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spot/bin/genltl.cc
Alexandre Duret-Lutz 57f47c16e7 genltl: support --positive and --negative 
* bin/genltl.cc: Implement these options.
* NEWS: Mention them.
* tests/core/genltl.test: New file with test cases.
* tests/Makefile.am: Add it.
2016-07-18 23:23:01 +02:00

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// -*- coding: utf-8 -*-
// Copyright (C) 2012, 2013, 2015, 2016 Laboratoire de Recherche et
// Développement de l'Epita (LRDE).
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
// Families defined here come from the following papers:
//
// @InProceedings{cichon.09.depcos,
// author = {Jacek Cicho{\'n} and Adam Czubak and Andrzej Jasi{\'n}ski},
// title = {Minimal {B\"uchi} Automata for Certain Classes of {LTL} Formulas},
// booktitle = {Proceedings of the Fourth International Conference on
// Dependability of Computer Systems},
// pages = {17--24},
// year = 2009,
// publisher = {IEEE Computer Society},
// }
//
// @InProceedings{geldenhuys.06.spin,
// author = {Jaco Geldenhuys and Henri Hansen},
// title = {Larger Automata and Less Work for LTL Model Checking},
// booktitle = {Proceedings of the 13th International SPIN Workshop},
// year = {2006},
// pages = {53--70},
// series = {Lecture Notes in Computer Science},
// volume = {3925},
// publisher = {Springer}
// }
//
// @InProceedings{gastin.01.cav,
// author = {Paul Gastin and Denis Oddoux},
// title = {Fast {LTL} to {B\"u}chi Automata Translation},
// booktitle = {Proceedings of the 13th International Conference on
// Computer Aided Verification (CAV'01)},
// pages = {53--65},
// year = 2001,
// editor = {G. Berry and H. Comon and A. Finkel},
// volume = {2102},
// series = {Lecture Notes in Computer Science},
// address = {Paris, France},
// publisher = {Springer-Verlag}
// }
//
// @InProceedings{rozier.07.spin,
// author = {Kristin Y. Rozier and Moshe Y. Vardi},
// title = {LTL Satisfiability Checking},
// booktitle = {Proceedings of the 12th International SPIN Workshop on
// Model Checking of Software (SPIN'07)},
// pages = {149--167},
// year = {2007},
// volume = {4595},
// series = {Lecture Notes in Computer Science},
// publisher = {Springer-Verlag}
// }
//
// @InProceedings{dwyer.98.fmsp,
// author = {Matthew B. Dwyer and George S. Avrunin and James C. Corbett},
// title = {Property Specification Patterns for Finite-state
// Verification},
// booktitle = {Proceedings of the 2nd Workshop on Formal Methods in
// Software Practice (FMSP'98)},
// publisher = {ACM Press},
// address = {New York},
// editor = {Mark Ardis},
// month = mar,
// year = {1998},
// pages = {7--15}
// }
//
// @InProceedings{etessami.00.concur,
// author = {Kousha Etessami and Gerard J. Holzmann},
// title = {Optimizing {B\"u}chi Automata},
// booktitle = {Proceedings of the 11th International Conference on
// Concurrency Theory (Concur'00)},
// pages = {153--167},
// year = {2000},
// editor = {C. Palamidessi},
// volume = {1877},
// series = {Lecture Notes in Computer Science},
