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12
The power of commuting with finite sets of words
 In Proc. STACS’05, Springer LNCS 3404
, 2005
"... We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on contextfreeness of maximal solutions of systems of semilinear ine ..."
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Cited by 19 (1 self)
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We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on contextfreeness of maximal solutions of systems of semilinear inequalities. 1
Unification in a Description Logic with Transitive Closure of Roles
, 2001
"... Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL 0 , which allows for conjunction, value restriction, and the top concept only, is already ExpTime comple ..."
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Cited by 13 (4 self)
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Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL 0 , which allows for conjunction, value restriction, and the top concept only, is already ExpTime complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in FL 0 ) is PSpacecomplete in the extended description logic.
Conway's Problem and the commutation of languages
 Bulletin of EATCS
, 2001
"... We survey the known results on two old open problems on commutation of languages. The first problem, raised by Conway in 1971, is asking if the centralizer of a rational language must be rational as well – the centralizer of a language is the largest set of words commuting with that language. The se ..."
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Cited by 8 (5 self)
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We survey the known results on two old open problems on commutation of languages. The first problem, raised by Conway in 1971, is asking if the centralizer of a rational language must be rational as well – the centralizer of a language is the largest set of words commuting with that language. The second problem, proposed by Ratoandromanana in 1989, is asking for a characterization of those languages commuting with a given code – the conjecture is that the commutation with codes may be characterized as in free monoids. We present here simple proofs for the known results on these two problems. 1
Decidability of TrajectoryBased Equations
 Theor. Comp. Sci
, 2003
"... We consider the decidability of existence of solutions to language equations involving the operations of shue and deletion along trajectories. These operations generalize the operations of concatenation, insertion, shue, quotient, sequential and scattered deletion, as well as many others. Our res ..."
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Cited by 8 (2 self)
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We consider the decidability of existence of solutions to language equations involving the operations of shue and deletion along trajectories. These operations generalize the operations of concatenation, insertion, shue, quotient, sequential and scattered deletion, as well as many others. Our results are constructive in the sense that if a solution exists, it can be eectively represented. We show both positive and negative decidability results.
Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
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Cited by 4 (3 self)
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language  the largest set commuting with a language , of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago  asking whether or not the centralizer of any rational language is rational  in the case of periodic, binary, and ternary sets of words, as well as for rational ccodes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an ccode X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.
Aspects of shuffle and deletion on trajectories
, 2005
"... Word and language operations on trajectories provide a general framework for the study of properties of sequential insertion and deletion operations. A trajectory gives a syntactical constraint on the scattered insertion (deletion) of a word into(from) another one, with an intuitive geometrical inte ..."
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Cited by 3 (0 self)
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Word and language operations on trajectories provide a general framework for the study of properties of sequential insertion and deletion operations. A trajectory gives a syntactical constraint on the scattered insertion (deletion) of a word into(from) another one, with an intuitive geometrical interpretation. Moreover, deletion on trajectories is an inverse of the shuffle on trajectories. These operations are a natural generalization of many binary word operations like catenation, quotient, insertion, deletion, shuffle, etc. Besides they were shown to be useful, e.g. in concurrent processes modelling and recently in biocomputing area. We begin with the study of algebraic properties of the deletion on trajectories. Then we focus on three standard decision problems concerning linear language equations with one variable, involving the above mentioned operations. We generalize previous results and obtain a sequence of new ones. Particularly, we characterize the class of binary word operations for which the validity of such a language equation is (un)decidable, for regular and contextfree operands.
Simple language equations
 Bull. Eur. Assoc. Theor. Comput. Sci. EATCS
, 2005
"... Abstract. We survey results, both positive and negative, on regularity of maximal solutions of systems of implicit language equations and inequalities. These results concern inequalities with constant righthand sides, onesided linear inequalities, inequalities with restrictions on constants, and c ..."
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Cited by 3 (1 self)
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Abstract. We survey results, both positive and negative, on regularity of maximal solutions of systems of implicit language equations and inequalities. These results concern inequalities with constant righthand sides, onesided linear inequalities, inequalities with restrictions on constants, and commutation equations and inequalities. In addition, we present some of these results in a generalized form in order to underline common principles. 1.
On the Centralizer of a Finite Set
 IN PROC. OF ICALP 2000, LNCS 1853
, 2000
"... We prove two results on commutation of languages. First, we show that the maximal language commuting with a three element language, i.e. its centralizer, is ..."
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Cited by 3 (2 self)
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We prove two results on commutation of languages. First, we show that the maximal language commuting with a three element language, i.e. its centralizer, is
Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A FORMALISATION OF THE MYHILLNERODE THEOREM BASED ON REGULAR EXPRESSIONS ∗
"... Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is th ..."
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Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Also convenient operations for disjoint unions of graphs, matrices and functions are not easily formalisiable in HOL. In contrast, regular expressions can be defined conveniently as a datatype and a corresponding reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory—the MyhillNerode Theorem—can be recreated using only regular expressions. From this theorem many closure properties of regular languages follow. 1991 Mathematics Subject Classification. 68Q45. 1.
Theoretical Informatics and Applications Will be set by the publisher ON CONJUGACY OF LANGUAGES ∗
"... Abstract. We say that two languages X and Y are conjugates if they satisfy the conjugacy equation XZ = ZY for some language Z. We study several problems associated to this equation. For example, we characterize all sets which are conjugated via a twoelement biprefix set Z, as well as all twoelemen ..."
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Abstract. We say that two languages X and Y are conjugates if they satisfy the conjugacy equation XZ = ZY for some language Z. We study several problems associated to this equation. For example, we characterize all sets which are conjugated via a twoelement biprefix set Z, as well as all twoelement sets which are conjugates. Mathematics Subject Classification. 68R15, 68Q70. 1.