p, std::string q, int n)
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{
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return G_(Implies_(formula::ap(p), phi_prime_n(q, n)));
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}
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static formula
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tv_g2(std::string p, std::string q, int n)
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{
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return G_(Implies_(formula::ap(p), phi_n(q, n)));
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}
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static formula
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tv_uu(std::string name, int n)
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{
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std::ostringstream p;
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p << name << n + 1;
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formula q = formula::ap(p.str());
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formula f = q;
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|
|
for (int i = n; i > 0; --i)
|
|
{
|
|
p.str("");
|
|
p << name << i;
|
|
q = formula::ap(p.str());
|
|
f = U_(q, f);
|
|
if (i > 1)
|
|
f = And_(q, f);
|
|
}
|
|
return G_(Implies_(q, f));
|
|
}
|
|
|
|
static void
|
|
bad_number(const char* pattern, int n, int max = 0)
|
|
{
|
|
std::ostringstream err;
|
|
err << "no pattern " << pattern << '=' << n
|
|
<< ", supported range is 1..";
|
|
if (max)
|
|
err << max;
|
|
throw std::runtime_error(err.str());
|
|
}
|
|
|
|
static formula
|
|
dac_pattern(int n)
|
|
{
|
|
static const char* formulas[] = {
|
|
"[](!p0)",
|
|
"<>p2 -> (!p0 U p2)",
|
|
"[](p1 -> [](!p0))",
|
|
"[]((p1 & !p2 & <>p2) -> (!p0 U p2))",
|
|
"[](p1 & !p2 -> (!p0 W p2))",
|
|
|
|
"<>(p0)",
|
|
"!p2 W (p0 & !p2)",
|
|
"[](!p1) | <>(p1 & <>p0)",
|
|
"[](p1 & !p2 -> (!p2 W (p0 & !p2)))",
|
|
"[](p1 & !p2 -> (!p2 U (p0 & !p2)))",
|
|
|
|
"(!p0 W (p0 W (!p0 W (p0 W []!p0))))",
|
|
"<>p2 -> ((!p0 & !p2) U (p2 | ((p0 & !p2) U (p2 |"
|
|
" ((!p0 & !p2) U (p2 | ((p0 & !p2) U (p2 | (!p0 U p2)))))))))",
|
|
"<>p1 -> (!p1 U (p1 & (!p0 W (p0 W (!p0 W (p0 W []!p0))))))",
|
|
"[]((p1 & <>p2) -> ((!p0 & !p2) U (p2 | ((p0 & !p2) U (p2 |"
|
|
"((!p0 & !p2) U (p2 | ((p0 & !p2) U (p2 | (!p0 U p2))))))))))",
|
|
"[](p1 -> ((!p0 & !p2) U (p2 | ((p0 & !p2) U (p2 | ((!p0 & !p2) U"
|
|
"(p2 | ((p0 & !p2) U (p2 | (!p0 W p2) | []p0)))))))))",
|
|
|
|
"[](p0)",
|
|
"<>p2 -> (p0 U p2)",
|
|
"[](p1 -> [](p0))",
|
|
"[]((p1 & !p2 & <>p2) -> (p0 U p2))",
|
|
"[](p1 & !p2 -> (p0 W p2))",
|
|
|
|
"!p0 W p3",
|
|
"<>p2 -> (!p0 U (p3 | p2))",
|
|