// address = {Pennsylvania, USA},
// publisher = {Springer-Verlag}
// }
//
// @InProceedings{somenzi.00.cav,
// author = {Fabio Somenzi and Roderick Bloem},
// title = {Efficient {B\"u}chi Automata for {LTL} Formul{\ae}},
// booktitle = {Proceedings of the 12th International Conference on
// Computer Aided Verification (CAV'00)},
// pages = {247--263},
// year = {2000},
// volume = {1855},
// series = {Lecture Notes in Computer Science},
// address = {Chicago, Illinois, USA},
// publisher = {Springer-Verlag}
// }
#include "common_sys.hh"
#include <iostream>
#include <fstream>
#include <argp.h>
#include <cstdlib>
#include "error.h"
#include <vector>
#include "common_setup.hh"
#include "common_output.hh"
#include "common_range.hh"
#include <cassert>
#include <iostream>
#include <sstream>
#include <set>
#include <string>
#include <cstdlib>
#include <cstring>
#include <spot/tl/formula.hh>
#include <spot/tl/relabel.hh>
#include <spot/tl/parse.hh>
using namespace spot;
const char argp_program_doc[] ="\
Generate temporal logic formulas from predefined patterns.";
enum {
OPT_AND_F = 1,
OPT_AND_FG,
OPT_AND_GF,
OPT_CCJ_ALPHA,
OPT_CCJ_BETA,
OPT_CCJ_BETA_PRIME,
OPT_DAC_PATTERNS,
OPT_EH_PATTERNS,
OPT_GH_Q,
OPT_GH_R,
OPT_GO_THETA,
OPT_OR_FG,
OPT_OR_G,
OPT_OR_GF,
OPT_R_LEFT,
OPT_R_RIGHT,
OPT_RV_COUNTER,
OPT_RV_COUNTER_CARRY,
OPT_RV_COUNTER_CARRY_LINEAR,
OPT_RV_COUNTER_LINEAR,
OPT_SB_PATTERNS,
OPT_U_LEFT,
OPT_U_RIGHT,
LAST_CLASS,
OPT_POSITIVE,
OPT_NEGATIVE,
};
const char* const class_name[LAST_CLASS] =
{
"and-f",
"and-fg",
"and-gf",
"ccj-alpha",
"ccj-beta",
"ccj-beta-prime",
"dac-patterns",
"eh-patterns",
"gh-q",
"gh-r",
"go-theta",
"or-fg",
"or-g",
"or-gf",
"or-r-left",
"or-r-right",
"rv-counter",
"rv-counter-carry",
"rv-counter-carry-linear",
"rv-counter-linear",
"sb-patterns",
"u-left",
"u-right",
};
#define OPT_ALIAS(o) { #o, 0, nullptr, OPTION_ALIAS, nullptr, 0 }
static const argp_option options[] =
{
/**************************************************/
// Keep this alphabetically sorted (expect for aliases).
{ nullptr, 0, nullptr, 0, "Pattern selection:", 1},
// J. Geldenhuys and H. Hansen (Spin'06): Larger automata and less
// work for LTL model checking.
{ "and-f", OPT_AND_F, "RANGE", 0, "F(p1)&F(p2)&...&F(pn)", 0 },
OPT_ALIAS(gh-e),
{ "and-fg", OPT_AND_FG, "RANGE", 0, "FG(p1)&FG(p2)&...&FG(pn)", 0 },
{ "and-gf", OPT_AND_GF, "RANGE", 0, "GF(p1)&GF(p2)&...&GF(pn)", 0 },
OPT_ALIAS(ccj-phi),
OPT_ALIAS(gh-c2),
{ "ccj-alpha", OPT_CCJ_ALPHA, "RANGE", 0,
"F(p1&F(p2&F(p3&...F(pn)))) & F(q1&F(q2&F(q3&...F(qn))))", 0 },
{ "ccj-beta", OPT_CCJ_BETA, "RANGE", 0,
"F(p&X(p&X(p&...X(p)))) & F(q&X(q&X(q&...X(q))))", 0 },
{ "ccj-beta-prime", OPT_CCJ_BETA_PRIME, "RANGE", 0,
"F(p&(Xp)&(XXp)&...(X...X(p))) & F(q&(Xq)&(XXq)&...(X...X(q)))", 0 },
{ "dac-patterns", OPT_DAC_PATTERNS, "RANGE", OPTION_ARG_OPTIONAL,
"Dwyer et al. [FMSP'98] Spec. Patterns for LTL "
"(range should be included in 1..45)", 0 },
{ "eh-patterns", OPT_EH_PATTERNS, "RANGE", OPTION_ARG_OPTIONAL,
"Etessami and Holzmann [Concur'00] patterns "
