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28
FiniteState Transducers in Language and Speech Processing
 Computational Linguistics
, 1997
"... Finitestate machines have been used in various domains of natural language processing. We consider here the use of a type of transducers that supports very efficient programs: sequential transducers. We recall classical theorems and give new ones characterizing sequential stringtostring transducer ..."
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Cited by 392 (42 self)
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Finitestate machines have been used in various domains of natural language processing. We consider here the use of a type of transducers that supports very efficient programs: sequential transducers. We recall classical theorems and give new ones characterizing sequential stringtostring transducers. Transducers that output weights also play an important role in language and speech processing. We give a specific study of stringtoweight transducers, including algorithms for determinizing and minimizing these transducers very efficiently, and characterizations of the transducers admitting determinization and the corresponding algorithms. Some applications of these algorithms in speech recognition are described and illustrated. 1.
SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 90 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
 J. of the American Mathematical Society
, 2001
"... A topical map is a map from Rn into itself verifying some conditions (see §1.2) and which, roughly speaking, behaves like a translation along some line, the amount of which is measured by a real number, called the average height (or average displacement) of the map. Then we look at a topical Iterate ..."
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Cited by 71 (5 self)
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A topical map is a map from Rn into itself verifying some conditions (see §1.2) and which, roughly speaking, behaves like a translation along some line, the amount of which is measured by a real number, called the average height (or average displacement) of the map. Then we look at a topical Iterated Function System (IFS),
The Equality Problem for Rational Series With Multiplicities in the Tropical Semiring is Undecidable
, 1994
"... this paper that the equality problem for Mrational series over an alphabet with at least two letters is undecidable. ..."
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Cited by 65 (2 self)
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this paper that the equality problem for Mrational series over an alphabet with at least two letters is undecidable.
On Semigroups of Matrices over the Tropical Semiring
, 1994
"... The tropical semiring M consists of the set of natural numbers extended with infinity, equipped with the operations of taking minimums (as semiring addition) and addition (as semiring multiplication). We use factorization forests to prove finiteness results related to semigroups of matrices over M. ..."
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Cited by 44 (0 self)
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The tropical semiring M consists of the set of natural numbers extended with infinity, equipped with the operations of taking minimums (as semiring addition) and addition (as semiring multiplication). We use factorization forests to prove finiteness results related to semigroups of matrices over M. Our method is used to recover results of Hashiguchi, Leung and the author in a unified combinatorial framework.
Recognizable Sets with Multiplicities in the Tropical Semiring
, 1988
"... The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the MinPlus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's ..."
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Cited by 43 (1 self)
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The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the MinPlus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's classical star height problem and the measure of the nondeterministic complexity of finite automata. We review here these results, their applications and point out some open problems. 1 Introduction One of the richest extensions of finite automaton theory is obtained by associating multiplicities to words, edges and states. Perhaps the most intuitive appearence of this concept is obtained by counting for every word the number of successful paths spelling it in a (nondeterministic) finite automaton. This is motivated by the formalization of ambiguity in a finite automaton and leads to the theory of recognizable subsets of a free monoid with multiplicities in the semiring of natural numbers. This...
On Rational Series in One Variable over certain Dioids
, 1994
"... We give a characterization of rational series in one variable over certain idempotent semirings (commutative dioids) such as for instance the "(max; +)" semiring. We show that a series is rational iff it is merge of ultimately geometric series. As a byproduct, we obtain a new proof of th ..."
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Cited by 26 (5 self)
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We give a characterization of rational series in one variable over certain idempotent semirings (commutative dioids) such as for instance the "(max; +)" semiring. We show that a series is rational iff it is merge of ultimately geometric series. As a byproduct, we obtain a new proof of the periodicity theorem for powers of irreducible matrices and also some more general auxiliary results. We apply this characterization of rational series to the minimal realization problem for which we obtain an upper bound. We also obtain a lower bound in terms of minors in a symmetrized semiring.
Fuzzy hideal of hemirings
 Inform. Sci
, 2007
"... Abstract: We introduce the notion of intuitionistic fuzzy (left) hideals of hemirings and investigate their properties connected with the corresponding level subsets. Methods of constructions of such intuitionistic fuzzy ideals from given sequences of left hideals of a hemiring R are presented. So ..."
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Cited by 21 (5 self)
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Abstract: We introduce the notion of intuitionistic fuzzy (left) hideals of hemirings and investigate their properties connected with the corresponding level subsets. Methods of constructions of such intuitionistic fuzzy ideals from given sequences of left hideals of a hemiring R are presented. Some natural classification of such intuitionistic fuzzy hideals is given. Key–Words: Hemiring, fuzzy set, intuitionistic fuzzy left hideal, descending chain. 1
AUTOMATE, a computing package for automata and finite semigroups
, 1991
"... AUTOMATE is a package for symbolic computation on finite automata, extended rational expressions and finite semigroups. On the one hand, it enables one to compute the deterministic minimal automaton of the language represented by a rational expression or given by its table. On the other hand, gi ..."
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Cited by 17 (1 self)
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AUTOMATE is a package for symbolic computation on finite automata, extended rational expressions and finite semigroups. On the one hand, it enables one to compute the deterministic minimal automaton of the language represented by a rational expression or given by its table. On the other hand, given the transition table of a deterministic automaton, AUTOMATE computes the associated transition monoid. The regular Dclasses structure, and many properties of the elements in the monoid are provided. The program AUTOMATE has been written in C and is quite portable. The user interface includes specialized editors for easy displaying of the computed results.