simplify: some new simplification rules
For #263, reported by Mikuláš Klokočka. G(a & Xe1 & F(b & e2)) = G(a & e1 & Fb & e2) F(a | Xu1 | G(b | u2)) = F(a | u1 | Gb | u2) * spot/tl/simplify.cc: Implement the rules. * doc/tl/tl.tex, NEWS: Document them. * tests/core/reduccmp.test, tests/core/eventuniv.test: Add test cases. * tests/core/det.test, tests/core/ltl2tgba2.test: Adjust to expect smaller automata. * THANKS: Add Mikuláš.
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Alexandre Duret-Lutz
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8 changed files with 89 additions and 20 deletions
4
NEWS
4
NEWS
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@ -173,6 +173,10 @@ New in spot 2.3.5.dev (not yet released)
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more (this threshold can be changed, see -x relabel-bool=N in
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the spot-x(7) man page).
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- The LTL simplification routines learned that an LTL formula like
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G(a & XF(b & XFc & Fd) can be simplified to G(a & Fb & Fc & Fd),
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and dually F(a | XG(b | XGc | Gd)) = F(a | Gb | Gc | Gd).
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- The new function spot::to_weak_alternating() is able to take an
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input automaton with generalized Büchi/co-Büchi acceptance and
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convert it to a weak alternating automaton.
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1
THANKS
1
THANKS
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@ -26,6 +26,7 @@ Martin Dieguez Lodeiro
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Matthias Heizmann
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Michael Tautschnig
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Michael Weber
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Mikuláš Klokočka
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Ming-Hsien Tsai
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Nikos Gorogiannis
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Reuben Rowe
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@ -1682,6 +1682,10 @@ $q,\,q_i$ & a pure eventuality that is also purely universal \\
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\end{align*}
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\begin{align*}
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\G(f_1\AND\ldots\AND f_n \AND \X e_1 \AND \ldots \AND \X e_p)&\equiv \G(f_1\AND\ldots\AND f_n \AND e_1 \AND \ldots \AND e_p) \\
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\G(f_1\AND\ldots\AND f_n \AND \F (g_1 \AND \ldots \AND g_p \AND \X e_1 \AND \X e_m))&\equiv \G(f_1\AND\ldots\AND f_n \AND \F(g_1 \AND \ldots \AND g_p) \AND e_1 \AND \ldots \AND e_m) \\
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\F(f_1\OR\ldots\OR f_n \OR \X u_1 \OR \ldots \OR \X u_p)&\equiv \F(f_1\OR\ldots\OR f_n \OR u_1 \OR \ldots \AND u_p) \\
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\F(f_1\OR\ldots\OR f_n \OR \G (g_1 \OR \ldots \OR g_p \OR \X u_1 \OR \X u_m))&\equiv \F(f_1\OR\ldots\AND f_n \OR \G(g_1 \OR \ldots \OR g_p) \OR u_1 \OR \ldots \OR u_m) \\
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\G(f_1\OR\ldots\OR f_n \OR q_1 \OR \ldots \OR q_p)&\equiv \G(f_1\OR\ldots\OR f_n)\OR q_1 \OR \ldots \OR q_p \\
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\F(f_1\AND\ldots\AND f_n \AND q_1 \AND \ldots \AND q_p)&\equivEU \F(f_1\AND\ldots\AND f_n)\AND q_1 \AND \ldots \AND q_p \\
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\G(f_1\AND\ldots\AND f_n \AND q_1 \AND \ldots \AND q_p)&\equivEU \G(f_1\AND\ldots\AND f_n)\AND q_1 \AND \ldots \AND q_p \\
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@ -995,28 +995,52 @@ namespace spot
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return recurse(res);
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}
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// If u3 and u4 are universal formulae and h is not:
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// F(f1 | f2 | Fu3 | u4 | FGg | Fh)
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// = F(f1 | f2 | u3 | u4 | Gg | h)
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// F(f1 | f2 | Fu3 | u4 | FGg | Fh | Xu5 | G(f6 | Xu7 | u8))
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// = F(f1 | f2 | u3 | u4 | Gg | h | u5 | Gf6 | u7 | u8)
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// or
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// F(f1 | f2 | Fu3 | u4 | FGg | Fh)
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// = F(f1 | f2 | h) | F(u3 | u4 | Gg)
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// F(f1 | f2 | Fu3 | u4 | FGg | Fh | Xu5)
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// = F(f1 | f2 | h) | F(u3 | u4 | Gg | u5 | Gf6 | u7 | u8)
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// depending on whether favor_event_univ is set.