"[]!p1 | <>(p1 & (!p0 W p3))",
|
|
"[]((p1 & !p2 & <>p2) -> (!p0 U (p3 | p2)))",
|
|
"[](p1 & !p2 -> (!p0 W (p3 | p2)))",
|
|
|
|
"[](p0 -> <>p3)",
|
|
"<>p2 -> (p0 -> (!p2 U (p3 & !p2))) U p2",
|
|
"[](p1 -> [](p0 -> <>p3))",
|
|
"[]((p1 & !p2 & <>p2) -> ((p0 -> (!p2 U (p3 & !p2))) U p2))",
|
|
"[](p1 & !p2 -> ((p0 -> (!p2 U (p3 & !p2))) W p2))",
|
|
|
|
"<>p0 -> (!p0 U (p3 & !p0 & X(!p0 U p4)))",
|
|
"<>p2 -> (!p0 U (p2 | (p3 & !p0 & X(!p0 U p4))))",
|
|
"([]!p1) | (!p1 U (p1 & <>p0 -> (!p0 U (p3 & !p0 & X(!p0 U p4)))))",
|
|
"[]((p1 & <>p2) -> (!p0 U (p2 | (p3 & !p0 & X(!p0 U p4)))))",
|
|
"[](p1 -> (<>p0 -> (!p0 U (p2 | (p3 & !p0 & X(!p0 U p4))))))",
|
|
|
|
"(<>(p3 & X<>p4)) -> ((!p3) U p0)",
|
|
"<>p2 -> ((!(p3 & (!p2) & X(!p2 U (p4 & !p2)))) U (p2 | p0))",
|
|
"([]!p1) | ((!p1) U (p1 & ((<>(p3 & X<>p4)) -> ((!p3) U p0))))",
|
|
"[]((p1 & <>p2)->((!(p3 & (!p2) & X(!p2 U (p4 & !p2)))) U (p2|p0)))",
|
|
"[](p1 -> (!(p3 & (!p2) & X(!p2 U (p4 & !p2))) U (p2 | p0) |"
|
|
" [](!(p3 & X<>p4))))",
|
|
|
|
"[] (p3 & X<> p4 -> X(<>(p4 & <> p0)))",
|
|
"<>p2 -> (p3 & X(!p2 U p4) -> X(!p2 U (p4 & <> p0))) U p2",
|
|
"[] (p1 -> [] (p3 & X<> p4 -> X(!p4 U (p4 & <> p0))))",
|
|
"[] ((p1 & <>p2)->(p3 & X(!p2 U p4) -> X(!p2 U (p4 & <> p0))) U p2)",
|
|
"[] (p1 -> (p3 & X(!p2 U p4) -> X(!p2 U (p4 & <> p0))) U (p2 |"
|
|
"[] (p3 & X(!p2 U p4) -> X(!p2 U (p4 & <> p0)))))",
|
|
|
|
"[] (p0 -> <>(p3 & X<>p4))",
|
|
"<>p2 -> (p0 -> (!p2 U (p3 & !p2 & X(!p2 U p4)))) U p2",
|
|
"[] (p1 -> [] (p0 -> (p3 & X<> p4)))",
|
|
"[] ((p1 & <>p2) -> (p0 -> (!p2 U (p3 & !p2 & X(!p2 U p4)))) U p2)",
|
|
"[] (p1 -> (p0 -> (!p2 U (p3 & !p2 & X(!p2 U p4)))) U (p2 | []"
|
|
"(p0 -> (p3 & X<> p4))))",
|
|
|
|
"[] (p0 -> <>(p3 & !p5 & X(!p5 U p4)))",
|
|
"<>p2 -> (p0 -> (!p2 U (p3 & !p2 & !p5 & X((!p2 & !p5) U p4)))) U p2",
|
|
"[] (p1 -> [] (p0 -> (p3 & !p5 & X(!p5 U p4))))",
|
|
"[] ((p1 & <>p2) -> (p0 -> (!p2 U (p3 & !p2 & !p5 & X((!p2 & !p5) U"
|
|
" p4)))) U p2)",
|
|
"[] (p1 -> (p0 -> (!p2 U (p3 & !p2 & !p5 & X((!p2 & !p5) U p4)))) U "
|
|
"(p2 | [] (p0 -> (p3 & !p5 & X(!p5 U p4)))))",
|
|
};
|
|
|
|
constexpr unsigned max = (sizeof formulas)/(sizeof *formulas);
|
|
if (n < 1 || (unsigned) n > max)
|
|
bad_number("dac-patterns", n, max);
|
|
return spot::relabel(parse_formula(formulas[n - 1]), Pnn);
|
|
}
|
|
|
|
static formula
|
|
hkrss_pattern(int n)
|
|
{
|
|
static const char* formulas[] = {
|
|
"G(Fp0 & F!p0)",
|
|
"GFp0 & GF!p0",
|
|
"GF(!(p1 <-> Xp1) | !(p0 <-> Xp0))",
|
|
"GF(!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | !(p3 <-> Xp3))",
|
|
"G!p0",
|
|
"G((p0 -> F!p0) & (!p0 -> Fp0))",
|
|
"G(p0 -> F(p0 & p1))",
|
|
"G(p0 -> F((!p0 & p1 & p2 & p3) -> Fp4))",
|
|
"G(p0 -> F!p1)",
|
|
"G(p0 -> Fp1)",
|
|
"G(p0 -> F(p1 -> Fp2))",
|
