simplifier: new PSL simplifications

{e[*0..j]}<>->f = {e[*1..j]}<>->f
{e[*0..j]}[]->f = {e[*1..j]}[]->f

Fixes #81.

This required a small change to the bounded-star-normal-form to prevent
infinite recursion.

* spot/tl/simplify.cc: Implement these rules.
* doc/tl/tl.tex, NEWS: Document them.
* tests/core/reduccmp.test: Add tests, and adjust others.
* tests/core/unambig.test: Replace formula that used to generated an
ambiguous automaton, but now generates a deterministic one.

NEWS

@@ -111,9 +111,11 @@ New in spot 2.0.3a (not yet released)
     implies that "autfilt --check=stutter" will now label all
     automata, not just deterministic automata.
 
-  * New LTL simplification rules:
+  * New LTL and PSL simplification rules:
     - if e is pure eventuality and g => e, then e U g = Fg
     - if u is purely universal and u => g, then u R g = Gg
+    - {s[*0..j]}[]->b = {s[*1..j]}[]->b
+    - {s[*0..j]}<>->b = {s[*1..j]}<>->b
 
   Python:
 

doc/tl/tl.tex

@@ -1565,7 +1565,8 @@ presence of \samp{$\AND$} operators, but unfortunately not when the
 
 We extend the above definition to bounded repetitions with:
 \begin{align*}
-  r\STAR{\mvar{i}..\mvar{j}} & \equiv r^\square\STAR{\0..\mvar{j}}\quad\text{if}\quad\varepsilon\VDash r\STAR{\mvar{i}..\mvar{j}}
+  r\STAR{\mvar{i}..\mvar{j}} & \equiv r^\square\STAR{0..\mvar{j}}\quad\text{if}\quad\varepsilon\VDash r\STAR{\mvar{i}..\mvar{j}}\text{~and~}\varepsilon\not\VDash r^\square\\
+  r\STAR{\mvar{i}..\mvar{j}} & \equiv r^\square\STAR{1..\mvar{j}}\quad\text{if}\quad\varepsilon\VDash r\STAR{\mvar{i}..\mvar{j}}\text{~and~}\varepsilon\VDash r^\square
 \end{align*}
 where $r^\square$ is recursively defined as follows:
 \begin{align*}
@@ -1603,6 +1604,7 @@ denoted with $\equiV$ can be disabled by setting the
   \sere{\STAR{}}\Asuffix f &\equiv \G f\\
   \sere{b\STAR{}}\Asuffix f &\equiv f \W \NOT b\\
   \sere{b\PLUS{}}\Asuffix f &\equiv f \W \NOT b\\
+  \sere{r\STAR{0..\mvar{j}}}\Asuffix f &\equiv \sere{r\STAR{1..\mvar{j}}}\Asuffix f \\
   \sere{r\STAR{\mvar{i}..\mvar{j}}}\Asuffix f &\equiV
     \sere{r}\Asuffix \X(
     \sere{r}\Asuffix \X(\ldots
@@ -1618,6 +1620,7 @@ denoted with $\equiV$ can be disabled by setting the
   \sere{\STAR{}}\Esuffix f &\equiv \F f\\
   \sere{b\STAR{}}\Esuffix f &\equiv f \M b\\
   \sere{b\PLUS{}}\Esuffix f &\equiv f \M b\\
+  \sere{r\STAR{0..\mvar{j}}}\Esuffix f &\equiv \sere{r\STAR{1..\mvar{j}}}\Esuffix f \\
   \sere{r\STAR{\mvar{i}..\mvar{j}}}\Esuffix f &\equiV
     \sere{r}\Esuffix \X(
     \sere{r}\Esuffix \X(\ldots
@@ -1632,7 +1635,7 @@ denoted with $\equiV$ can be disabled by setting the
   \sere{r_1\OR r_2}\Esuffix f &\equiV (\sere{r_1}\Esuffix f)\OR(\sere{r_2}\Esuffix f)
 \end{align*}
 
