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Implement a favor_even_univ option in the rewriting rules.

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The set of rules enabled by favor_even_univ try to "lift" the
subformulae that are both eventual and universal, so they appear
higher in the AST.  This is contrary to what we used to do (and still
do when the option is unset), were we try to postpone such subformulae
(by moving them down the AST).  It is still a bit experimental.

* src/ltlvisit/simplify.hh: Add option favor_event_univ.
* src/ltlvisit/simplify.cc: Implement new rewriting rules.
* doc/tl/tl.tex: Document them.
* src/tgbatest/ltl2tgba.cc: Add option -ra to enable them.
* src/tgbatest/spotlbtt.test: Test the translation with this option.
* src/ltltest/reduc.cc, src/ltltest/equals.cc: Add option
to enable the new rules.
* src/ltltest/eventuniv.test: New file to test them.
* src/ltltest/Makefile.am: Add it.
This commit is contained in:
Alexandre Duret-Lutz 2012-06-11 19:09:34 +02:00
parent 969d927145
commit 9caa9ad134
9 changed files with 489 additions and 43 deletions
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48
doc/tl/tl.tex
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@ -108,6 +108,9 @@
% rewriting rules that enlarge the formula
\newcommand{\equiV}{\stackrel{\star}{\equiv}}
% rewriting rules that favors event/univ
\newcommand{\equivEU}{\stackrel{\blacktriangleup}{\equiv}}
\newcommand{\equivNeu}{\stackrel{\smalltriangledown}{\equiv}}
% marked rewriting rules
\newcommand{\equivM}{\stackrel{\dag}{\equiv}}
@ -1298,6 +1301,13 @@ The goals in most of these simplification are to:
limit the sources of indeterminism.
\end{itemize}
Rewritings defined with $\equivEU$ are applied only when
\verb|ltl_simplifier_options::favor_event_univ|' is \texttt{true}:
they try to lift subformulas that are both eventual and universal
\emph{higher} in the syntax tree. Conversely, rules defined with $\equivNeu$
are applied only when \verb|favor_event_univ|' is \texttt{false}: they
try to \textit{lower} subformulas that are both eventual and universal.
\subsection{Basic Simplifications}\label{sec:basic-simp}
These simplifications are enabled with
@ -1356,10 +1366,10 @@ $\OR$):
(\G\F f) \OR (\G\F g) &\equiv \G\F(f\OR g) \\
(\X f) \AND(\X g) &\equiv \X(f\AND g) &
(\X f) \OR (\X g) &\equiv \X(f\OR g) \\
(\X f) \AND(\F\G g) &\equiv \X(f\AND \F\G g) &
(\X f) \OR (\G\F g) &\equiv \X(f\OR \G\F g) \\
(\G f) \AND(\G g) &\equiv \G(f\AND g) &
(\F f) \OR (\F g) &\equiv \F(f\OR g) \\
(\X f) \AND(\F\G g) &\equivNeu \X(f\AND \F\G g) &
(\X f) \OR (\G\F g) &\equivNeu \X(f\OR \G\F g) \\
(\G f) \AND(\G g) &\equivNeu \G(f\AND g) &
(\F f) \OR (\F g) &\equivNeu \F(f\OR g) \\
(f_1 \U f_2)\AND (f_3 \U f_2)&\equiv (f_1\AND f_3)\U f_2&
(f_1 \U f_2)\OR (f_1 \U f_3)&\equiv f_1\U (f_2\OR f_3) \\
(f_1 \U f_2)\AND (f_3 \W f_2)&\equiv (f_1\AND f_3)\U f_2&
@ -1409,8 +1419,8 @@ $b \OR c\OR \X(\F(a\OR b\OR c)\OR \G d)$.
