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41
Recent Results In Sturmian Words
, 1996
"... In this survey paper, we present some recent results concerning finite and infinite Sturmian words. We emphasize on the different definitions of Sturmian words, and various subclasses, and give the ways to construct them related to continued fraction expansion. Next, we give properties of special ..."
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Cited by 37 (2 self)
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In this survey paper, we present some recent results concerning finite and infinite Sturmian words. We emphasize on the different definitions of Sturmian words, and various subclasses, and give the ways to construct them related to continued fraction expansion. Next, we give properties of special finite Sturmian words, called standard words. Among these, a decomposition into palindromes, a relation with the periodicity theorem of Fine and Wilf, and the fact that all these words are Lyndon words. Finally, we describe the structure of Sturmian morphisms (i.e. morphisms that preserve Sturmian words) which is now rather well understood. 1 Introduction Combinatorial properties of finite and infinite words are of increasing importance in various fields of physics, biology, mathematics and computer science. Infinite words generated by various devices have been considered [9]. We are interested here in a special family of infinite words, namely Sturmian words. Sturmian words represent...
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 clas ..."
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Cited by 30 (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...
Axel Thue's work on repetitions in words
 Invited Lecture at the 4th Conference on Formal Power Series and Algebraic Combinatorics
, 1992
"... The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched. ..."
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Cited by 22 (3 self)
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The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.
DataOblivious Stream Productivity
 Utrecht University
"... Abstract. We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be obtained. The usual analysis, also adopted here, d ..."
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Cited by 14 (3 self)
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Abstract. We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be obtained. The usual analysis, also adopted here, disregards the identity of data, thus leading to approaches that we call dataoblivious. We present a method that is provably optimal among all such dataoblivious approaches. This means that in order to improve on our algorithm one has to proceed in a dataaware fashion. 3 1
DNA Computing, Sticker Systems, and Universality
 ACTA INFORMATICA
, 1998
"... We introduce the sticker systems, a computability model, which is an abstraction of the computations using the WatsonCrick complementarity as in Adleman's DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hence th ..."
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Cited by 12 (3 self)
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We introduce the sticker systems, a computability model, which is an abstraction of the computations using the WatsonCrick complementarity as in Adleman's DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hence the power of finite automata. One variant is proven to be equivalent to Turing machines. Another one is found to have a strictly intermediate power.
Unavoidable Binary Patterns
 Acta Informatica
, 1993
"... Peter Roth proved that there are no binary patterns of length six or more that are unavoidable on the twoletter alphabet. He gave an almost complete description of unavoidable binary patterns. In this paper we prove one of his conjectures: the pattern ff 2 fi 2 ff is 2avoidable. From this we d ..."
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Cited by 10 (1 self)
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Peter Roth proved that there are no binary patterns of length six or more that are unavoidable on the twoletter alphabet. He gave an almost complete description of unavoidable binary patterns. In this paper we prove one of his conjectures: the pattern ff 2 fi 2 ff is 2avoidable. From this we deduce the complete classification of unavoidable binary patterns. We also study the concept of avoidability by iterated morphisms and prove that there are a few 2avoidable patterns which are not avoided by any iterated morphism. 1 Introduction The concept of unavoidable pattern was introduced by Bean, Ehrenfeucht & McNulty [2] and independently by Zimin [10]. They gave a characterization of unavoidable patterns, but there is still no characterization of kunavoidable patterns, i.e. patterns that are unavoidable over a kletter alphabet. However, we can try to find all kunavoidable patterns that can be written with a given alphabet. The case of unary patterns (in other terms: powers of a ...
Turing, WatsonCrick And Lindenmayer. Aspects Of DNA Complementarity
 In Calude
, 1997
"... WatsonCrick complementarity is one of the very central components of DNA computing, the other central component being the massive parallelism of DNA strands. While the latter component drastically reduces time complexity, the former component is the cause behind the Turing universality of models of ..."