|
"G(p0 -> F((p1 & p2) -> Fp3))",
|
|
"G((p0 -> Fp1) & (p2 -> Fp3) & (p4 -> Fp5) & (p6 -> Fp7))",
|
|
"G(!p0 & !p1)",
|
|
"G!(p0 & p1)",
|
|
"G(p0 -> p1)",
|
|
"G((p0 -> !p1) & (p1 -> !p0))",
|
|
"G(!p0 -> (p1 <-> !p2))",
|
|
"G((!p0 & (p1 | p2 | p3)) -> p4)",
|
|
"G((p0 & p1) -> (p2 | !(p3 & p4)))",
|
|
"G((!p0 & p1 & !p2 & !p3 & !p4) -> F(!p5 & !p6 & !p7 & !p8))",
|
|
"G((p0 & p1 & !p2 & !p3 & !p4) -> F(p5 & !p6 & !p7 & !p8))",
|
|
"G(!p0 -> !(p1 & p2 & p3 & p4 & p5))",
|
|
"G(!p0 -> ((p1 & p2 & p3 & p4) -> !p5))",
|
|
"G((p0 & p1) -> (p2 | p3 | !(p4 & p5)))",
|
|
"G((!p0 & (p1 | p2 | p3 | p4)) -> (!p5 <-> p6))",
|
|
"G((p0 & p1) -> (p2 | p3 | p4 | !(p5 & p6)))",
|
|
"G((p0 & p1) -> (p2 | p3 | p4 | p5 | !(p6 & p7)))",
|
|
"G((p0 & p1 & !p2 & Xp2) -> X(p3 | X(!p1 | p3)))",
|
|
"G((p0 & p1 & !p2 & Xp2)->X(X!p1 | (p2 U (!p2 U (p2 U (!p1|p3))))))",
|
|
"G(p0 & p1 & !p2 & Xp2)->X(X!p1 | (p2 U (!p2 U (p2 U (!p1 | p3)))))",
|
|
"G(p0 -> (p1 U (!p1 U (!p2 | p3))))",
|
|
"G(p0 -> (p1 U (!p1 U (p2 | p3))))",
|
|
"G((!p0 & p1) -> Xp2)",
|
|
"G(p0 -> X(p0 | p1))",
|
|
("G((!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | !(p3 <-> Xp3)) "
|
|
"-> (X!p4 & X(!(!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | "
|
|
"!(p3 <-> Xp3)) U p4)))"),
|
|
"G((p0 & !p1 & Xp1 & Xp0) -> (p2 -> Xp3))",
|
|
"G(p0 -> X(!p0 U p1))",
|
|
"G((!p0 & Xp0) -> X((p0 U p1) | Gp0))",
|
|
"G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0 & p1))))",
|
|
("G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0 & p1 & (p0 U (p0 & !p1 & "
|
|
"X(p0 & p1)))))))"),
|
|
("G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(!p0 & p1 & (!p0 U (!p0 & "
|
|
"!p1 & X(!p0 & p1)))))))"),
|
|
("G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(!p0 & p1 & (!p0 U (!p0 & "
|
|
"!p1 & X(!p0 & p1 & (!p0 U (!p0 & !p1 & X(!p0 & p1))))))))))"),
|
|
"G((!p0 & Xp0) -> X(!(!p0 & Xp0) U (!p1 & Xp1)))",
|
|
("G(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | "
|
|
"X(!p0 | X(!p0 | X(!p0 | X!p0)))))))))))"),
|
|
"G((Xp0 -> p0) -> (p1 <-> Xp1))",
|
|
"G((Xp0 -> p0) -> ((p1 -> Xp1) & (!p1 -> X!p1)))",
|
|
("!p0 U G!((p1 & p2) | (p3 & p4) | (p2 & p3) | (p2 & p4) | "
|
|
"(p1 & p4) | (p1 & p3))"),
|
|
"!p0 U p1",
|
|
"(p0 U p1) | Gp0",
|
|
"p0 & XG!p0",
|
|
"XG(p0 -> (G!p1 | (!Xp1 U p2)))",
|
|
"XG((p0 & !p1) -> (G!p1 | (!p1 U p2)))",
|
|
"XG((p0 & p1) -> ((p1 U p2) | Gp1))",
|
|
"Xp0 & G((!p0 & Xp0) -> XXp0)",
|
|
};
|
|
|
|
constexpr unsigned max = (sizeof formulas)/(sizeof *formulas);
|
|
if (n < 1 || (unsigned) n > max)
|
|
bad_number("hkrss-patterns", n, max);
|
|
return spot::relabel(parse_formula(formulas[n - 1]), Pnn);
|
|
}
|
|
|
|
static formula
|
|
eh_pattern(int n)
|
|
{
|
|
static const char* formulas[] = {
|
|
"p0 U (p1 & G(p2))",
