// Introduce symbols from a set S into an input string not containing symbols in S
static Fst Intro(ISet <char> alphabet, ISet <char> symbols) =>
FsaBuilder.FromSymbolSet(alphabet.Except(symbols))
.Identity()
.Union(
FsaBuilder.FromEpsilon()
.Product(FsaBuilder.FromSymbolSet(symbols)))
.Star();
public void EpsilonFsaBuilderTest()
{
var fsa = FsaBuilder.FromEpsilon();
Assert.Single(fsa.States);
Assert.False(fsa.Recognize("a"));
Assert.False(fsa.Recognize("abc"));
Assert.True(fsa.Recognize(string.Empty));
}
Fsa Term()
{
if (this.HasMoreChars() && this.Peek() != ')' && this.Peek() != '|')
{
return(this.Factor().Concat(this.Term()));
}
return(FsaBuilder.FromEpsilon());
}
public void UnionEpsilonFsaTest()
{
var fsa1 = FsaBuilder.FromWord("abc");
var fsa2 = FsaBuilder.FromEpsilon();
var fsa = fsa1.Union(fsa2);
Assert.Equal(5, fsa.States.Count);
Assert.Equal(2, fsa.Initial.Count);
Assert.Equal(2, fsa.Final.Count);
Assert.True(fsa.Recognize(string.Empty));
Assert.False(fsa.Recognize("a"));
Assert.True(fsa.Recognize("abc"));
Assert.False(fsa.Recognize("abca"));
}
// Convert to an obligatory leftmost-longest match rewrite transducer (van Noord, Gerdemann 1999)
public static Fst ToLmlRewriter2(this Fst fst, ISet <char> alphabet)
{
const char notMarkerSymbol = '0';
const char isMarkerSymbol = '1';
var markers = new[] { notMarkerSymbol, isMarkerSymbol };
var sigFsa = FsaBuilder.FromSymbolSet(alphabet)
.Concat(FsaBuilder.FromSymbolSet(new[] { notMarkerSymbol }));
var sigStarFsa = sigFsa.Star().Minimal();
var xSig = alphabet.Concat(markers).ToHashSet();
var xSigFsa = sigFsa.Concat(FsaBuilder.FromSymbolSet(markers));
var xSigStarFsa = xSigFsa.Star().Minimal();
const char lb1Marker = '<'; // <1
const char lb2Marker = '≪'; // <2
const char rb1Marker = '>'; // 1>
const char rb2Marker = '≫'; // 2>
var lb1 = FsaBuilder.FromSymbol(lb1Marker).Concat(FsaBuilder.FromSymbol(isMarkerSymbol));
var lb2 = FsaBuilder.FromSymbol(lb2Marker).Concat(FsaBuilder.FromSymbol(isMarkerSymbol));
var rb2 = FsaBuilder.FromSymbol(rb2Marker).Concat(FsaBuilder.FromSymbol(isMarkerSymbol));
var rb1 = FsaBuilder.FromSymbol(rb1Marker).Concat(FsaBuilder.FromSymbol(isMarkerSymbol));
var lb = lb1.Union(lb2);
var rb = rb1.Union(rb2);
var b1 = lb1.Union(rb1);
var b2 = lb2.Union(rb2);
var brack = lb.Union(rb);
Fsa Not(Fsa lang) => xSigStarFsa.Difference(lang);
Fsa Contain(Fsa lang) => xSigStarFsa.Concat(lang, xSigStarFsa);
Fsa IfPThenS(Fsa l1, Fsa l2) => Not(l1.Concat(Not(l2)));
Fsa IfSThenP(Fsa l1, Fsa l2) => Not(Not(l1).Concat(l2));
Fsa PiffS(Fsa l1, Fsa l2) => IfPThenS(l1, l2).Intersect(IfSThenP(l1, l2));
Fsa LiffR(Fsa l1, Fsa l2) => PiffS(xSigStarFsa.Concat(l1), l2.Concat(xSigStarFsa));
var trueFsa = xSigStarFsa;
var falseFsa = FsaBuilder.FromEpsilon();
// Fsa CoerceToBoolean(Fsa l) => l.Identity()