"(range should be included in 1..12)", 0 },
{ "gh-q", OPT_GH_Q, "RANGE", 0,
"(F(p1)|G(p2))&(F(p2)|G(p3))&...&(F(pn)|G(p{n+1}))", 0 },
{ "gh-r", OPT_GH_R, "RANGE", 0,
"(GF(p1)|FG(p2))&(GF(p2)|FG(p3))&... &(GF(pn)|FG(p{n+1}))", 0},
{ "go-theta", OPT_GO_THETA, "RANGE", 0,
"!((GF(p1)&GF(p2)&...&GF(pn)) -> G(q->F(r)))", 0 },
{ "or-fg", OPT_OR_FG, "RANGE", 0, "FG(p1)|FG(p2)|...|FG(pn)", 0 },
OPT_ALIAS(ccj-xi),
{ "or-g", OPT_OR_G, "RANGE", 0, "G(p1)|G(p2)|...|G(pn)", 0 },
OPT_ALIAS(gh-s),
{ "or-gf", OPT_OR_GF, "RANGE", 0, "GF(p1)|GF(p2)|...|GF(pn)", 0 },
OPT_ALIAS(gh-c1),
{ "r-left", OPT_R_LEFT, "RANGE", 0, "(((p1 R p2) R p3) ... R pn)", 0 },
{ "r-right", OPT_R_RIGHT, "RANGE", 0, "(p1 R (p2 R (... R pn)))", 0 },
{ "rv-counter", OPT_RV_COUNTER, "RANGE", 0,
"n-bit counter", 0 },
{ "rv-counter-carry", OPT_RV_COUNTER_CARRY, "RANGE", 0,
"n-bit counter w/ carry", 0 },
{ "rv-counter-carry-linear", OPT_RV_COUNTER_CARRY_LINEAR, "RANGE", 0,
"n-bit counter w/ carry (linear size)", 0 },
{ "rv-counter-linear", OPT_RV_COUNTER_LINEAR, "RANGE", 0,
"n-bit counter (linear size)", 0 },
{ "sb-patterns", OPT_SB_PATTERNS, "RANGE", OPTION_ARG_OPTIONAL,
"Somenzi and Bloem [CAV'00] patterns "
"(range should be included in 1..27)", 0 },
{ "u-left", OPT_U_LEFT, "RANGE", 0, "(((p1 U p2) U p3) ... U pn)", 0 },
OPT_ALIAS(gh-u),
{ "u-right", OPT_U_RIGHT, "RANGE", 0, "(p1 U (p2 U (... U pn)))", 0 },
OPT_ALIAS(gh-u2),
OPT_ALIAS(go-phi),
RANGE_DOC,
/**************************************************/
{ nullptr, 0, nullptr, 0, "Output options:", -20 },
{ "negative", OPT_NEGATIVE, nullptr, 0,
"output the negated versions of all formulas", 0 },
OPT_ALIAS(negated),
{ "positive", OPT_POSITIVE, nullptr, 0,
"output the positive versions of all formulas (done by default, unless"
" --negative is specified without --positive)", 0 },
{ nullptr, 0, nullptr, 0, "The FORMAT string passed to --format may use "
"the following interpreted sequences:", -19 },
{ "%f", 0, nullptr, OPTION_DOC | OPTION_NO_USAGE,
"the formula (in the selected syntax)", 0 },
{ "%F", 0, nullptr, OPTION_DOC | OPTION_NO_USAGE,
"the name of the pattern", 0 },
{ "%L", 0, nullptr, OPTION_DOC | OPTION_NO_USAGE,
"the argument of the pattern", 0 },
{ "%%", 0, nullptr, OPTION_DOC | OPTION_NO_USAGE,
"a single %", 0 },
{ nullptr, 0, nullptr, 0, "Miscellaneous options:", -1 },
{ nullptr, 0, nullptr, 0, nullptr, 0 }
};
struct job
{
int pattern;
struct range range;
};
typedef std::vector<job> jobs_t;
static jobs_t jobs;
bool opt_positive = false;
bool opt_negative = false;
const struct argp_child children[] =
{
{ &output_argp, 0, nullptr, -20 },
{ &misc_argp, 0, nullptr, -1 },
{ nullptr, 0, nullptr, 0 }
};
static void
enqueue_job(int pattern, const char* range_str)
{
job j;
j.pattern = pattern;
j.range = parse_range(range_str);
jobs.push_back(j);
}
static void
enqueue_job(int pattern, int min, int max)
{
job j;
j.pattern = pattern;
j.range = {min, max};
jobs.push_back(j);
}
static int
parse_opt(int key, char* arg, struct argp_state*)
{
// This switch is alphabetically-ordered.