|
|
"p0 U (p1 & X(p2 U p3))",
|
|
"p0 U (p1 & X(p2 & (F(p3 & X(F(p4 & X(F(p5 & X(F(p6))))))))))",
|
|
"F(p0 & X(G(p1)))",
|
|
"F(p0 & X(p1 & X(F(p2))))",
|
|
"F(p0 & X(p1 U p2))",
|
|
"(F(G(p0))) | (G(F(p1)))",
|
|
"G(p0 -> (p1 U p2))",
|
|
"G(p0 & X(F(p1 & X(F(p2 & X(F(p3)))))))",
|
|
"(G(F(p0))) & (G(F(p1))) & (G(F(p2))) & (G(F(p3))) & (G(F(p4)))",
|
|
"(p0 U (p1 U p2)) | (p1 U (p2 U p0)) | (p2 U (p0 U p1))",
|
|
"G(p0 -> (p1 U ((G(p2)) | (G(p3)))))",
|
|
};
|
|
|
|
constexpr unsigned max = (sizeof formulas)/(sizeof *formulas);
|
|
if (n < 1 || (unsigned) n > max)
|
|
bad_number("eh-patterns", n, max);
|
|
return spot::relabel(parse_formula(formulas[n - 1]), Pnn);
|
|
}
|
|
|
|
static formula
|
|
p_pattern(int n)
|
|
{
|
|
static const char* formulas[] = {
|
|
"G(p0 -> Fp1)",
|
|
"(GFp1 & GFp0) -> GFp2",
|
|
"G(p0 -> (p1 & (p2 U p3)))",
|
|
"F(p0 | p1)",
|
|
"GF(p0 | p1)",
|
|
"(p0 U p1) -> ((p2 U p3) | Gp2)",
|
|
"G(p0 -> (!p1 U (p1 U (!p1 & (p2 R !p1)))))",
|
|
"G(p0 -> (p1 R !p2))",
|
|
"G(!p0 -> Fp0)",
|
|
"G(p0 -> F(p1 | p2))",
|
|
"!(!(p0 | p1) U p2) & G(p3 -> !(!(p0 | p1) U p2))",
|
|
"G!p0 -> G!p1",
|
|
"G(p0 -> (G!p1 | (!p2 U p1)))",
|
|
"G(p0 -> (p1 R (p1 | !p2)))",
|
|
"G((p0 & p1) -> (!p1 R (p0 | !p1)))",
|
|
"G(p0 -> F(p1 & p2))",
|
|
"G(p0 -> (!p1 U (p1 U (p1 & p2))))",
|
|
"G(p0 -> (!p1 U (p1 U (!p1 U (p1 U (p1 & p2))))))",
|
|
"GFp0 -> GFp1",
|
|
"GF(p0 | p1) & GF(p1 | p2)",
|
|
};
|
|
|
|
constexpr unsigned max = (sizeof formulas)/(sizeof *formulas);
|
|
if (n < 1 || (unsigned) n > max)
|
|
bad_number("p-patterns", n, max);
|
|
return spot::relabel(parse_formula(formulas[n - 1]), Pnn);
|
|
}
|
|
|
|
static formula
|
|
sb_pattern(int n)
|
|
{
|
|
static const char* formulas[] = {
|
|
"p0 U p1",
|
|
"p0 U (p1 U p2)",
|
|
"!(p0 U (p1 U p2))",
|
|
"G(F(p0)) -> G(F(p1))",
|
|
"(F(p0)) U (G(p1))",
|
|
"(G(p0)) U p1",
|
|
"!((F(F(p0))) <-> (F(p)))",
|
|
"!((G(F(p0))) -> (G(F(p))))",
|
|
"!((G(F(p0))) <-> (G(F(p))))",
|
|
"p0 R (p0 | p1)",
|
|
"(Xp0 U Xp1) | !X(p0 U p1)",
|
|
"(Xp0 U p1) | !X(p0 U (p0 & p1))",
|
|
"G(p0 -> F(p1)) & (((X(p0)) U p1) | !X(p0 U (p0 & p1)))",
|
|
"G(p0 -> F(p1)) & (((X(p0)) U X(p1)) | !X(p0 U p1))",
|
|
"G(p0 -> F(p1))",
|
|
"!G(p0 -> X(p1 R p2))",
|
|
"!(F(G(p0)) | F(G(p1)))",
|
|
"G(F(p0) & F(p1))",
|
|
"F(p0) & F(!p0)",
|
|
"(X(p1) & p2) R X(((p3 U p0) R p2) U (p3 R p2))",
|
|
"(G(p1 | G(F(p0))) & G(p2 | G(F(!p0)))) | G(p1) | G(p2)",
|
|
"(G(p1 | F(G(p0))) & G(p2 | F(G(!p0)))) | G(p1) | G(p2)",
|
|
"!((G(p1 | G(F(p0))) & G(p2 | G(F(!p0)))) | G(p1) | G(p2))",
|
|
"!((G(p1 | F(G(p0))) & G(p2 | F(G(!p0)))) | G(p1) | G(p2))",
|
|
"(G(p1 | X(G p0))) & (G (p2 | X(G !p0)))",
|
|
"G(p1 | (Xp0 & X!p0))",
|
|
// p0 U p0 can't be represented other than as p0 in Spot
|
