############################################################################
##
#W sgpslinks.gi Manuel Delgado <mdelgado@fc.up.pt>
#W Jose Morais <josejoao@fc.up.pt>
##
##
#Y Copyright (C) 2004, CMUP, Universidade do Porto, Portugal
##
##
##
#############################################################################
##
## This file contains some links between automata and semigroups.
##
##
############################################################################
##
#F TransitionSemigroup(aut)
##
## Computes the transition semigroup of a deterministic automaton
##
InstallGlobalFunction(TransitionSemigroup, function(aut)
local g, tr, i;
if not IsAutomaton(aut) then
Error("the argument must be an automaton");
fi;
if not aut!.type = "det" then
Error("<A> must be deterministic");
fi;
g := [];
tr := NullCompletionAut(aut)!.transitions;
for i in tr do
g := Concatenation(g, [Transformation(i)]);
od;
return Semigroup( g );
end);
###########################################################################
##
#F SyntacticSemigroupAut
## Computes the syntactic semigroup of a deterministic automaton
## (i.e. the transition semigroup of the equivalent minimal automaton)
##
InstallGlobalFunction(SyntacticSemigroupAut, function(aut)
local g, A, tr, i;
if not IsAutomaton(aut) then
Error("the argument must be an automaton");
fi;
if not aut!.type = "det" then
Error("<aut> must be deterministic");
fi;
g := [];
A := MinimalizedAut(NullCompletionAut(aut));
if A!.accepting = [] then
return fail;
fi;
tr := A!.transitions;
for i in tr do
g := Concatenation(g, [Transformation(i)]);
od;
return Semigroup( g );
end);
###########################################################################
##
#F SyntacticSemigroupLang(rat)
##
## Computes the syntactic semigroup of the rational language given by the
## rational expression rat.
##
##
InstallGlobalFunction(SyntacticSemigroupLang, function(rat)
return SyntacticSemigroupAut(RatExpToAut(rat));
end);
#E