switch (key)
{
case OPT_AND_F:
case OPT_AND_FG:
case OPT_AND_GF:
case OPT_CCJ_ALPHA:
case OPT_CCJ_BETA:
case OPT_CCJ_BETA_PRIME:
case OPT_GH_Q:
case OPT_GH_R:
case OPT_GO_THETA:
case OPT_OR_FG:
case OPT_OR_G:
case OPT_OR_GF:
case OPT_R_LEFT:
case OPT_R_RIGHT:
case OPT_RV_COUNTER:
case OPT_RV_COUNTER_CARRY:
case OPT_RV_COUNTER_CARRY_LINEAR:
case OPT_RV_COUNTER_LINEAR:
case OPT_U_LEFT:
case OPT_U_RIGHT:
enqueue_job(key, arg);
break;
case OPT_DAC_PATTERNS:
if (arg)
enqueue_job(key, arg);
else
enqueue_job(key, 1, 55);
break;
case OPT_EH_PATTERNS:
if (arg)
enqueue_job(key, arg);
else
enqueue_job(key, 1, 12);
break;
case OPT_SB_PATTERNS:
if (arg)
enqueue_job(key, arg);
else
enqueue_job(key, 1, 27);
break;
case OPT_POSITIVE:
opt_positive = true;
break;
case OPT_NEGATIVE:
opt_negative = true;
break;
default:
return ARGP_ERR_UNKNOWN;
}
return 0;
}
#define G_(x) formula::G(x)
#define F_(x) formula::F(x)
#define X_(x) formula::X(x)
#define Not_(x) formula::Not(x)
#define Implies_(x, y) formula::Implies((x), (y))
#define Equiv_(x, y) formula::Equiv((x), (y))
#define And_(x, y) formula::And({(x), (y)})
#define Or_(x, y) formula::Or({(x), (y)})
#define U_(x, y) formula::U((x), (y))
// F(p_1 & F(p_2 & F(p_3 & ... F(p_n))))
static formula
E_n(std::string name, int n)
{
if (n <= 0)
return formula::tt();
formula result = nullptr;
for (; n > 0; --n)
{
std::ostringstream p;
p << name << n;
formula f = formula::ap(p.str());
if (result)
result = And_(f, result);
else
result = f;
result = F_(result);
}
return result;
}
// p & X(p & X(p & ... X(p)))
static formula
phi_n(std::string name, int n)
{
if (n <= 0)
return formula::tt();
formula result = nullptr;
formula p = formula::ap(name);
for (; n > 0; --n)
{
if (result)
result = And_(p, X_(result));
else
result = p;
}
return result;
}
static formula
N_n(std::string name, int n)
{
return formula::F(phi_n(name, n));
}
// p & X(p) & XX(p) & XXX(p) & ... X^n(p)
static formula
phi_prime_n(std::string name, int n)
{
if (n <= 0)
return formula::tt();
formula result = nullptr;
formula p = formula::ap(name);
for (; n > 0; --n)
{
if (result)
{
p = X_(p);
result = And_(result, p);
}
else
{
result = p;
}
}
return result;
}
static formula
N_prime_n(std::string name, int n)
{
return F_(phi_prime_n(name, n));
}
// GF(p_1) & GF(p_2) & ... & GF(p_n) if conj == true
// GF(p_1) | GF(p_2) | ... | GF(p_n) if conj == false
static formula
GF_n(std::string name, int n, bool conj = true)
{
if (n <= 0)
return conj ? formula::tt() : formula::ff();
formula result = nullptr;
op o = conj ? op::And : op::Or;
for (int i = 1; i <= n; ++i)
{
std::ostringstream p;
p << name << i;
formula f = G_(F_(formula::ap(p.str())));
if (result)
result = formula::multop(o, {f, result});
else
result = f;
}
return result;
}
// FG(p_1) | FG(p_2) | ... | FG(p_n) if conj == false
// FG(p_1) & FG(p_2) & ... & FG(p_n) if conj == true
static formula
FG_n(std::string name, int n, bool conj = false)
{
if (n <= 0)
return conj ? formula::tt() : formula::ff();
formula result = nullptr;
op o = conj ? op::And : op::Or;
for (int i = 1; i <= n; ++i)
{
std::ostringstream p;
p << name << i;
formula f = F_(G_(formula::ap(p.str())));
if (result)
result = formula::multop(o, {f, result});
else
result = f;
}
return result;
}
// (((p1 OP p2) OP p3)...OP pn) if right_assoc == false