|
"(p0 U p0) | (p1 U p0)",
|
|
};
|
|
|
|
constexpr unsigned max = (sizeof formulas)/(sizeof *formulas);
|
|
if (n < 1 || (unsigned) n > max)
|
|
bad_number("sb-patterns", n, max);
|
|
return spot::relabel(parse_formula(formulas[n - 1]), Pnn);
|
|
}
|
|
|
|
static formula
|
|
X_n_kv_exp(formula a, int n, formula b)
|
|
{
|
|
formula f = X_n(a, n);
|
|
return And_(f, G_(Implies_(b, f)));
|
|
}
|
|
|
|
static formula
|
|
kv_exp(int n, std::string a, std::string b, std::string c, std::string d)
|
|
{
|
|
formula fa = formula::ap(a);
|
|
formula fb = formula::ap(b);
|
|
formula fc = formula::ap(c);
|
|
formula fd = formula::ap(d);
|
|
|
|
exclusive_ap m;
|
|
m.add_group({ fa, fb, fc, fd });
|
|
|
|
formula xn = X_(G_(fc));
|
|
for (int i = 0; i < n; i++)
|
|
xn = X_(And_(Or_(fa, fb), xn));
|
|
formula f1 = U_(Not_(fd), And_(fd, xn));
|
|
|
|
formula f_and = nullptr;
|
|
for (int i = 1; i <= n; i++)
|
|
f_and = And_(f_and, Or_(X_n_kv_exp(fa, i, fd),
|
|
X_n_kv_exp(fb, i, fd)));
|
|
|
|
formula f2 = F_(And_(fc, And_(f_and, X_n(fc, n + 1))));
|
|
|
|
return m.constrain(And_(f1, f2));
|
|
}
|
|
|
|
static formula
|
|
bit_ni(unsigned i, unsigned j, formula fbin[2])
|
|
{
|
|
return fbin[((1u << j) & (i - 1)) != 0];
|
|
}
|
|
|
|
static formula
|
|
binary_ki(int k, unsigned i, formula fbin[2])
|
|
{
|
|
formula res = bit_ni(i, k - 1, fbin);
|
|
for (int j = k - 1; j >= 1; j--)
|
|
res = And_(bit_ni(i, j - 1, fbin), X_(res));
|
|
return res;
|
|
}
|
|
|
|
static formula
|
|
kr1_exp_1(int k, formula fc, formula fd, formula fbin[2])
|
|
{
|
|
return And_(fc, X_(Or_(binary_ki(k, 1, fbin), fd)));
|
|
}
|
|
|
|
static formula
|
|
kr1_exp_2(int n, int k, formula fa, formula fb, formula fbin[2])
|
|
{
|
|
formula res = formula::tt();
|
|
for (int i = 1; i <= n - 1; i++)
|
|
res = And_(res,
|
|
Implies_(binary_ki(k, i, fbin),
|
|
X_n(And_(Or_(fa, fb),
|
|
X_(binary_ki(k, i + 1, fbin))), k)));
|
|
|
|
return G_(res);
|
|
}
|
|
|
|
static formula
|
|
kr1_exp_3(int n, int k, formula fa, formula fb, formula fc, formula fd,
|
|
formula fbin[2])
|
|
{
|
|
return G_(Implies_(binary_ki(k, n, fbin),
|
|
X_n(And_(Or_(fa, fb),
|
|
X_(And_(fc,
|
|
X_(Or_(binary_ki(k, 1, fbin),
|
|
Or_(fd,
|
|
G_(fc))))))), k)));
|
|
}
|
|
|
|
static formula
|
|
kr1_exp_4(int n, int k, formula fc, formula fd, formula fbin[2])
|
|
{
|
|
return U_(Not_(fd),
|
|
And_(fd, X_(And_(binary_ki(k, 1, fbin),
|
|
X_n(G_(fc), n * (k + 1))))));
|
|
}
|
|
|
|
static formula
|
|
kr1_exp_5_r(int k, int i, formula fr, formula fd, formula fbin[2])
|
|
{
|
|
return And_(fr, F_(And_(fd, F_(And_(binary_ki(k, i, fbin),
|
|
X_n(fr, k))))));
|
|
}
|
|
|
|
static formula
|
|
kr1_exp_5(int n, int k, formula fa, formula fb, formula fc, formula fd,
|
|
formula fbin[2])
|
|
{
|
|