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if (c.is(op::Or))
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{
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int w = mospliter::Strip_F;
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int w = mospliter::Strip_F
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| mospliter::Strip_X | mospliter::Split_G;
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if (opt_.favor_event_univ)
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w |= mospliter::Split_Univ;
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mospliter s(w, c, c_);
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s.res_other->insert(s.res_other->end(),
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s.res_F->begin(), s.res_F->end());
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for (formula f: *s.res_X)
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if (f.is_universal())
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s.res_other->push_back(f);
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else
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s.res_other->push_back(formula::X(f));
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std::vector<formula>* to = opt_.favor_event_univ ?
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s.res_Univ.get() : s.res_other.get();
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for (formula g: *s.res_G)
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if (g[0].is(op::Or))
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{
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mospliter s2(mospliter::Split_Univ, g[0], c_);
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for (formula u: *s2.res_Univ)
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to->push_back(u.is(op::X) ? u[0] : u);
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to->push_back(unop_multop(op::G, op::Or,
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std::move(*s2.res_other)));
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}
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else
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{
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to->push_back(g);
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}
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formula res = unop_multop(op::F, op::Or,
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std::move(*s.res_other));
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if (s.res_Univ)
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{
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// Strip any F.
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std::vector<formula> toadd;
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for (auto& g: *s.res_Univ)
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if (g.is(op::F))
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// Strip any F or X
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if (g.is(op::F, op::X))
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g = g[0];
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s.res_Univ->insert(s.res_Univ->end(),
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toadd.begin(), toadd.end());
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formula fu = unop_multop(op::F, op::Or,
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std::move(*s.res_Univ));
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res = formula::Or({res, fu});
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@ -1071,29 +1095,55 @@ namespace spot
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return recurse(res);
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}
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// If e3 and e4 are eventual formulae and h is not:
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// G(f1 & f2 & Ge3 & e4 & GFg & Gh)
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// = G(f1 & f2 & e3 & e4 & Fg & h)
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// G(f1 & f2 & Ge3 & e4 & GFg & Gh & Xe5 & F(f6 & Xe7 & e8))
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// = G(f1 & f2 & e3 & e4 & Fg & h & e5 & Ff6 & e7 & e8)
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// or
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// G(f1 & f2 & Ge3 & e4 & GFg & Gh)
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// = G(f1 & f2 & h) & G(e3 & e4 & Fg)
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// G(f1 & f2 & Ge3 & e4 & GFg & Gh & Xe5 & F(f6 & Xe7 & e8))
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// = G(f1 & f2 & h) & G(e3 & e4 & Fg & e5 & Ff6 & e7 & e8)
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// depending on whether favor_event_univ is set.
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else if (c.is(op::And))
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{
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int w = mospliter::Strip_G;
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int w = mospliter::Strip_G |
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mospliter::Strip_X | mospliter::Split_F;
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if (opt_.favor_event_univ)
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w |= mospliter::Split_Event;
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mospliter s(w, c, c_);
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s.res_other->insert(s.res_other->end(),
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s.res_G->begin(), s.res_G->end());
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for (formula f: *s.res_X)
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if (f.is_eventual())
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s.res_other->push_back(f);
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else
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s.res_other->push_back(formula::X(f));
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std::vector<formula>* to = opt_.favor_event_univ ?
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s.res_Event.get() : s.res_other.get();
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for (formula f: *s.res_F)
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if (f[0].is(op::And))
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{
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mospliter s2(mospliter::Split_Event, f[0], c_);
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for (formula e: *s2.res_Event)
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to->push_back(e.is(op::X) ? e[0] : e);
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to->push_back
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(unop_multop(op::F, op::And,
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std::move(*s2.res_other)));
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}
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else
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{
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to->push_back(f);
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}
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formula res = unop_multop(op::G, op::And,
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std::move(*s.res_other));
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if (s.res_Event)
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{
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// Strip any G.