// (p1 OP (p2 OP (p3 OP (... pn) if right_assoc == true
static formula
bin_n(std::string name, int n, op o, bool right_assoc = false)
{
if (n <= 0)
n = 1;
formula result = nullptr;
for (int i = 1; i <= n; ++i)
{
std::ostringstream p;
p << name << (right_assoc ? (n + 1 - i) : i);
formula f = formula::ap(p.str());
if (!result)
result = f;
else if (right_assoc)
result = formula::binop(o, f, result);
else
result = formula::binop(o, result, f);
}
return result;
}
// (GF(p1)|FG(p2))&(GF(p2)|FG(p3))&...&(GF(pn)|FG(p{n+1}))"
static formula
R_n(std::string name, int n)
{
if (n <= 0)
return formula::tt();
formula pi;
{
std::ostringstream p;
p << name << 1;
pi = formula::ap(p.str());
}
formula result = nullptr;
for (int i = 1; i <= n; ++i)
{
formula gf = G_(F_(pi));
std::ostringstream p;
p << name << i + 1;
pi = formula::ap(p.str());
formula fg = F_(G_(pi));
formula f = Or_(gf, fg);
if (result)
result = And_(f, result);
else
result = f;
}
return result;
}
// (F(p1)|G(p2))&(F(p2)|G(p3))&...&(F(pn)|G(p{n+1}))"
static formula
Q_n(std::string name, int n)
{
if (n <= 0)
return formula::tt();
formula pi;
{
std::ostringstream p;
p << name << 1;
pi = formula::ap(p.str());
}
formula result = nullptr;
for (int i = 1; i <= n; ++i)
{
formula f = F_(pi);
std::ostringstream p;
p << name << i + 1;
pi = formula::ap(p.str());
formula g = G_(pi);
f = Or_(f, g);
if (result)
result = And_(f, result);
else
result = f;
}
return result;
}
// OP(p1) | OP(p2) | ... | OP(Pn) if conj == false
// OP(p1) & OP(p2) & ... & OP(Pn) if conj == true
static formula
combunop_n(std::string name, int n, op o, bool conj = false)
{
if (n <= 0)
return conj ? formula::tt() : formula::ff();
formula result = nullptr;
op cop = conj ? op::And : op::Or;
for (int i = 1; i <= n; ++i)
{
std::ostringstream p;
p << name << i;
formula f = formula::unop(o, formula::ap(p.str()));
if (result)
result = formula::multop(cop, {f, result});
else
result = f;
}
return result;
}
// !((GF(p1)&GF(p2)&...&GF(pn))->G(q -> F(r)))
// From "Fast LTL to Büchi Automata Translation" [gastin.01.cav]
static formula
fair_response(std::string p, std::string q, std::string r, int n)
{
formula fair = GF_n(p, n);
formula resp = G_(Implies_(formula::ap(q), F_(formula::ap(r))));
return Not_(Implies_(fair, resp));
}
// Builds X(X(...X(p))) with n occurrences of X.
static formula
X_n(formula p, int n)
{
assert(n >= 0);
formula res = p;
while (n--)
res = X_(res);
return res;
}
// Based on LTLcounter.pl from Kristin Rozier.
// http://shemesh.larc.nasa.gov/people/kyr/benchmarking_scripts/
static formula
ltl_counter(std::string bit, std::string marker, int n, bool linear)
{
formula b = formula::ap(bit);
formula neg_b = Not_(b);
formula m = formula::ap(marker);
formula neg_m = Not_(m);
std::vector<formula> res(4);
// The marker starts with "1", followed by n-1 "0", then "1" again,
// n-1 "0", etc.
if (!linear)
{
// G(m -> X(!m)&XX(!m)&XXX(m)) [if n = 3]
std::vector<formula> v(n);
for (int i = 0; i + 1 < n; ++i)
v[i] = X_n(neg_m, i + 1);
v[n - 1] = X_n(m, n);
res[0] = And_(m, G_(Implies_(m, formula::And(std::move(v)))));
}
else
{
// G(m -> X(!m & X(!m X(m)))) [if n = 3]
formula p = m;
for (int i = n - 1; i > 0; --i)
p = And_(neg_m, X_(p));
res[0] = And_(m, G_(Implies_(m, X_(p))));
}
// All bits are initially zero.
