// Convert to an obligatory rewrite transducer
public static Fst ToRewriter(this Fst fst, ISet <char> alphabet)
{
var all = FsaBuilder.All(alphabet);
var notInDomain = all
.Difference(all.Concat(fst.Domain()).Concat(all))
.Identity()
.Optional();
return(notInDomain.Concat(fst.Concat(notInDomain).Star()));
}
// Convert to an obligatory leftmost-longest match rewrite transducer (Karttunen 1996)
public static Fst ToLmlRewriter(this Fst fst, ISet <char> alphabet)
{
if (alphabet.Intersect(markers).Any())
{
throw new ArgumentException("The alphabet contains invalid symbols.");
}
var alphabetStarFsa = FsaBuilder.All(alphabet).Minimal();
var allSymbols = alphabet.Concat(markers).ToHashSet();
var allSymbolsStarFsa = FsaBuilder.All(allSymbols).Minimal();
// Automaton recognizing all words that are not in the language of the input automaton (complement)
Fsa NotInLang(Fsa lang) => allSymbolsStarFsa.Difference(lang);
// Automaton recognizing all words that contain an occurrence of a word from the input automaton
Fsa ContainsLang(Fsa lang) => allSymbolsStarFsa.Concat(lang, allSymbolsStarFsa);
// All words w where each prefix of w representing a string in "P" is followed by a suffix which is in "S"
Fsa IfPThenS(Fsa p, Fsa s) => NotInLang(p.Concat(NotInLang(s)));
// All words for which each suffix from "S" is preceeded by a prefix from "P"
Fsa IfSThenP(Fsa p, Fsa s) => NotInLang(NotInLang(p).Concat(s));
Fsa PiffS(Fsa l, Fsa r) => IfPThenS(l, r).Intersect(IfSThenP(l, r));
/* Describes the words where every position is preceded by a string with a suffix in "L"
* if and only if it is followed by a string with a prefix in "R" */
Fsa LiffR(Fsa l, Fsa r) => PiffS(allSymbolsStarFsa.Concat(l), r.Concat(allSymbolsStarFsa));
var fstDomain = fst.Domain();
var initialMatch = // mark the beginnings of all rewrite occurrences by inserting "cb"
Intro(allSymbols, new HashSet <char> {
cb
})
.Compose(
LiffR(
FsaBuilder.FromSymbol(cb),
XIgnore(fstDomain, allSymbols, new HashSet <char> {
cb
}))
.Identity());
var leftToRight = // insert boundary markers ("lb", "rb") around the leftmost rewrite occurrences
alphabetStarFsa.Identity() // preceeded by arbitrary text that is not matched by the rule
.Concat(
FstBuilder.FromWordPair(cb.ToString(), lb.ToString()), // replace intial match marker with the left boundary marker
IgnoreX(fstDomain, allSymbols, new HashSet <char> {
cb
}).Identity(), // recognize matches with the leftover "cb" symbol inbetween the markers
FstBuilder.FromWordPair(string.Empty, rb.ToString())) // insert right boundary marker at the end of the matched substring
.Star() // handle multiple rewrite occurrences
.Concat(alphabetStarFsa.Identity()) // succeeded by arbitrary text that is not matched by the rule
.Compose(
FstBuilder.FromWordPair(cb.ToString(), string.Empty).ToRewriter(allSymbols)); // delete the remaining initial match markers
var includesNotLongestMatches =
ContainsLang(
FsaBuilder.FromSymbol(lb)
.Concat(
IgnoreX(fstDomain, allSymbols, new HashSet <char> {
lb, rb
})
.Intersect(ContainsLang(FsaBuilder.FromSymbol(rb)))));
// amongst occurrences with the same starting point, preserve only the longest ones
var longestMatch = NotInLang(includesNotLongestMatches).Identity();
var replacement = // replace the rewrite occurrence and delete the left and right markers
FstBuilder.FromWordPair(lb.ToString(), string.Empty) // delete the left boundary marker
.Concat(
fst, // perform the replacement
FstBuilder.FromWordPair(rb.ToString(), string.Empty)) // delete the right boundary marker
.ToRewriter(allSymbols);
return(initialMatch.Compose(leftToRight, longestMatch, replacement));
}
// 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);
}