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std::vector<formula> toadd;
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// Strip any G or X
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for (auto& g: *s.res_Event)
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if (g.is(op::G))
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g = g[0];
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if (g.is(op::G, op::X))
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{
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g = g[0];
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}
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s.res_Event->insert(s.res_Event->end(),
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toadd.begin(), toadd.end());
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formula ge =
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unop_multop(op::G, op::And,
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std::move(*s.res_Event));
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@ -51,7 +51,7 @@ cat >formulas <<'EOF'
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1,2,Ga R Fb
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1,3,G(a U (b | X((!a & !c) | (a & c))))
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1,5,XG((G!a & F!b) | (Fa & (a | Gb)))
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1,10,(a U X!a) | XG(!b & XFc)
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1,9,(a U X!a) | XG(!b & Fc)
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1,4,X(G!a | GFa)
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1,4,G(G!a | F!c | G!b)
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EOF
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@ -1,6 +1,6 @@
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#! /bin/sh
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# -*- coding: utf-8 -*-
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# Copyright (C) 2012, 2013, 2014 Laboratoire de Recherche et
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# Copyright (C) 2012, 2013, 2014, 2017 Laboratoire de Recherche et
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# Developpement 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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@ -41,6 +41,11 @@ G(Ga & GXFb & c & FGd & FGe & Fc), G(Fb & FG(d & e)) & G(a & c)
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Ga & Gb & GFd & FGe & FGf, G(Fd & FG(e & f)) & G(a & b)
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G(Ga & Gb & GFd & FGe) & FGf, G(Fd & FG(e & f)) & G(a & b)
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G(a & XFb), Ga & GFb
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G(a & XF(b & XFc & Fd)), Ga & G(Fb & Fc & Fd)
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F(a | XGb), Fa | FGb
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F(a | XG(b | XGc | Gd)), Fa | F(Gb | Gc | Gd)
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a U (b | Fc), (a U b) | Fc
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a W (b | Fc), (a W b) | Fc
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a U (b & GFc), (a U b) & GFc
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@ -100,7 +100,7 @@ eh-patterns,5, 4,32, 4,32, 4,32, 4,32
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eh-patterns,6, 3,24, 3,24, 3,24, 3,24
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eh-patterns,7, 3,14, 3,14, 4,18, 4,18
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eh-patterns,8, 2,13, 2,13, 2,13, 2,13
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eh-patterns,9, 5,58, 5,58, 8,80, 8,80
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eh-patterns,9, 1,8, 1,8, 4,32, 4,32
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eh-patterns,10, 1,32, 1,32, 6,192, 6,192
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eh-patterns,11, 2,15, 2,15, 2,15, 2,15
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eh-patterns,12, 4,60, 4,60, 4,60, 4,60
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@ -264,7 +264,7 @@ p-patterns,20, 1,8, 1,8, 3,24, 3,24
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!eh-patterns,6, 2,12, 2,12, 2,12, 2,12
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!eh-patterns,7, 2,7, 2,7, 3,9, 3,9
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!eh-patterns,8, 3,21, 3,21, 3,21, 3,21
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!eh-patterns,9, 5,80, 5,80, 5,80, 5,80
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!eh-patterns,9, 5,68, 5,68, 5,68, 5,68
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!eh-patterns,10, 6,192, 6,192, 6,192, 6,192
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!eh-patterns,11, 2,9, 2,9, 2,9, 2,9
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!eh-patterns,12, 6,103, 6,103, 8,135, 8,135
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@ -300,6 +300,11 @@ a W ((a&b) W c), a W c
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Fa M b, Fa & b
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GFa M b, GFa & b
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G(a & XFb), G(a & Fb)
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G(a & XF(b & XFc & Fd)), G(a & Fb & Fc & Fd)
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F(a | XGb), F(a | Gb)
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F(a | XG(b | XGc | Gd)), F(a | Gb | Gc | Gd)
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Fa|Xb|GFc, Fa | X(b|GFc)
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Fa|GFc, F(a|GFc)
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FGa|GFc, F(Ga|GFc)
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