formula fand = formula::tt();
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
formula for1 = kr1_exp_5_r(k, i, fa, fd, fbin);
|
|
formula for2 = kr1_exp_5_r(k, i, fb, fd, fbin);
|
|
fand = And_(fand, Implies_(binary_ki(k, i, fbin),
|
|
X_n(Or_(for1, for2), k)));
|
|
}
|
|
|
|
return F_(And_(fc,
|
|
X_(And_(Not_(fc),
|
|
U_(fand, fc)))));
|
|
}
|
|
|
|
static formula
|
|
kr1_exp(int n, std::string a, std::string b, std::string c, std::string d,
|
|
std::string bin0, std::string bin1)
|
|
{
|
|
int k = ceil(log2(n)) + (n == 1);
|
|
|
|
if (n <= 0)
|
|
bad_number("kr1-exp", n);
|
|
|
|
formula fa = formula::ap(a);
|
|
formula fb = formula::ap(b);
|
|
formula fc = formula::ap(c);
|
|
formula fd = formula::ap(d);
|
|
|
|
formula fbin0 = formula::ap(bin0);
|
|
formula fbin1 = formula::ap(bin1);
|
|
|
|
exclusive_ap m;
|
|
m.add_group({ fa, fb, fc, fd, fbin0, fbin1 });
|
|
|
|
formula fbin[2] = { fbin0, fbin1 };
|
|
|
|
formula res = formula::And({ kr1_exp_1(k, fc, fd, fbin),
|
|
kr1_exp_2(n, k, fa, fb, fbin),
|
|
kr1_exp_3(n, k, fa, fb, fc, fd, fbin),
|
|
kr1_exp_4(n, k, fc, fd, fbin),
|
|
kr1_exp_5(n, k, fa, fb, fc, fd, fbin) });
|
|
|
|
return m.constrain(res);
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_1(formula* fa, formula* fb, formula fc, formula fd)
|
|
{
|
|
(void) fd;
|
|
return And_(fc,
|
|
X_(Or_(fa[0],
|
|
Or_(fb[0], fd))));
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_2(int n, formula* fa, formula* fb)
|
|
{
|
|
formula res = formula::tt();
|
|
for (int i = 1; i <= n - 1; i++)
|
|
res = And_(res, Implies_(Or_(fa[i - 1], fb[i - 1]),
|
|
X_(Or_(fa[i], fb[i]))));
|
|
|
|
return G_(res);
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_3(int n, formula* fa, formula* fb, formula fc, formula fd)
|
|
{
|
|
return G_(Implies_(Or_(fa[n - 1], fb[n - 1]),
|
|
X_(And_(fc,
|
|
X_(Or_(fa[0],
|
|
Or_(fb[0],
|
|
Or_(fd, G_(fc)))))))));
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_4(int n, formula* fa, formula* fb, formula fc, formula fd)
|
|
{
|
|
return U_(Not_(fd),
|
|
And_(fd, X_(And_(Or_(fa[0], fb[0]), X_n(G_(fc), n)))));
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_5_r(int i, formula* fr, formula fd)
|
|
{
|
|
return And_(fr[i - 1], F_(And_(fd, F_(fr[i - 1]))));
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_5(int n, formula* fa, formula* fb, formula fc, formula fd)
|
|
{
|
|
formula facc = formula::ff();
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
formula for1 = kr2_exp_5_r(i, fa, fd);
|
|
formula for2 = kr2_exp_5_r(i, fb, fd);
|
|
facc = Or_(facc, (Or_(for1, for2)));
|
|
}
|
|
|
|
return F_(And_(fc,
|
|
X_(And_(Not_(fc), U_(facc, fc)))));
|
|
}
|
|
|
|
static formula
|
|
kr2_exp_mutex(int n, formula* fa, formula* fb, formula fc, formula fd)
|