// .Compose(trueFsa.Product(trueFsa)).Range();
// Fst If(Fsa cond, Fst then, Fst @else) =>
// CoerceToBoolean(cond).Identity().Compose(then)
// .Union(Not(CoerceToBoolean(cond)).Identity().Compose(@else));
var leftCtx = FsaBuilder.FromEpsilon();
var rightCtx = FsaBuilder.FromEpsilon();
var domainT = fst.Domain();
var nonMarkersFst = FsaBuilder.FromSymbolSet(alphabet)
.Identity()
.Concat(FstBuilder.FromWordPair(string.Empty, notMarkerSymbol.ToString()));
Fsa NonMarkers(Fsa l) => l.Identity().Compose(nonMarkersFst).Range();
// begin R
var cond = FsaBuilder.FromEpsilon().Intersect(rightCtx);
var then = FsaBuilder.FromEpsilon().Product(rb2).Concat(sigFsa.Identity()).Star()
.Concat(FsaBuilder.FromEpsilon().Product(rb2));
var @else = Intro(xSig, new HashSet <char> {
rb2Marker
}).Compose(
LiffR(rb2, XIgnore(NonMarkers(rightCtx), xSig, new HashSet <char> {
rb2Marker
})).Identity());
// var r = If(cond, then, @else);
var r = FsaBuilder.FromEpsilon().Product(rb2).Concat(sigFsa.Identity()).Star()
.Concat(FsaBuilder.FromEpsilon().Product(rb2));
// end R
var f = Intro(xSig, new HashSet <char> {
lb2Marker
})
.Compose(
LiffR(lb2, XIgnoreX(NonMarkers(domainT), xSig, new HashSet <char> {
lb2Marker, rb2Marker
})
.Concat(lb2.Optional(), rb2)).Identity());
// begin lr
var leftToRightBody = lb2.Product(lb1)
.Concat(
Ignore(NonMarkers(domainT), xSig, new HashSet <char> {
lb2Marker, rb2Marker
}).Identity()
.Compose(Intro(xSig, new HashSet <char> {
lb2Marker
}).Inverse()))
.Concat(rb2.Product(rb1));
var leftToRight = xSigStarFsa.Identity()
.Concat(leftToRightBody)
.Star()
.Concat(xSigStarFsa.Identity());
// end lr
// begin longest match
var longestBody = lb1
.Concat(
IgnoreX(NonMarkers(domainT), xSig, new HashSet <char> {
lb1Marker, lb2Marker, rb1Marker, rb2Marker
})
.Intersect(Contain(rb1)))
.Concat(rb);
var longestMatch = Not(Contain(longestBody)).Identity()
.Compose(Intro(xSig, new HashSet <char> {
rb2Marker
}).Inverse());
// end longest match
var auxReplace = sigFsa.Union(lb2).Identity()
.Union(lb1.Identity()
.Concat(nonMarkersFst.Inverse().Compose(fst, nonMarkersFst))
.Concat(rb1.Product(FsaBuilder.FromEpsilon())))
.Star();
var l1 = Ignore(
IfSThenP(
IgnoreX(xSigStarFsa.Concat(NonMarkers(leftCtx)), xSig, new HashSet <char> {
lb1Marker
}),
lb1.Concat(xSigStarFsa)),
xSig,
new HashSet <char> {
lb2Marker
})
.Identity()
.Compose(Intro(xSig, new HashSet <char> {
lb1Marker
}).Inverse());
var l2 = IfSThenP(
IgnoreX(Not(xSigStarFsa.Concat(NonMarkers(leftCtx))), xSig, new HashSet <char> {
lb2Marker
}),
lb2.Concat(xSigStarFsa))
.Identity()
.Compose(Intro(xSig, new HashSet <char> {
lb2Marker
}).Inverse());
var replace = nonMarkersFst.Compose(
r, f,
leftToRight, longestMatch, auxReplace,
l1, l2,
nonMarkersFst.Inverse());
return(replace);
}