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Domain mu-calculus

Guo-Qiang Zhang (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The basic framework of domain μ -calculus was formulated in [39] more than ten years ago. This paper provides an improved formulation of a fragment of the μ -calculus without function space or powerdomain constructions, and studies some open problems related to this μ -calculus such as decidability and expressive power. A class of language equations is introduced for encoding μ -formulas in order to derive results related to decidability and expressive power of non-trivial fragments of the domain μ -calculus....

Domain mu-calculus

Guo-Qiang Zhang (2010)

RAIRO - Theoretical Informatics and Applications

The basic framework of domain μ-calculus was formulated in [39] more than ten years ago. This paper provides an improved formulation of a fragment of the μ-calculus without function space or powerdomain constructions, and studies some open problems related to this μ-calculus such as decidability and expressive power. A class of language equations is introduced for encoding μ-formulas in order to derive results related to decidability and expressive power of non-trivial fragments of the domain...

Dynamic programming for reduced NFAs for approximate string and sequence matching

Jan Holub (2002)

Kybernetika

searching for all occurrences of a pattern (string or sequence) in some text, where the pattern can occur with some limited number of errors given by edit distance. Several methods were designed for the approximate string matching that simulate nondeterministic finite automata (NFA) constructed for this problem. This paper presents reduced NFAs for the approximate string matching usable in case, when we are interested only in occurrences having edit distance less than or equal to a given integer,...

Dynamical directions in numeration

Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner (2006)

Annales de l’institut Fourier

This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to β -numeration and its generalisations, abstract numeration systems and...

Efficiency of automata in semi-commutation verification techniques

Gérard Cécé, Pierre-Cyrille Héam, Yann Mainier (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Computing the image of a regular language by the transitive closure of a relation is a central question in regular model checking. In a recent paper Bouajjani et al. [IEEE Comput. Soc. (2001) 399–408] proved that the class of regular languages L – called APC – of the form ∪ j L 0 ...

Efficiency of automata in semi-commutation verification techniques

Gérard Cécé, Pierre-Cyrille Héam, Yann Mainier (2007)

RAIRO - Theoretical Informatics and Applications

Computing the image of a regular language by the transitive closure of a relation is a central question in regular model checking. In a recent paper Bouajjani et al. [IEEE Comput. Soc. (2001) 399–408] proved that the class of regular languages L – called APC – of the form UjL0,jL1,jL2,j...Lkj,j, where the union is finite and each Li,j is either a single symbol or a language of the form B* with B a subset of the alphabet, is closed under all semi-commutation relations R. Moreover a recursive...

Efficient simulation of synchronous systems by multi-speed systems

Tomasz Jurdziński, Mirosław Kutyłowski, Jan Zatopiański (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider systems consisting of finite automata communicating by exchanging messages and working on the same read-only data. We investigate the situation in which the automata work with constant but different speeds. We assume furthermore that the automata are not aware of the speeds and they cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata. Complexity measure that we consider here is the number...

Efficient simulation of synchronous systems by multi-speed systems

Tomasz Jurdziński, Mirosław Kutyłowski, Jan Zatopiański (2010)

RAIRO - Theoretical Informatics and Applications

We consider systems consisting of finite automata communicating by exchanging messages and working on the same read-only data. We investigate the situation in which the automata work with constant but different speeds. We assume furthermore that the automata are not aware of the speeds and they cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata. Complexity measure that we consider here is the...

Efficient validation and construction of border arrays and validation of string matching automata

Jean-Pierre Duval, Thierry Lecroq, Arnaud Lefebvre (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We present an on-line linear time and space algorithm to check if an integer array f is the border array of at least one string w built on a bounded or unbounded size alphabet Σ . First of all, we show a bijection between the border array of a string w and the skeleton of the DFA recognizing Σ * w , called a string matching automaton (SMA). Different strings can have the same border array but the originality of the presented method is that the correspondence between a border array and a skeleton of SMA...

Efficient validation and construction of border arrays and validation of string matching automata

Jean-Pierre Duval, Thierry Lecroq, Arnaud Lefebvre (2008)

RAIRO - Theoretical Informatics and Applications

We present an on-line linear time and space algorithm to check if an integer array f is the border array of at least one string w built on a bounded or unbounded size alphabet Σ. First of all, we show a bijection between the border array of a string w and the skeleton of the DFA recognizing Σ*ω, called a string matching automaton (SMA). Different strings can have the same border array but the originality of the presented method is that the correspondence between a border array and a...

Efficient weighted expressions conversion

Faissal Ouardi, Djelloul Ziadi (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε -free nondeterministic finite automaton having O ( n ) states and O ( n log 2 ( n ) ) transitions. This method has been implemented efficiently in O ( n log 2 ( n ) ) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O ( n log 2 ( n ) ) time.

Efficient weighted expressions conversion

Faissal Ouardi, Djelloul Ziadi (2007)

RAIRO - Theoretical Informatics and Applications

J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε-free nondeterministic finite automaton having O(n) states and O(nlog2(n)) transitions. This method has been implemented efficiently in O(nlog2(n)) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O(nlog2(n)) time.

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