|
{
|
|
formula f1or = formula::ff();
|
|
formula f3and = formula::tt();
|
|
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
f1or = Or_(f1or, Or_(fa[i - 1], fb[i - 1]));
|
|
f3and = And_(f3and, Implies_(fa[i - 1], Not_(fb[i - 1])));
|
|
}
|
|
|
|
formula f1 = G_(Implies_(Or_(fc, fd), Not_(f1or)));
|
|
formula f2 = G_(Implies_(fc, Not_(fd)));
|
|
formula f3 = G_(f3and);
|
|
|
|
return And_(f1, And_(f2, f3));
|
|
}
|
|
|
|
static formula
|
|
kr2_exp(int n, std::string a, std::string b, std::string c, std::string d)
|
|
{
|
|
if (n <= 0)
|
|
bad_number("kr-n", n);
|
|
|
|
formula fc = formula::ap(c);
|
|
formula fd = formula::ap(d);
|
|
|
|
formula* fa = new formula[n];
|
|
formula* fb = new formula[n];
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
fa[i] = formula::ap(a + std::to_string(i + 1));
|
|
fb[i] = formula::ap(b + std::to_string(i + 1));
|
|
}
|
|
|
|
formula res = formula::And({ kr2_exp_1(fa, fb, fc, fd),
|
|
kr2_exp_2(n, fa, fb),
|
|
kr2_exp_3(n, fa, fb, fc, fd),
|
|
kr2_exp_4(n, fa, fb, fc, fd),
|
|
kr2_exp_5(n, fa, fb, fc, fd),
|
|
kr2_exp_mutex(n, fa, fb, fc, fd) });
|
|
|
|
return res;
|
|
}
|
|
}
|
|
|
|
formula ltl_pattern(ltl_pattern_id pattern, int n)
|
|
{
|
|
if (n < 0)
|
|
{
|
|
std::ostringstream err;
|
|
err << "pattern argument for " << ltl_pattern_name(pattern)
|
|
<< " should be positive";
|
|
throw std::runtime_error(err.str());
|
|
}
|
|
|
|
switch (pattern)
|
|
{
|
|
// Keep this alphabetically-ordered!
|
|
case AND_F:
|
|
return combunop_n("p", n, op::F, true);
|
|
case AND_FG:
|
|
return FG_n("p", n, true);
|
|
case AND_GF:
|
|
return GF_n("p", n, true);
|
|
case CCJ_ALPHA:
|
|
return formula::And({E_n("p", n), E_n("q", n)});
|
|
case CCJ_BETA:
|
|
return formula::And({N_n("p", n), N_n("q", n)});
|
|
case CCJ_BETA_PRIME:
|
|
return formula::And({N_prime_n("p", n), N_prime_n("q", n)});
|
|
case DAC_PATTERNS:
|
|
return dac_pattern(n);
|
|
case EH_PATTERNS:
|
|
return eh_pattern(n);
|
|
case GH_Q:
|
|
return Q_n("p", n);
|
|
case GH_R:
|
|
return R_n("p", n);
|
|
case GO_THETA:
|
|
return fair_response("p", "q", "r", n);
|
|
case HKRSS_PATTERNS:
|
|
return hkrss_pattern(n);
|
|
case KR_N:
|
|
return kr2_exp(n, "a", "b", "c", "d");
|
|
case KR_NLOGN:
|
|
return kr1_exp(n, "a", "b", "c", "d", "y", "z");
|
|
case KV_PSI:
|
|
return kv_exp(n, "a", "b", "c", "d");
|
|
case OR_FG:
|
|
return FG_n("p", n, false);
|
|
case OR_G:
|
|
return combunop_n("p", n, op::G, false);
|
|
case OR_GF:
|
|
return GF_n("p", n, false);
|
|
case P_PATTERNS:
|
|
return p_pattern(n);
|
|
case R_LEFT:
|
|
return bin_n("p", n, op::R, false);
|
|
case R_RIGHT:
|
|
return bin_n("p", n, op::R, true);
|
|
case RV_COUNTER_CARRY:
|
|
return ltl_counter_carry("b", "m", "c", n, false);
|
|
