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11
Capturing Practical Natural Language Transformations
"... We study automata for capturing transformations employed by practical natural language processing systems, such as those that translate between human languages. For several variations of finitestate string and tree transducers, we ask formal questions about expressiveness, modularity, teachability, ..."
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We study automata for capturing transformations employed by practical natural language processing systems, such as those that translate between human languages. For several variations of finitestate string and tree transducers, we ask formal questions about expressiveness, modularity, teachability, and generalization.
Crucial words and the complexity of some extremal problems for sets of prohibited words
 J. Combin. Theory Ser. A
, 2004
"... We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for each of them examine the length of a crucial word. One of th ..."
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Cited by 6 (4 self)
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We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for each of them examine the length of a crucial word. One of these sets is proved to be incomplete. The problem of determining lengths of words that are free from a set of prohibitions is shown to be NPcomplete, although the related problem of whether or not a given set of prohibitions is complete is known to be effectively solvable. 1
Binary Equality Set Is Generated By Two Words
, 2002
"... We show that the equality set Eq(g; h) of two nonperiodic binary morphisms g; h : is generated by at most two words. If the rank of Eq(g; h) = f; g is two, then and start and end with dierent letters. This in particular implies that any binary language has a test set of cardinality at most t ..."
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Cited by 3 (2 self)
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We show that the equality set Eq(g; h) of two nonperiodic binary morphisms g; h : is generated by at most two words. If the rank of Eq(g; h) = f; g is two, then and start and end with dierent letters. This in particular implies that any binary language has a test set of cardinality at most two. 1
Many Aspects of Defect Theorems
 Theor. Comput. Sci
"... We give a survey and a unified presentation of the defect theorem, its generalizations and recent aspects of interest. In its basic form the defect theorem states that if a set of n words satisfies a nontrivial relation, then these words can be expressed simultaneously as products of at most n 1 wor ..."
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We give a survey and a unified presentation of the defect theorem, its generalizations and recent aspects of interest. In its basic form the defect theorem states that if a set of n words satisfies a nontrivial relation, then these words can be expressed simultaneously as products of at most n 1 words. In other words, dependency of words causes a defect effect. There does not exist just one defect theorem, but several ones depending on the restrictions that are put to the n 1 words. The defect theorem is closely related to equations of words, and in this way to the compactness theorem for systems of word equations.
Decision Questions on Integer Matrices
"... We give a survey of simple undecidability results and open problems concerning matrices of low order with integer entries. Connections to the theory of finite automata (with multiplicities) are also provided. ..."
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We give a survey of simple undecidability results and open problems concerning matrices of low order with integer entries. Connections to the theory of finite automata (with multiplicities) are also provided.
On unavoidable sets of word patterns
 SIAM J. on Discrete Math
"... Abstract. We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgrap ..."
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Abstract. We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgraph of the de Bruijn graph and which we prove to be Hamiltonian. In other cases we reduce a problem under consideration to known facts on unavoidable sets of words. We also give a relation between our problem and the intensively studied universal cycles, and prove that there exists a universal cycle for word patterns of any length over any alphabet. The Stirling numbers of the second kind and the Möbius function appear in our results.
On Finding Small 2Generating Sets
"... Abstract. Given a set of positive integers S, we consider the problem of finding a minimum cardinality set of positive integers X (called a minimum 2generating set of S) such that every element of S is an element of X or is the the sum of two (nonnecessarily distinct) elements of X. We give some e ..."
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Abstract. Given a set of positive integers S, we consider the problem of finding a minimum cardinality set of positive integers X (called a minimum 2generating set of S) such that every element of S is an element of X or is the the sum of two (nonnecessarily distinct) elements of X. We give some elementary properties of 2generating sets and prove that finding a minimum cardinality 2generating set is hard to approximate within ratio 1 + ε for any ε> 0. We then prove our main result, which consists in a standard representation lemma for minimum cardinality 2generating sets.
Regular Star Languages
"... We consider equality sets of prefix morphisms, that is, sets EG(g1, g2) = {w  g1(w) = g2(w)}, where g1 and g2 are prefix morphisms. Recall that a morphism g is prefix if, for all different letters a and b, g(a) is not a prefix of g(b). We prove a rather surprising equality on families of languages ..."
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We consider equality sets of prefix morphisms, that is, sets EG(g1, g2) = {w  g1(w) = g2(w)}, where g1 and g2 are prefix morphisms. Recall that a morphism g is prefix if, for all different letters a and b, g(a) is not a prefix of g(b). We prove a rather surprising equality on families of languages, namely, that the family of regular star languages coincides with the family of languages of form πA(EG(g1, g2)) for some prefix morphisms g1 and g2, and a projection πA which deletes the letters not in A.
Linear Size Test Sets for Certain Commutative Languages

, 2001
"... We prove that for each positive integer n; the nite commutative language E n = c(a 1 a 2 a n ) possesses a test set of size at most 5n: Moreover, it is shown that each test set for E n has at least n 1 elements. The result is then generalized to commutative languages L containing a word w such t ..."
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We prove that for each positive integer n; the nite commutative language E n = c(a 1 a 2 a n ) possesses a test set of size at most 5n: Moreover, it is shown that each test set for E n has at least n 1 elements. The result is then generalized to commutative languages L containing a word w such that (i) alph(w) = alph(L); and (ii) each symbol a 2 alph(L) occurs at least twice in w if it occurs at least twice in some word of L: each such L possesses a test set of size 11n, where n = Card(alph(L)). The considerations rest on the analysis of some basic types of word equations.