Commit c6605e95 authored by Alexandre Duret-Lutz's avatar Alexandre Duret-Lutz

tl: add some simplifications for first_match

Following a discussion with Victor Khomenko.

* doc/tl/tl.tex: Document those rules.
* spot/tl/simplify.cc: Implement them.
* tests/core/reduccmp.test: Test them.
parent b7cd4756
Pipeline #8972 passed with stages
in 292 minutes and 21 seconds
......@@ -801,7 +801,8 @@ $b_1$, $b_2$ are assumed to be Boolean formulas.
&&
f\FSTAR{\mvar{i}..\mvar{j}}\FSTAR{\mvar{k}..\mvar{l}} &\equiv f\FSTAR{\mvar{ik}..\mvar{jl}}\text{~if~}i(k+1)\le jk+1 \\
f\FSTAR{0}&\equiv \1 & f\FSTAR{1}&\equiv f\text{~if~}\varepsilon\nVDash f\\
\FIRSTMATCH\code(b\code) &\equiv b & \FIRSTMATCH\code(f\code) &\equiv \eword\text{~if~}\varepsilon\VDash f
\FIRSTMATCH\code(b\code) &\equiv b & \FIRSTMATCH\code(f\code) &\equiv \eword\text{~if~}\varepsilon\VDash f \\
&& \FIRSTMATCH\code(\FIRSTMATCH\code(f\code)\code) &\equiv \FIRSTMATCH\code(f\code)
\end{align*}
\noindent
......@@ -995,22 +996,6 @@ operator, even if the operator has multiple synonyms (like \samp{|},
\end{align*}
\section{Operator precedence}
The following operator precedence describes the current parser of
......@@ -1600,7 +1585,14 @@ SERE.
\sere{b_1\FUSION r_1}\ANDALT\sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\ANDALT r_2} &
\sere{r_1\FUSION b_1}\ANDALT\sere{r_2\FUSION b_2} &\equiv \sere{r_1\ANDALT r_2}\FUSION\sere{b_1\ANDALT b_2} \\
\sere{b_1\CONCAT r_1}\AND \sere{b_2\CONCAT r_2} &\equiv \sere{b_1\ANDALT b_2}\CONCAT\sere{r_1\AND r_2} \\
\sere{b_1\FUSION r_1}\AND \sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\AND r_2} \mathrlap{\quad\text{if~}\varepsilon\nVDash r_1\land\varepsilon\nVDash r_2}\\
\sere{b_1\FUSION r_1}\AND \sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\AND r_2} \mathrlap{\quad\text{if~}\varepsilon\nVDash r_1\land\varepsilon\nVDash r_2}
\end{align*}
\begin{align*}
\FIRSTMATCH\code(b\STAR{\mvar{i}..\mvar{j}}\code) &\equiv b\STAR{\mvar{i}} \\
\FIRSTMATCH\code(r\STAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r\STAR{\mvar{i}}\code) \\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\STAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH(r_1\CONCAT\mathrlap{r_2\STAR{\mvar{i}})} \\
\FIRSTMATCH\code(b\CONCAT{}r\code) &\equiv b\CONCAT\FIRSTMATCH\code(r\code) \\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\code) &\equiv\FIRSTMATCH(r_1)\mathrlap{\quad\text{if~} \varepsilon\VDash r_2}
\end{align*}
Starred subformulas are rewritten in Star Normal
......
......@@ -856,7 +856,6 @@ namespace spot
case op::ap:
case op::Not:
case op::FStar:
case op::first_match:
return f;
case op::X:
{
......@@ -1429,6 +1428,58 @@ namespace spot
}
return formula::Star(h, min, f.max());
}
case op::first_match:
{
formula h = f[0];
if (h.is(op::Star))
{
// first_match(b[*i..j]) = b[*i]
// first_match(f[*i..j]) = first_match(f[*i])
unsigned m = h.min();
formula s = formula::Star(h[0], m, m);
return h[0].is_boolean() ? s : formula::first_match(s);
}
else if (h.is(op::Concat))
{
// If b is Boolean and e accepts [*0], we have
// first_match(b;f) = b;first_match(f)
// first_match(f;e) = first_match(f)
// first_match(f;g[*i..j]) = first_match(f;g[*i])
// the first two rules can be repeated, so we will loop
// to save the recursion and intermediate caching.
// Extract Boolean formulas at the beginning.
int i = 0;
int n = h.size();
while (i < n && h[i].is_boolean())
++i;
vec prefix;
prefix.reserve(i + 1); // +1 to append first_match()
for (int ii = 0; ii < i; ++ii)
prefix.push_back(h[ii]);
// Extract suffix, minus trailing formulas that accept [*0].
// "i" is the start of the suffix.
do
--n;
while (i <= n && h[n].accepts_eword());
vec suffix;
suffix.reserve(n + 1 - i);
for (int ii = i; ii <= n; ++ii)
suffix.push_back(h[ii]);
if (!suffix.empty() && suffix.back().is(op::Star))
{
formula s = suffix.back();
unsigned smin = s.min();
suffix.back() = formula::Star(s[0], smin, smin);
}
prefix.push_back(formula::first_match
(formula::Concat(suffix)));
formula res = formula::Concat(prefix);
if (res != f)
return recurse(res);
}
return f;
}
}
SPOT_UNREACHABLE();
}
......
#! /bin/sh
# -*- coding: utf-8 -*-
# Copyright (C) 2009-2014, 2016-2018 Laboratoire de Recherche et
# Copyright (C) 2009-2014, 2016-2019 Laboratoire de Recherche et
# Developpement de l'Epita (LRDE).
# Copyright (C) 2004, 2006 Laboratoire d'Informatique de Paris 6 (LIP6),
# département Systèmes Répartis Coopératifs (SRC), Université Pierre
......@@ -436,6 +436,16 @@ GF(a && GF(b) && c), G(F(a & c) & Fb)
# not reduced
{a;(b[*2..4];c*;([*0]+{d;e}))*}!, {a;(b[*2..4];c*;([*0]+{d;e}))*}!
{c[*];e[*]}[]-> a, {c[*];e[*]}[]-> a
# first_match
{first_match(a*);b}, b
{first_match(a)}, a
{first_match(a;b*)}, a
{first_match(a;c;b*)}, a & Xc
{first_match(a;c;b*;e)}, a & X(c & X{first_match(b[*];e)})
{first_match(a;c;b*;(e | [*0]))}, a & Xc
{first_match(a;c;b[+];(e | [*0]))}, a & X(c & Xb)
{first_match(b[+];(e | [*0]))}, b
{first_match(b[*2..3])}, b & Xb
EOF
run 0 ../reduccmp nottau.txt
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment