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11
Symbolic Dynamics and Finite Automata
, 1999
"... this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund. ..."
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Cited by 26 (9 self)
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this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.
Data Compression Using Antidictionaries
 in Proceedings of the IEEE, Lossless Data Compression
, 2000
"...  We give a new text compression scheme based on Forbidden Words ("antidictionary"). We prove that our algorithms attain the entropy for balanced binary sources. They run in linear time. Moreover, one of the main advantages of this approach is that it produces very fast decompressors. A second advan ..."
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Cited by 7 (4 self)
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 We give a new text compression scheme based on Forbidden Words ("antidictionary"). We prove that our algorithms attain the entropy for balanced binary sources. They run in linear time. Moreover, one of the main advantages of this approach is that it produces very fast decompressors. A second advantage is a synchronization property that is helpful to search compressed data and allows parallel compression. The techniques used in this paper are from Information Theory and Finite Automata. Keywords Data Compression, Lossless compression, Information Theory, Finite Automaton, Forbidden Word, Pattern Matching. I.
Length Distributions and Regular Sequences
 CODES, SYSTEMS AND GRAPHICAL MODELS, IMA VOLUMES IN MATHEMATICS AND ITS APPLICATIONS
, 2000
"... This paper presents a survey on length distributions of regular languages. The accent is problems in coding theory and the relation with symbolic dynamics. ..."
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Cited by 5 (2 self)
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This paper presents a survey on length distributions of regular languages. The accent is problems in coding theory and the relation with symbolic dynamics.
Minimal Forbidden Patterns Of MultiDimensional Shifts
"... We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semistrongly irreducible shifts. We prove a w ..."
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Cited by 4 (1 self)
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We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semistrongly irreducible shifts. We prove a weaker invariant in the general case.
A survey on certain pattern problems
"... Abstract. The paper contains all the definitions and notations needed to understand the results concerning the field dealing with occurrences of patterns in permutations and words. Also, this paper includes a historical overview on the results obtained in this subject. The authors tried to collect a ..."
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Cited by 4 (3 self)
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Abstract. The paper contains all the definitions and notations needed to understand the results concerning the field dealing with occurrences of patterns in permutations and words. Also, this paper includes a historical overview on the results obtained in this subject. The authors tried to collect all the currently existing references to the papers directly related to the subject. Moreover, a number of basic approaches to study the pattern problems are discussed.
Words, univalent factors and boxes
 ACTA INFORMATICA
, 2002
"... A factor u of a word w is (right) univalent if there exists a unique letter a such that ua is still a factor of w. A univalent factor is minimal if none of its proper suffixes is univalent. The starting block of w is the shortest prefix hw of w such that all proper prefixes of w of length ≥hw ar ..."
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Cited by 1 (0 self)
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A factor u of a word w is (right) univalent if there exists a unique letter a such that ua is still a factor of w. A univalent factor is minimal if none of its proper suffixes is univalent. The starting block of w is the shortest prefix hw of w such that all proper prefixes of w of length ≥hw are univalent. We study univalent factors of a word and their relationship with the well known notions of boxes, superboxes, and minimal forbidden factors. Moreover, we prove some new uniqueness conditions for words based on univalent factors. In particular, we show that a word is uniquely determined by its starting block, the set of the extensions of its minimal univalent factors, and its length or its terminal box. Finally, we show how the results and techniques presented can be used to solve the problem of sequence assembly for DNA molecules, under reasonable assumptions on the repetitive structure of the considered molecule and on the set of known fragments.
Computing Forbidden Words of . . .
 FUNDAMENTA INFORMATICAE XX (2003) 115 1 IOS PRESS
, 2003
"... We give a quadratictime algorithm to compute the set of minimal forbidden words of a factorial regular language. We give a lineartime algorithm to compute the minimal forbidden words of a finite set of words. This extends a previous result given for the case of a single word only. We also ..."
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We give a quadratictime algorithm to compute the set of minimal forbidden words of a factorial regular language. We give a lineartime algorithm to compute the minimal forbidden words of a finite set of words. This extends a previous result given for the case of a single word only. We also
Coding of twodimensional contraints of finite type by substitutions
 JOURNAL OF AUTOMATA, LANGUAGES AND COMBINATORICS
"... We give an automatic method to generate transition matrices associated with twodimensional contraints of finite type by using squared substitutions of constant dimension. ..."
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We give an automatic method to generate transition matrices associated with twodimensional contraints of finite type by using squared substitutions of constant dimension.
PeriodicFiniteType Shift Spaces
"... Abstract — We study the class of periodicfinitetype (PFT) shift spaces, which can be used to model timevarying constrained codes used in digital magnetic recording systems. A PFT shift is determined by a finite list of periodically forbidden words. We show that the class of PFT shifts properly co ..."
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Abstract — We study the class of periodicfinitetype (PFT) shift spaces, which can be used to model timevarying constrained codes used in digital magnetic recording systems. A PFT shift is determined by a finite list of periodically forbidden words. We show that the class of PFT shifts properly contains all finitetype (FT) shifts, and the class of almost finitetype (AFT) shifts properly contains all PFT shifts. We establish several basic properties of PFT shift spaces of a given period T, and provide a characterization of such a shift in terms of properties of its Shannon cover (i.e., its unique minimal, deterministic, irreducible graph presentation). We present an algorithm that, given the Shannon cover G of an irreducible sofic shift X, decides whether or not X is PFT in time that is quadratic in the number of states of G. From any periodic irreducible presentation of a given period, we define a periodic forbidden list, unique up to conjugacy (a circular permutation) for that period, that satisfies certain minimality properties. We show that an irreducible sofic shift is PFT if and only if the list corresponding to its Shannon cover G and its period is finite. Finally, we discuss methods for computing the capacity of a PFT shift from a periodic forbidden list, either by construction of a corresponding graph or in a combinatorial manner directly from the list itself. Index Terms — Shift spaces, sofic system, constrained code, finitetype, capacity of constrained system, periodic constraint. I.