-Here are basic the rewritings for the weak closure and its negation:
+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}\\

spot/tl/simplify.cc

@@ -1290,14 +1290,20 @@ namespace spot
             return f;
           case op::Star:
             {
+              if (!f.accepts_eword())
+                return f;
               formula h = f[0];
-              auto min = f.min();
+              auto min = 0;
-              if (h.accepts_eword())
+              if (f.max() == formula::unbounded())
-                min = 0;
+                {
-              if (min == 0)
+                  h = c_->star_normal_form(h);
-                h = f.max() == formula::unbounded()
+                }
-                  ? c_->star_normal_form(h)
+              else
-                  : c_->star_normal_form_bounded(h);
+                {
+                  h = c_->star_normal_form_bounded(h);
+                  if (h.accepts_eword())
+                    min = 1;
+                }
               return formula::Star(h, min, f.max());
             }
           }
@@ -1359,12 +1365,19 @@ namespace spot
                 // b W !s
                 return recurse(formula::binop(op_w, b, ns));
               }
+            // {s[*0..j]}[]->b = {s[*1..j]}[]->b
+            // {s[*0..j]}<>->b = {s[*1..j]}<>->b
+            if (min == 0)
+              return recurse(formula::binop(bindop,
+                                            formula::Star(s, 1, max), b));
+
             if (opt_.reduce_size_strictly)
               return orig;
             // {s[*i..j]}[]->b = {s;s;...;s[*1..j-i+1]}[]->b
             // = {s}[]->X({s}[]->X(...[]->X({s[*1..j-i+1]}[]->b)))
             // if i>0 and s does not accept the empty word
-            if (min == 0 || s.accepts_eword())
+            assert(min > 0);
+            if (s.accepts_eword())
               return orig;
             --min;
             if (max != formula::unbounded())

tests/core/reduccmp.test

@@ -395,12 +395,16 @@ G(GFc|GFd|FGe|FGf), F(GF(c|d)|Ge|Gf)
 {(a;c*;d)|(b;c)}, (a & X{c*;d}) | (b & Xc)
 !{(a;c*;d)|(b;c)}, (X(!{c*;d}) | !a) & (X!c | !b)
 (Xc R b) & (Xc W 0), b & XGc
-{{c*|1}[*0..1]}<>-> v, {{c[+]|1}[*0..1]}<>-> v
+{{c*|1}[*0..1]}<>-> v, v | (v M c)
-{{b*;c*}[*3..5]}<>-> v, {{b*;c*}[*0..5]} <>-> v
+{{b*;c*}[*3..5]}<>-> v, {{b*;c*}[*1..5]} <>-> v
-{{b*&c*}[*3..5]}<>-> v, {{b[+]|c[+]}[*0..5]} <>-> v
+{{b*&c*}[*3..5]}<>-> v, {{b[+]|c[+]}[*1..5]} <>-> v
+{((a*;b)+[*0])[*4..6]}!, {((a*;b))[*1..6]}!
+# issue 81
+{e[*0..5]}<>->f, {e[*1..5]}<>->f
+{e[*0..5]}[]->f, {e[*1..5]}[]->f
+{(e+[*0])[*0..5]}[]->f, {e[*1..5]}[]->f
 # not reduced
 {a;(b[*2..4];c*;([*0]+{d;e}))*}!, {a;(b[*2..4];c*;([*0]+{d;e}))*}!
-{((a*;b)+[*0])[*4..6]}!, {((a*;b))[*0..6]}!
 {c[*];e[*]}[]-> a, {c[*];e[*]}[]-> a
 EOF
 

tests/core/unambig.test

@@ -42,7 +42,7 @@ do
       grep -E 'properties:.* (unambiguous|deterministic)'
 done
 
-for f in FGa '(({p1[*0..1]}[]-> 0) R XFp0)'
+for f in FGa '{[*1..4]}<>-> (p1 & (p1 U p0))'
 do
   $ltl2tgba -H "$f" | $autfilt -qv --is-unambiguous
   $ltl2tgba -UH "$f" | $autfilt -q --is-unambiguous