simplify: reduce {r;1} to {r} or {1}

Fixes #3.

* spot/tl/simplify.cc: Implement this new rule.
* doc/tl/tl.tex, NEWS: Document it.
* tests/core/reduccmp.test: Test it.

NEWS

@@ -18,6 +18,10 @@ New in spot 2.5.1.dev (not yet released)
     update an external structure that references states of the twa
     that we want to purge.
 
+  - the PSL simplification routines learned that {SERE;1} can be
+    simplified to {1} or {SERE} depending on whether SERE accepts
+    the empty word or not.
+
   Bugs fixed:
 
   - acc_cond::is_generalized_rabin() and

doc/tl/tl.tex

@@ -1636,6 +1636,10 @@ Here are the basic rewritings for the weak closure and its negation:
 \begin{align*}
   \sere{r\STAR{}}&\equiv \sere{r}&
   \nsere{r\STAR{}}&\equiv \nsere{r}\\
+  \sere{r;\1}&\equiv \sere{r} \quad\text{if~}\varepsilon\not\VDash r&
+  \nsere{r;\1}&\equiv \nsere{r} \quad\text{if~}\varepsilon\not\VDash r\\
+  \sere{r;\1}&\equiv \1 \quad\text{if~}\varepsilon\VDash r&
+  \nsere{r;\1}&\equiv \0 \quad\text{if~}\varepsilon\VDash r\\
   \sere{r_1;r_2}&\equiv \sere{r_1}\phantom{{}\OR\sere{r_2}}\quad\text{if~}\varepsilon\not\VDash r_1\land\varepsilon\VDash r_2&
   \nsere{r_1;r_2}&\equiv \nsere{r_1}\phantom{{}\AND\nsere{r_2}}\quad\text{if~}\varepsilon\not\VDash r_1\land\varepsilon\VDash r_2\\
   \sere{r_1;r_2}&\equiv \sere{r_1}\OR\sere{r_2}\quad\text{if~}\varepsilon\VDash r_1\land\varepsilon\VDash r_2&

spot/tl/simplify.cc

@@ -1268,12 +1268,26 @@ namespace spot
 
                   // Some term does not accept the empty word.
                   unsigned end = c.size() - 1;
+
+                  // {r;1} = 1 if r accepts [*0], else {r}
+                  // !{r;1} = 0 if r accepts [*0], else !{r}
+                  if (c[end].is_tt())
+                    {
+                      formula rest = c.all_but(end);
+                      if (rest.accepts_eword())
+                        return o == op::Closure ? formula::tt() : formula::ff();
+                      return recurse(formula::unop(o, rest));
+                    }
+
                   // {b₁;b₂;e₁;f₁;e₂;f₂;e₂;e₃;e₄}
                   //    = b₁&X(b₂&X({e₁;f₁;e₂;f₂}))
                   // !{b₁;b₂;e₁;f₁;e₂;f₂;e₂;e₃;e₄}
                   //    = !b₁|X(!b₂|X(!{e₁;f₁;e₂;f₂}))
                   // if e denotes a term that accepts [*0]
                   // and b denotes a Boolean formula.
+                  //
+                  // if reduce_size_strictly is set, we simply remove
+                  // the trailing e2;e3;e4.
                   while (c[end].accepts_eword())
                     --end;
                   unsigned start = 0;

tests/core/reduccmp.test

 #! /bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2009-2014, 2016-2017 Laboratoire de Recherche et
+# Copyright (C) 2009-2014, 2016-2018 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
@@ -388,6 +388,12 @@ G(GFc|GFd|FGe|FGf), F(GF(c|d)|Ge|Gf)
 {a|b*|c|d*}[]->e, (e | !(a | c)) & (e W !b) & (e W !d)
 {{[*0]|a};b;{[*0]|a};c;e[*]}[]->f,{{[*0]|a};b;{[*0]|a}}[]->X((f&X(f W !e))|!c)
 {(a[*]|b)[*0..1];c}, {{b | a[*]};c}
+{{a|b*};1}, 1
+!{{a|b*};1}, 0
+{{a|b[+]};1}, a|b
+!{{a|b[+]};1}, !a&!b
+{{{a|b[+]}&c[*]};1}, {{a|b[+]}&c[*]}
+!{{{a|b[+]}&c[*]};1}, !{{a|b[+]}&c[*]}
 
 {a&b&c*}<>->!Xb, (a & b & X!b) | (a & b & c & X(c U !b))
 {[*]}<>->b, Fb