if (!linear)
{
// !b & X(!b) & XX(!b) [if n = 3]
std::vector<formula> v2(n);
for (int i = 0; i < n; ++i)
v2[i] = X_n(neg_b, i);
res[1] = formula::And(std::move(v2));
}
else
{
// !b & X(!b & X(!b)) [if n = 3]
formula p = neg_b;
for (int i = n - 1; i > 0; --i)
p = And_(neg_b, X_(p));
res[1] = p;
}
#define AndX_(x, y) (linear ? X_(And_((x), (y))) : And_(X_(x), X_(y)))
// If the least significant bit is 0, it will be 1 at the next time,
// and other bits stay the same.
formula Xnm1_b = X_n(b, n - 1);
formula Xn_b = X_(Xnm1_b);
res[2] = G_(Implies_(And_(m, neg_b),
AndX_(Xnm1_b, U_(And_(Not_(m), Equiv_(b, Xn_b)), m))));
// From the least significant bit to the first 0, all the bits
// are flipped on the next value. Remaining bits are identical.
formula Xnm1_negb = X_n(neg_b, n - 1);
formula Xn_negb = X_(Xnm1_negb);
res[3] = G_(Implies_(And_(m, b),
AndX_(Xnm1_negb,
U_(And_(And_(b, neg_m), Xn_negb),
Or_(m, And_(And_(neg_m, neg_b),
AndX_(Xnm1_b,
U_(And_(neg_m,
Equiv_(b, Xn_b)),
m))))))));
return formula::And(std::move(res));
}
static formula
ltl_counter_carry(std::string bit, std::string marker,
std::string carry, int n, bool linear)
{
formula b = formula::ap(bit);
formula neg_b = Not_(b);
formula m = formula::ap(marker);
formula neg_m = Not_(m);
formula c = formula::ap(carry);
formula neg_c = Not_(c);
std::vector<formula> res(6);
// The marker starts with "1", followed by n-1 "0", then "1" again,
// n-1 "0", etc.
if (!linear)
{
// G(m -> X(!m)&XX(!m)&XXX(m)) [if n = 3]
std::vector<formula> v(n);
for (int i = 0; i + 1 < n; ++i)
v[i] = X_n(neg_m, i + 1);
v[n - 1] = X_n(m, n);
res[0] = And_(m, G_(Implies_(m, formula::And(std::move(v)))));
}
else
{
// G(m -> X(!m & X(!m X(m)))) [if n = 3]
formula p = m;
for (int i = n - 1; i > 0; --i)
p = And_(neg_m, X_(p));
res[0] = And_(m, G_(Implies_(m, X_(p))));
}
// All bits are initially zero.
if (!linear)
{
// !b & X(!b) & XX(!b) [if n = 3]
std::vector<formula> v2(n);
for (int i = 0; i < n; ++i)
v2[i] = X_n(neg_b, i);
res[1] = formula::And(std::move(v2));
}
else
{
// !b & X(!b & X(!b)) [if n = 3]
formula p = neg_b;
for (int i = n - 1; i > 0; --i)
p = And_(neg_b, X_(p));
res[1] = p;
}
formula Xn_b = X_n(b, n);
formula Xn_negb = X_n(neg_b, n);
// If m is 1 and b is 0 then c is 0 and n steps later b is 1.
res[2] = G_(Implies_(And_(m, neg_b), And_(neg_c, Xn_b)));
// If m is 1 and b is 1 then c is 1 and n steps later b is 0.
res[3] = G_(Implies_(And_(m, b), And_(c, Xn_negb)));
if (!linear)
{
// If there's no carry, then all of the bits stay the same n steps later.
res[4] = G_(Implies_(And_(neg_c, X_(neg_m)),
And_(X_(Not_(c)), Equiv_(X_(b), X_(Xn_b)))));
// If there's a carry, then add one: flip the bits of b and
// adjust the carry.
res[5] = G_(Implies_(c, And_(Implies_(X_(neg_b),
And_(X_(neg_c), X_(Xn_b))),
Implies_(X_(b),
And_(X_(c), X_(Xn_negb))))));
}
else
{
// If there's no carry, then all of the bits stay the same n steps later.
