Commit 212c7ebd by Alexandre Duret-Lutz

### Add implication-based rewritings from Babiak et al. (TACAS'12)

* src/ltlvisit/simplify.cc: Implement them here, and augment them
to support M, and W operators.
* doc/tl/tl.bib (babiak.12.tacas): New entry.
 ... ... @@ -1472,8 +1472,8 @@ implication can be done in two ways: In the following rewritings rules, $f\simp g$ means that $g$ was proved to be implied by $f$ using either of the above two methods. Additionally, implications denoted by $f\Simp g$ are only checked if the \verb|ltl_simplifier_options::containment_checks_stronger|'' Additionally, implications denoted by $f\Simp g$ are only checked if the \verb|ltl_simplifier_options::containment_checks_stronger|'' option is set (otherwise the rewriting rule is not applied). \begin{equation*} ... ... @@ -1487,23 +1487,36 @@ option is set (otherwise the rewriting rule is not applied). \text{if}& (\NOT f)\simp g &\text{then}& f\U g &\equiv \F g \\ \text{if}& f\simp g &\text{then}& f\U (g \U h) &\equiv g \U h \\ \text{if}& f\simp g &\text{then}& f\U (g \W h) &\equiv g \W h \\ \text{if}& g\simp f &\text{then}& f\U (g \U h) &\equiv f \U h \\ \text{if}& f\simp h &\text{then}& f\U (g \R (h \U k)) &\equiv g \R (h \U k) \\ \text{if}& f\simp h &\text{then}& f\U (g \R (h \W k)) &\equiv g \R (h \W k) \\ \text{if}& f\simp h &\text{then}& f\U (g \M (h \U k)) &\equiv g \M (h \U k) \\ \text{if}& f\simp h &\text{then}& f\U (g \M (h \W k)) &\equiv g \M (h \W k) \\ \text{if}& f\simp g &\text{then}& f\W g &\equiv g \\ \text{if}& (f\W g)\Simp g &\text{then}& f\W g &\equiv g \\ \text{if}& (\NOT f)\simp g &\text{then}& f\W g &\equiv \1 \\ \text{if}& f\simp g &\text{then}& f\W (g \W h) &\equiv g \W h \\ \text{if}& g\simp f &\text{then}& f\W (g \U h) &\equiv f \W h \\ \text{if}& g\simp f &\text{then}& f\W (g \W h) &\equiv f \W h \\ \text{if}& g\simp f &\text{then}& f\R g &\equiv g \\ \text{if}& g\simp \NOT f &\text{then}& f\R g &\equiv \G g \\ \text{if}& g\simp f &\text{then}& f\R (g \R h) &\equiv g \R h \\ \text{if}& g\simp f &\text{then}& f\R (g \M h) &\equiv g \M h \\ \text{if}& f\simp g &\text{then}& f\R (g \R h) &\equiv f \R h \\ \text{if}& h\simp f &\text{then}& (f\R g) \R h &\equiv g \R h \\ \text{if}& h\simp f &\text{then}& (f\M g) \R h &\equiv g \R h \\ \text{if}& g\simp f &\text{then}& f\M g &\equiv g \\ \text{if}& g\simp \NOT f &\text{then}& f\M g &\equiv \0 \\ \text{if}& g\simp f &\text{then}& f\M (g \M h) &\equiv g \M h \\ \text{if}& f\simp g &\text{then}& f\M (g \M h) &\equiv f \M h \\ \text{if}& f\simp g &\text{then}& f\M (g \R h) &\equiv f \M h \\ \text{if}& h\simp f &\text{then}& (f\M g) \M h &\equiv g \M h \\ \end{array} \end{equation*} The above rules were collected from various sources~\cite{somenzi.00.cav,tauriainen.03.a83,babiak.12.tacas} and sometimes generalized to support operators such as $\M$ and $\W$. \appendix \chapter{Syntactic Implications}\label{ann:syntimpl} ... ...
 #! /bin/sh # Copyright (C) 2009, 2010, 2011 Laboratoire de Recherche et Developpement #! /bin/sh # Copyright (C) 2009, 2010, 2011, 2012 Laboratoire de Recherche et Developpement # de l'Epita (LRDE). # Copyright (C) 2004, 2006 Laboratoire d'Informatique de Paris 6 (LIP6), # dpartement Systmes Rpartis Coopratifs (SRC), Universit Pierre ... ... @@ -174,6 +174,20 @@ for x in ../reduccmp ../reductaustr; do run 0 $x '(a & b) M (a R c)' '(a & b)M c' run 0$x '(a & b) M (a M c)' '(a & b)M c' run 0 $x 'a U ((a & b) U c)' 'a U c' run 0$x '(a&c) U (b R (c U d))' 'b R (c U d)' run 0 $x '(a&c) U (b R (c W d))' 'b R (c W d)' run 0$x '(a&c) U (b M (c U d))' 'b M (c U d)' run 0 $x '(a&c) U (b M (c W d))' 'b M (c W d)' run 0$x '(a R c) R (b & a)' 'c R (b & a)' run 0 $x '(a M c) R (b & a)' 'c R (b & a)' run 0$x 'a W ((a&b) U c)' 'a W c' run 0 $x 'a W ((a&b) W c)' 'a W c' run 0$x '(a M c) M (b&a)' 'c M (b&a)' # Eventuality and universality class reductions run 0 $x 'Fa M b' 'Fa & b' run 0$x 'GFa M b' 'GFa & b' ... ...