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Cited by 9 (7 self)
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WatsonCrick complementarity is one of the very central components of DNA computing, the other central component being the massive parallelism of DNA strands. While the latter component drastically reduces time complexity, the former component is the cause behind the Turing universality of models of DNA computing. This paper makes this cause explicit and also discusses it in terms of some specific models. Finally, another aspect of complementarity, the operational one, will be discussed in terms of Lindenmayer systems. TUCS Research Group Mathematical Structures of Computer Science 1 Introduction Adleman's successful experiment, [1], demonstrated how standard methods of molecular biology can be used to solve (a small instance of) a computationally intractable problem. The experiment gave immediately rise to considerable optimism concerning the possibilities of DNA computing. For instance, David Gifford wrote, [4], in the issue of Science containing Adleman's original work: "If we a...
String NonInclusion Optimization Problems
"... . For every string inclusion relation there are two optimization problems: nd a longest string included in every string of a given nite language, and nd a shortest string including every string of a given nite language. As an example, the two wellknown pairs of problems, the longest common subst ..."
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Cited by 9 (4 self)
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. For every string inclusion relation there are two optimization problems: nd a longest string included in every string of a given nite language, and nd a shortest string including every string of a given nite language. As an example, the two wellknown pairs of problems, the longest common substring (or subsequence) problem and the shortest common superstring (or supersequence) problem, are interpretations of these two problems. In this paper we consider a class of opposite problems connected with string noninclusion relations: nd a shortest string included in no string of a given nite language and nd a longest string including no string of a given nite language. The predicate \string is not included in string " is interpreted either as \ is not a substring of " or as \ is not a subsequence of ". The main purpose is to determine the complexity status of the string noninclusion optimization problems. Using graph approaches we present polynomialtime algorith...
Towards the Systematic Development of Description Logic Reasoners: CLASP reconstructed
 Proceedings of the Third International Conference on the Principles of Knowledge Representation and Reasoning (KR92
, 1992
"... It is argued that considerable benefits can be obtained by making KR&R systems easily extendable, so that new language constructs can be added on a perapplication basis. In order to achieve this extensibility we need techniques for formally specifying the extensions, and for modularly and locally m ..."
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Cited by 8 (0 self)
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It is argued that considerable benefits can be obtained by making KR&R systems easily extendable, so that new language constructs can be added on a perapplication basis. In order to achieve this extensibility we need techniques for formally specifying the extensions, and for modularly and locally modifying the implementations. We present two such techniques applicable to the family of reasoners based on Description/Terminological Logics, namely natural semantics rules of inference, and the protodl customizable KBMS architecture. The bulk of the paper aims to demonstrate the efficacy of these techniques, together with some heuristics for their use, by showing how we could reconstruct a previously proposed description logic: Devanbu and Litman's extension to classic, called clasp, designed to reason about actions and plans. In the process, we uncover a few deficiencies in the original proposal, and provide for the first time a formal semantics for clasp. 1 Introduction and Aims Knowl...
On RepetitionFree Binary Words of Minimal Density
 Theoretical Computer Science
, 1999
"... We study the minimal proportion (density) of one letter in nth powerfree binary words. First, we introduce and analyse a general notion of minimal letter density for any innite set of words which don't contain a specied set of \prohibited" subwords. We then prove that for nth powerfree binary w ..."
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Cited by 8 (2 self)
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We study the minimal proportion (density) of one letter in nth powerfree binary words. First, we introduce and analyse a general notion of minimal letter density for any innite set of words which don't contain a specied set of \prohibited" subwords. We then prove that for nth powerfree binary words the density function is 1 n + 1 n 3 + 1 n 4 + O( 1 n 5 ). We also consider a generalization of nth powerfree words for fractional powers (exponents): a word is xth powerfree for a real x, if it does not contain subwords of exponent x or more. We study the minimal proportion of one letter in xth powerfree binary words as a function of x and prove, in particular, that this function is discontinuous at 7 3 as well as at all integer points n 3. Finally, we give an estimate of the size of the jumps. Keywords: Unavoidable patterns, powerfree words, exponent, minimal density. 1 Introduction One of classical topics of formal language theory and word combinatorics is th...