Finally the following rule is applied only when no other terms are present
in the OR arguments:
\begin{align*}
\F(f_1) \OR \ldots \OR \F(f_n) \OR \G\F(g_1) \OR \ldots \OR \G\F(g_m)
&\equiv \F(f_1\OR \ldots \OR f_n \OR \G\F(g_1\OR \ldots \OR g_m)) \\
\F(f_1) \OR \ldots \OR \F(f_n) \OR \G\F(g)
&\equivNeu \F(f_1\OR \ldots \OR f_n \OR \G\F(g)) \\
\end{align*}
\subsubsection{Basic Simplifications for SERE Operators}
@ -1558,17 +1568,29 @@ $q,\,q_i$ & a pure eventuality that is also purely universal \\
\end{center}
\begin{align*}
\F e &\equiv e & f \U e &\equiv e & e \M f &\equiv e\AND f & u_1 \M u_2 &\equiV (\F u_1) \AND u_2 \\
\G u &\equiv u & f \R u &\equiv u & u \W f &\equiv u\OR f & e_1 \W e_2 &\equiV (\G e_1) \OR e_2 \\
\X q &\equiv q & q \AND \X f &\equiv \X(q \AND f) & q\OR \X f &\equiv \X(q \OR f)
\F e & \equiv e & f \U e & \equiv e & e \M g & \equiv e\AND g & u_1 \M u_2 & \equiV (\F u_1) \AND u_2 \\
\F(u)\OR q & \equivEU \F(u\OR q) & f \U (g\OR e) & \equivEU (f \U g)\OR e & f\M (g\AND u) & \equivEU (f \M g)\AND u \\
& & f \U (g\AND q) & \equivEU (f \U g)\AND q & (f\AND q)\M g & \equivEU (f \M g)\AND q \\
\G u & \equiv u & u \W g & \equiv u\OR g & f \R u & \equiv u & e_1 \W e_2 & \equiV (\G e_1) \OR e_2 \\
\G(e)\AND q & \equiv \G(e\AND q) & f \W (g\OR e) & \equivEU (f \W g)\OR e & f\R (g\AND u) & \equivEU (f \R g)\AND u \\
& & (f\OR u) \W g & \equivEU (f \W g)\OR u \\
\X q & \equiv q & q \AND \X f & \equivNeu \X(q \AND f) & q\OR \X f & \equivNeu \X(q \OR f) \\
& & \X(q \AND f) & \equivEU q \AND \X f & \X(q \OR f) & \equivEU q\OR \X f \\
\end{align*}
\begin{align*}
\G(f_1\OR\ldots\OR f_n \OR \G\F(g_1)\OR\ldots\OR \G\F(g_m)\OR q_1 \OR \ldots \OR q_p)&\equiv \G(f_1\OR\ldots\OR f_n)\OR \G\F(g_1\OR\ldots\OR g_m)\OR q_1 \OR \ldots q_p \\
\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 \\
\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 \\
\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 \\
\G(f_1\AND\ldots\AND f_n \AND e_1 \AND \ldots \AND e_m \AND \G(e_{m+1}) \AND \ldots\AND \G(e_p))&\equivEU \G(f_1\AND\ldots\AND f_n)\AND \G(e_1 \AND \ldots \AND e_p) \\
\G(f_1\AND\ldots\AND f_n \AND \G(g_1) \AND \ldots \AND \G(g_m) &\equiv \G(f_1\AND\ldots\AND f_n\AND g_1 \AND \ldots \AND g_m) \\
\F(f_1 \OR \ldots \OR f_n \OR u_1 \OR \ldots \OR u_m \OR \F(u_{m+1})\OR\ldots\OR \F(u_p)) &\equivEU \F(f_1\OR \ldots\OR f_n) \OR \F(u_1 \OR \ldots \OR u_p)\\
\F(f_1 \OR \ldots \OR f_n \OR \F(g_1) \OR \ldots \OR \G(g_m)) &\equiv \F(f_1\OR \ldots\OR f_n \OR g_1 \OR \ldots \OR g_m)\\
\G(f_1)\AND\ldots\AND \G(f_n) \AND \G(e_1) \AND \ldots\AND \G(e_p)&\equivEU \G(f_1\AND\ldots\AND f_n)\AND \G(e_1 \AND \ldots \AND e_p) \\
\F(f_1) \OR\ldots\OR \F(f_n) \OR \F(u_1)\OR\ldots\OR \F(u_p) &\equivEU \F(f_1\OR \ldots\OR f_n) \OR \F(u_1 \OR \ldots \OR u_p)\\
\intertext{Finally the following rule is applied only when no other
terms are present in the OR arguments:}
\F(f_1) \OR \ldots \OR \F(f_n) \OR \G\F(g_1) \OR \ldots \OR \G\F(g_m)
\OR q_1 \OR \ldots \OR q_p
&\equiv \F(f_1\OR \ldots \OR f_n \OR \G\F(g_1\OR \ldots\OR g_m) \OR q_1\OR \ldots q_p)
\F(f_1) \OR \ldots \OR \F(f_n) \OR q_1 \OR \ldots \OR q_p &\equivNeu \F(f_1\OR \ldots \OR f_n \OR q_1\OR \ldots q_p)
\end{align*}
\subsection{Simplifications Based on Implications}