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286
COLLISION FREE HASH FUNCTIONS AND PUBLIC KEY SIGNATURE SCHEMES
, 1988
"... In this paper, we present a construction of hash functions. These functions are collision free in the sense that under some cryptographic assumption, it is provably hard for an enemy to find collisions. Assumptions that would be sufficient are the hardness of factoring, of discrete log, or the (poss ..."
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Cited by 108 (1 self)
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In this paper, we present a construction of hash functions. These functions are collision free in the sense that under some cryptographic assumption, it is provably hard for an enemy to find collisions. Assumptions that would be sufficient are the hardness of factoring, of discrete log, or the (possibly) more general assumption about the existence of claw free sets of permutations. The ablllty of a hash function to improve security and speed of a signature scheme is discussed: for example, we can combine the RSAsystem with a collision free hash function based on factoring to get a scheme which is more efficient and much more secure. Also, the effect of combining the GoldwasserMicaliRest signature scheme with one of our functions is studied. In the factoring based implementation of the scheme using a kbit modulus, the signing process can be speeded up by a factor roughly equal to k 0 (logz(k)), while the signature checking process will be faster by a factor of 0 (10g2(k)).
A characterization of substitutive sequences using return words
 DISCRETE MATHEMATICS
, 1998
"... We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here. ..."
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Cited by 84 (11 self)
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We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.
Testing primitivity on partial words.
 Discrete Applied Mathematics,
, 2007
"... Abstract: The study of the combinatorial properties of strings of symbols from a finite alphabet (also referred to as words) is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. In this paper, we examine to which extent some fundamental combinatori ..."
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Cited by 30 (13 self)
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Abstract: The study of the combinatorial properties of strings of symbols from a finite alphabet (also referred to as words) is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. In this paper, we examine to which extent some fundamental combinatorial properties of words, such as conjugacy, remain true for partial words. The motivation behind the notion of a partial word is the comparison of two genes (alignment of two such strings can be viewed as a construction of two partial words that are said to be compatible). This study on partial words was initiated by Berstel and Boasson. Article: Introduction The study of the combinatorial properties of strings of symbols from a finite alphabet is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. The symbols from the alphabet are also referred to as letters and the strings as words. The stimulus for recent works on combinatorics of finite words is the study of molecules such as DNA that play a central role in molecular biology Partial words appear in comparing genes. Indeed, alignment of two strings can be viewed as a construction of two partial words that are compatible in a sense that will be described in Section 3. More precisely, a word of length n over a finite alphabet A is a map from {1, …, n} into A while a partial word of length n over A is a partial map from {1, …, n} into A. In the latter case, elements of {1, …, n} without an image are called holes (a word is just a partial word without holes). In this paper, we extend some fundamental combinatorial properties of words to partial words with an arbitrary number of holes. This study was initiated by Berstel and Boasson [2]. In particular, in Section 4, we extend results which were proved for partial words with a single hole to partial words with an arbitrary number of holes. The definition of special partial word is crucial for these extensions. In Section 5, we extend the important combinatorial property of conjugacy of words to partial words with an arbitrary number of holes by answering a question that was raised. Preliminaries on words This section is devoted to reviewing basic concepts on words. For more information on the matters discussed here, see the book by Lothaire [11] or the Handbook of Formal Languages (Vol. 1, Chapter 6 by Choffrut and
The Nondeterministic Complexity of a Finite Automaton
, 1990
"... We define the nondeterministic complexity of a finite automaton and show that there exist, for any integer p>=1, automata which need \Theta(k^{1/p}) nondeterministic transitions to spell words of length k. This leads to a subdivision of the family of recognizable Msubsets of a free monoid into a ..."
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Cited by 28 (2 self)
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We define the nondeterministic complexity of a finite automaton and show that there exist, for any integer p>=1, automata which need \Theta(k^{1/p}) nondeterministic transitions to spell words of length k. This leads to a subdivision of the family of recognizable Msubsets of a free monoid into a hierarchy whose members are indexed by polynomials, where M denotes the MinPlus semiring.
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 28 (8 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.
Coding properties of DNA languages
 In: Theoretical Computer Science
, 2002
"... The computation language of a DNAbased system consists of all the words (DNA strands) that can appear in any computation step of the system. In this work we define properties of languages which ensure that the words of such languages will not form undesirable bonds when used in DNA computations ..."
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Cited by 27 (14 self)
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The computation language of a DNAbased system consists of all the words (DNA strands) that can appear in any computation step of the system. In this work we define properties of languages which ensure that the words of such languages will not form undesirable bonds when used in DNA computations. We give several characterizations of the desired properties and provide methods for obtaining languages with such properties. The decidability of these properties is addressed as well. As an application we consider splicing systems whose computation language is free of certain undesirable bonds and is generated by nearly optimal commafree codes. 1 Introduction DNA (deoxyribonucleic acid) is found in every cellular organism as the storage medium for genetic information. It is composed of units called nucleotides, distinguished by the chemical group, or base, attached to them. The four bases, are adenine, guanine, cytosine and thymine, abbreviated as A, G, C, and T . (The names of th...
The groups of Richard Thompson and complexity
 International Conference on Semigroups and Groups in honor of the 65th birthday of Prof
, 2004
"... We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C ⋆algebra. For the finitely presented simple group Tfin we show that the wordlengt ..."
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Cited by 27 (10 self)
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We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C ⋆algebra. For the finitely presented simple group Tfin we show that the wordlength and the table size satisfy an n log n relation, just like the symmetric groups. We show that the word problem of Tfin belongs to the parallel complexity class AC 1 (a subclass of P). We show that the generalized word problem of Tfin is undecidable. We study the distortion functions of Tfin and we show that Tfin contains all finite direct products of finitely generated free groups as subgroups with linear distortion. As a consequence, up to polynomial equivalence of functions, the following three sets are the same: the set of distortions of Tfin, the set of all Dehn functions of finitely presented groups, and the set of time complexity functions of nondeterministic Turing machines. 1
State complexity of basic operations on suffixfree regular languages
, 2007
"... We investigate the state complexity of basic operations for suffixfree regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worstcase for the minimal deterministic finitestate automaton that accepts the lan ..."
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Cited by 21 (5 self)
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We investigate the state complexity of basic operations for suffixfree regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worstcase for the minimal deterministic finitestate automaton that accepts the language obtained from the operation. We establish the precise state complexity of catenation, Kleene star, reversal and the Boolean operations for suffixfree regular languages.