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Rewrite a&XGa as Ga, and a|XFa as Fa.

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The actual rules are a bit more complex:
a & X(G(a&b...)&c...) = Ga & X(G(b...)&c...)
a | X(Fa | c) = F(a) | c
with the second rule being applied only if all XF can
be removed.  See the documentation for an example.

* src/ltlvisit/simplify.cc: Implement these new rules.
* doc/tl/tl.tex: Document them.
* src/ltltest/reduccmp.test: Add test cases.
This commit is contained in:
Alexandre Duret-Lutz 2012-01-17 11:50:32 +01:00
parent 58f99203ad
commit 395793d986
3 changed files with 273 additions and 5 deletions
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23
doc/tl/tl.tex
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@ -1008,8 +1008,8 @@ instance using the following methods:
\\\texttt{is\_universal()}& Whether the formula is purely universal.
\\\texttt{is\_syntactic\_safety()}& Whether the formula is a syntactic
safety property.
\\\texttt{is\_syntactic\_guaranty()}& Whether the formula is a syntactic
guaranty property.
\\\texttt{is\_syntactic\_guarantee()}& Whether the formula is a syntactic
guarantee property.
\\\texttt{is\_syntactic\_obligation()}& Whether the formula is a syntactic
obligation property.
\\\texttt{is\_syntactic\_recurrence()}& Whether the formula is a syntactic
@ -1144,7 +1144,7 @@ The following grammar rules describes extend the aforementioned
work slightly by dealing with PSL operators. These are the
rules used by Spot to decide upon
construction to which class a formula belongs (see the methods
\texttt{is\_syntactic\_safety()}, \texttt{is\_syntactic\_guaranty()},
\texttt{is\_syntactic\_safety()}, \texttt{is\_syntactic\_guarantee()},
\texttt{is\_syntactic\_obligation()},
\texttt{is\_syntactic\_recurrence()}, and
\texttt{is\_syntactic\_persistence()} listed on
@ -1291,7 +1291,7 @@ The goals in most of these simplification are to:
a kind of disjunctive form: $\displaystyle\bigvee_i
\left(\beta_i\land\X\psi_i\right)$ where $\beta_i$s are Boolean
formul\ae{} and $\psi_i$s are LTL formul\ae{}. Moving $\X$ to the
front therefore simplify the translation.
front therefore simplifies the translation.
\item move the $\F$ operators to the front of the formula (e.g., $\F(f
\OR g)$ is better than the equivalent $(\F f)\OR (\F g)$), but not
before $\X$ ($\X\F f$ is better than $\F\X f$). Because $\F f$
@ -1347,6 +1347,8 @@ $\OR$):
(\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) \\
(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&
@ -1372,6 +1374,19 @@ The above rules are applied even if more terms are presents in the
operator's arguments. For instance $\F\G(a)\AND \G(b) \AND \F\G(c) \AND
\X(d)$ will be rewritten as $\X(d \AND \F\G(a\AND c))\AND \G(b)$.
The following more complicated rules are generalization of $f\AND
\X\G f\equiv \G f$ and $f\OR \X\F f\equiv \F f$:
\begin{align*}
f\AND \X(\G(f\AND g\ldots)\AND h\ldots) &\equiv \G(f) \AND \X(\G(g\ldots)\AND h\ldots) \\
f\OR \X(\F(f)\OR h\ldots) &\equiv \F(f) \OR \X(h\ldots)
\end{align*}
The latter rule for $f\OR \X(\F(f)\OR h\ldots)$ is only applied if all
$\F$-formul\ae{} can be removed from the argument of $\X$ with the
rewriting. For instance $a \OR b \OR c\OR \X(\F(a\OR b)\OR \F(c)\OR \G d)$
will be rewritten to $\F(a \OR b \OR c) \OR \X\G d$ but
$b \OR c\OR \X(\F(a\OR b)\OR \F(c)\OR \G d)$ would only become
$b \OR c\OR \X(\F(a\OR b\OR c)\OR \G d)$.
Finally the following rule is applied only when no other terms are present
in the OR arguments:
\begin{align*}