public void LmlRewriterTest() { var alphabet = new HashSet <char> { 'a', 'b', 'c', 'd' }; // ab|bc -> d var rule1 = FstBuilder.FromWordPair("ab", "d") .Union(FstBuilder.FromWordPair("bc", "d")); // cd -> CD var rule2 = FstBuilder.FromWordPair("cd", "CD"); var transducer = rule1.ToLmlRewriter(alphabet) .Compose(rule2.ToLmlRewriter(alphabet)) .PseudoMinimal(); Assert.Equal(string.Empty, transducer.Process(string.Empty).Single()); Assert.Equal("dc", transducer.Process("abc").Single()); Assert.Equal("dCDdc", transducer.Process("abcbcabc").Single()); var bm = transducer.ToBimachine(alphabet); // Assert.Equal(string.Empty, bm.Process(string.Empty)); Assert.Equal("dc", bm.Process("abc")); Assert.Equal("dCDdc", bm.Process("abcbcabc")); }
public static Bimachine CreateForEnglish() { var alphabet = Enumerable.Range(32, 95).Select(x => (char)x) .Concat(new[] { '\t', '\n', '\v', '\f', '\r' }) .ToHashSet(); var whitespaces = new[] { ' ', '\t', '\n' }; var upperCaseLetters = Enumerable.Range(65, 27).Select(x => (char)x); var lowerCaseLetters = Enumerable.Range(97, 27).Select(x => (char)x); var digits = new[] { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9' }; var letters = upperCaseLetters.Concat(lowerCaseLetters); var riseCase = alphabet .Select(symbol => FstBuilder.FromWordPair( symbol.ToString(), char.IsLower(symbol) ? symbol.ToString().ToUpper() : symbol.ToString())) .Aggregate((aggr, fst) => aggr.Union(fst)) .Star(); var multiWordExprList = new[] { "AT LEAST", "IN SPITE OF", "HEAD OVER HEELS" }; var multiWordExpr = multiWordExprList .Select(exp => FsaBuilder.FromWord(exp)) .Aggregate((aggr, fsa) => aggr.Union(fsa)); var token = FsaBuilder.FromSymbolSet(letters) .Plus() .Union( FsaBuilder.FromSymbolSet(digits).Plus(), riseCase.Compose(multiWordExpr.Identity()).Domain(), FsaBuilder.FromSymbolSet(alphabet.Except(whitespaces))); var insertLeadingNewLine = FstBuilder.FromWordPair(string.Empty, "\n") .Concat(FsaBuilder.FromSymbolSet(alphabet).Star().Identity()); var clearSpaces = FsaBuilder.FromSymbolSet(whitespaces) .Plus() .Product(FsaBuilder.FromWord(" ")) .ToLmlRewriter(alphabet); var markTokens = token.Identity() .Concat(FstBuilder.FromWordPair(string.Empty, "\n")) .ToLmlRewriter(alphabet); var clearLeadingSpace = insertLeadingNewLine.Compose( FstBuilder.FromWordPair("\n ", "\n").ToRewriter(alphabet), insertLeadingNewLine.Inverse()); return(clearSpaces.Compose(markTokens, clearLeadingSpace).ToBimachine(alphabet)); }
public void SingleRuleLmlRewriterTest() { var alphabet = new HashSet <char> { 'a', 'b' }; var rule = FstBuilder.FromWordPair("a", "b"); var tr = rule.ToLmlRewriter(alphabet); Assert.Equal("bb", tr.Process("aa").Single()); }
public void ObligatoryRewriteRelTest() { // ab|bc -> d var fst = FstBuilder.FromWordPair("ab", "d").Union(FstBuilder.FromWordPair("bc", "d")); var obl = fst.ToRewriter(new HashSet <char> { 'a', 'b', 'c', 'd' }); Assert.Equal(string.Empty, obl.Process(string.Empty).Single()); Assert.Equal("d", obl.Process("ab").Single()); Assert.Equal("dacda", obl.Process("abacbca").Single()); Assert.Equal(new[] { "ad", "dc" }, obl.Process("abc").OrderBy(w => w)); }
public void OptionalRewriteRelTest() { // ab|bc -> d var fst = FstBuilder.FromWordPair("ab", "d").Union(FstBuilder.FromWordPair("bc", "d")); var opt = fst.ToOptionalRewriter(new HashSet <char> { 'a', 'b', 'c', 'd' }); Assert.Equal(string.Empty, opt.Process(string.Empty).Single()); Assert.Equal(new[] { "ab", "d" }, opt.Process("ab").OrderBy(s => s)); Assert.Equal( new[] { "abacbca", "abacda", "dacbca", "dacda" }, opt.Process("abacbca").OrderBy(s => s)); }
// 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); }