res[4] = G_(Implies_(And_(neg_c, X_(neg_m)),
X_(And_(Not_(c), Equiv_(b, Xn_b)))));
// If there's a carry, then add one: flip the bits of b and
// adjust the carry.
res[5] = G_(Implies_(c, X_(And_(Implies_(neg_b, And_(neg_c, Xn_b)),
Implies_(b, And_(c, Xn_negb))))));
}
return formula::And(std::move(res));
}
static void bad_number(const char* pattern, int n, int max)
{
std::ostringstream err;
err << "no pattern " << n << " for " << pattern
<< ", supported range is 1.." << 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
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
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 void
output_pattern(int pattern, int n)
{
formula f = nullptr;
switch (pattern)
{
// Keep this alphabetically-ordered!
case OPT_AND_F:
f = combunop_n("p", n, op::F, true);
break;
case OPT_AND_FG:
f = FG_n("p", n, true);
break;
case OPT_AND_GF:
f = GF_n("p", n, true);
break;
case OPT_CCJ_ALPHA:
f = formula::And({E_n("p", n), E_n("q", n)});
break;
case OPT_CCJ_BETA:
f = formula::And({N_n("p", n), N_n("q", n)});
break;
case OPT_CCJ_BETA_PRIME:
f = formula::And({N_prime_n("p", n), N_prime_n("q", n)});
break;
case OPT_DAC_PATTERNS:
f = dac_pattern(n);
break;
case OPT_EH_PATTERNS:
f = eh_pattern(n);
break;
case OPT_GH_Q:
f = Q_n("p", n);
break;
case OPT_GH_R:
f = R_n("p", n);
break;
case OPT_GO_THETA:
f = fair_response("p", "q", "r", n);
break;
case OPT_OR_FG:
f = FG_n("p", n, false);
break;
case OPT_OR_G:
f = combunop_n("p", n, op::G, false);
break;
case OPT_OR_GF:
f = GF_n("p", n, false);
break;
case OPT_R_LEFT:
f = bin_n("p", n, op::R, false);
break;
case OPT_R_RIGHT:
f = bin_n("p", n, op::R, true);
break;
case OPT_RV_COUNTER_CARRY:
f = ltl_counter_carry("b", "m", "c", n, false);
break;
case OPT_RV_COUNTER_CARRY_LINEAR:
f = ltl_counter_carry("b", "m", "c", n, true);
break;
case OPT_RV_COUNTER:
f = ltl_counter("b", "m", n, false);
break;
case OPT_RV_COUNTER_LINEAR:
f = ltl_counter("b", "m", n, true);
break;
case OPT_SB_PATTERNS:
f = sb_pattern(n);
break;
case OPT_U_LEFT:
f = bin_n("p", n, op::U, false);
break;
case OPT_U_RIGHT:
f = bin_n("p", n, op::U, true);
break;
default:
error(100, 0, "internal error: pattern not implemented");
}
// Make sure we use only "p42"-style of atomic propositions
// in lbt's output.
if (output_format == lbt_output && !f.has_lbt_atomic_props())
f = relabel(f, Pnn);
if (opt_positive || !opt_negative)
{
output_formula_checked(f, class_name[pattern - 1], n);
}
if (opt_negative)
{
std::string tmp = "!";
tmp += class_name[pattern - 1];
output_formula_checked(spot::formula::Not(f), tmp.c_str(), n);
}
}
static void
run_jobs()
{
for (auto& j: jobs)
{
int inc = (j.range.max < j.range.min) ? -1 : 1;
int n = j.range.min;
for (;;)
{
output_pattern(j.pattern, n);
if (n == j.range.max)
break;
n += inc;
}
}
}
int
main(int argc, char** argv)
{
setup(argv);
const argp ap = { options, parse_opt, nullptr, argp_program_doc,
children, nullptr, nullptr };
if (int err = argp_parse(&ap, argc, argv, ARGP_NO_HELP, nullptr, nullptr))
exit(err);
if (jobs.empty())
error(1, 0, "Nothing to do. Try '%s --help' for more information.",
program_name);
try
{
run_jobs();
}
catch (const std::runtime_error& e)
{
error(2, 0, "%s", e.what());
}
return 0;
}
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