Trivially reduce [*];f to [*] if f accepts the empty word.

* src/ltlast/multop.cc (instance): Implement the reduction.
* src/ltlast/multop.hh, doc/tl/tl.tex: Document it.
* src/ltltest/equals.test: Test it.

doc/tl/tl.tex

@@ -707,17 +707,17 @@ The following rules are all valid with the two arguments swapped.
   \0 \CONCAT f &\equiv \0 \\
   \1\AND f&\equiv
   \begin{cases}
-    1 &\mathrlap{\text{if~} \varepsilon\VDash f} \\
-    f &\mathrlap{\text{if~} \varepsilon\nVDash f} \\
+    1\mathrlap{\text{~if~} \varepsilon\VDash f} \\
+    f\mathrlap{\text{~if~} \varepsilon\nVDash f} \\
   \end{cases} &
   \1\ANDALT b   &\equiv b &
   \1\OR b &\equiv \1 &
   \1 \FUSION f & \equiv f\mathrlap{\text{~if~}\varepsilon\nVDash f}\\
   &&
-  \1\STAR{} \AND f &\equiv f &
-  \1\STAR{} \OR f &\equiv \1\STAR{} &
+  \STAR{} \AND f &\equiv f &
+  \STAR{} \OR f &\equiv \1\STAR{} &
   &&
-  && \\
+  \STAR{} \CONCAT f &\equiv \STAR{}\mathrlap{\text{~if~}\varepsilon\VDash f}& \\
   \eword\AND f &\equiv f &
   \eword\ANDALT f &\equiv
   \begin{cases}

src/ltlast/multop.cc

@@ -337,6 +337,44 @@ namespace spot
 	  abs = constant::false_instance();
 	  abs2 = 0;
 	  weak_abs = 0;
+
+	  // - Concat(Exps1...,FExps2...,1[*],FExps3...,Exps4) =
+	  //     Concat(Exps1...,1[*],Exps4)
+	  // If FExps2... and FExps3 all accept [*0].
+	  {
+	    vec::iterator i = v->begin();
+	    formula* os = bunop::one_star();
+	    while (i != v->end())
+	      {
+		while (i != v->end() && !(*i)->accepts_eword())
+		  ++i;
+		if (i == v->end())
+		  break;
+		vec::iterator b = i;
+		// b is the first expressions that accepts [*0].
+		// let's find more, and locate the position of
+		// 1[*] at the same time.
+		bool os_seen = false;
+		do
+		  {
+		    os_seen |= (*i == os);
+		    ++i;
+		  }
+		while (i != v->end() && (*i)->accepts_eword());
+
+		if (os_seen) // [b..i) is a range that contains [*].
+		  {
+		    // Place [*] at the start of the range, and erase
+		    // all other formulae.
+		    (*b)->destroy();
+		    *b++ = os->clone();
+		    for (vec::iterator c = b; c < i; ++c)
+		      (*c)->destroy();
+		    i = v->erase(b, i);
+		  }
+	      }
+	  }
+
 	  break;
 	case Fusion:
 	  neutral = constant::true_instance();

src/ltlast/multop.hh

@@ -108,6 +108,8 @@ namespace spot
       /// - OrRat(Exps1...,1[*],Exps2...) = 1[*]
       /// - Concat(Exps1...,0,Exps2...) = 0
       /// - Concat(Exps1...,[*0],Exps2...) = Concat(Exps1...,Exps2...)
+      /// - Concat(Exps1...,FExps2...,1[*],FExps3...,Exps4) =
+      ///     Concat(Exps1...,1[*],Exps4) if FExps2...FExps3... all accept [*0]
       /// - Concat(Exp) = Exp
       /// - Fusion(Exps1...1,Exps2...) = Fusion(Exps1...,Exps2...)
       ///     if at least one exp reject [*0]

src/ltltest/equals.test

@@ -162,6 +162,8 @@ run 0 ../equals '{c*:1:{a;b}:1}!' '{c*:{a;b}}!'
 run 1 ../equals '{(a;!a)*:(a;!a)*:b}!' '{(a;!a)*:b}!'
 # make sure 1:a* is not reduced to a*.
 run 1 ../equals '{(1:a*);b}!' '{a*;b}!'
+run 0 ../equals '{z;a*;b*;*;c;d;*;b*;e;a*;*;b*}' '{z;[*];c;d;[*];e;[*]}'
+run 0 ../equals '{((a;b)|[*0]);[*];c}!' '{[*];c}!'
 
 run 0 ../equals '{a[*0]}' '{[*0]}'
 run 0 ../equals '{a[*..]}' '{a[*]}'