case RV_COUNTER_CARRY_LINEAR:
|
|
return ltl_counter_carry("b", "m", "c", n, true);
|
|
case RV_COUNTER:
|
|
return ltl_counter("b", "m", n, false);
|
|
case RV_COUNTER_LINEAR:
|
|
return ltl_counter("b", "m", n, true);
|
|
case SB_PATTERNS:
|
|
return sb_pattern(n);
|
|
case TV_F1:
|
|
return tv_f1("p", "q", n);
|
|
case TV_F2:
|
|
return tv_f2("p", "q", n);
|
|
case TV_G1:
|
|
return tv_g1("p", "q", n);
|
|
case TV_G2:
|
|
return tv_g2("p", "q", n);
|
|
case TV_UU:
|
|
return tv_uu("p", n);
|
|
case U_LEFT:
|
|
return bin_n("p", n, op::U, false);
|
|
case U_RIGHT:
|
|
return bin_n("p", n, op::U, true);
|
|
case LAST_CLASS:
|
|
break;
|
|
}
|
|
throw std::runtime_error("unsupported pattern");
|
|
}
|
|
|
|
|
|
const char* ltl_pattern_name(ltl_pattern_id pattern)
|
|
{
|
|
static const char* const class_name[] =
|
|
{
|
|
"and-f",
|
|
"and-fg",
|
|
"and-gf",
|
|
"ccj-alpha",
|
|
"ccj-beta",
|
|
"ccj-beta-prime",
|
|
"dac-patterns",
|
|
"eh-patterns",
|
|
"gh-q",
|
|
"gh-r",
|
|
"go-theta",
|
|
"hkrss-patterns",
|
|
"kr-n",
|
|
"kr-nlogn",
|
|
"kv-psi",
|
|
"or-fg",
|
|
"or-g",
|
|
"or-gf",
|
|
"p-patterns",
|
|
"r-left",
|
|
"r-right",
|
|
"rv-counter",
|
|
"rv-counter-carry",
|
|
"rv-counter-carry-linear",
|
|
"rv-counter-linear",
|
|
"sb-patterns",
|
|
"tv-f1",
|
|
"tv-f2",
|
|
"tv-g1",
|
|
"tv-g2",
|
|
"tv-uu",
|
|
"u-left",
|
|
"u-right",
|
|
};
|
|
// Make sure we do not forget to update the above table every
|
|
// time a new pattern is added.
|
|
static_assert(sizeof(class_name)/sizeof(*class_name)
|
|
== LAST_CLASS - FIRST_CLASS, "size mismatch");
|
|
if (pattern < FIRST_CLASS || pattern >= LAST_CLASS)
|
|
throw std::runtime_error("unsupported pattern");
|
|
return class_name[pattern - FIRST_CLASS];
|
|
}
|
|
|
|
int ltl_pattern_max(ltl_pattern_id pattern)
|
|
{
|
|
switch (pattern)
|
|
{
|
|
// Keep this alphabetically-ordered!
|
|
case AND_F:
|
|
case AND_FG:
|
|
case AND_GF:
|
|
case CCJ_ALPHA:
|
|
case CCJ_BETA:
|
|
case CCJ_BETA_PRIME:
|
|
return 0;
|
|
case DAC_PATTERNS:
|
|
return 55;
|
|
case EH_PATTERNS:
|
|
return 12;
|
|
case GH_Q:
|
|
case GH_R:
|
|
case GO_THETA:
|
|
return 0;
|
|
case HKRSS_PATTERNS:
|
|
return 55;
|
|
case KR_N:
|
|
case KR_NLOGN:
|
|
case KV_PSI:
|
|
case OR_FG:
|
|
case OR_G:
|
|
case OR_GF:
|
|
return 0;
|
|
case P_PATTERNS:
|
|
return 20;
|
|
case R_LEFT:
|
|
case R_RIGHT:
|
|
case RV_COUNTER_CARRY:
|
|
case RV_COUNTER_CARRY_LINEAR:
|
|
case RV_COUNTER:
|
|
case RV_COUNTER_LINEAR:
|
|
return 0;
|
|
case SB_PATTERNS:
|
|
return 27;
|
|
case TV_F1:
|
|
case TV_F2:
|
|
case TV_G1:
|
|
case TV_G2:
|
|
case TV_UU:
|
|
case U_LEFT:
|
|
case U_RIGHT:
|
|
return 0;
|
|
case LAST_CLASS:
|
|
break;
|
|
}
|
|
throw std::runtime_error("unsupported pattern");
|
|
|
|
}
|
|
|
|
}
|
|
}
|