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Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 68 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
On the Expressive Power of Temporal Logic
 J. COMPUT. SYSTEM SCI
, 1993
"... We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective ..."
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Cited by 42 (4 self)
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We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective algorithm to decide whether a given rational language is expressible. Our main result states a similar condition for the "restricted" temporal logic (RTL), obtained by discarding the "until" operator. A formal language is RTLexpressible if and only if its syntactic semigroup is finite and satisfies a certain simple algebraic condition. This leads
A Survey of Arithmetical Definability
, 2002
"... We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions. ..."
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Cited by 2 (0 self)
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We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions.
Bertrand Numeration Systems and Recognizability
, 1995
"... . There exist various wellknown characterizations of sets of numbers recognizable by a finite automaton, when they are represented in some integer base p 2. We show how to modify these characterizations, when integer bases p are replaced by linear numeration systems whose characteristic polynomial ..."
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. There exist various wellknown characterizations of sets of numbers recognizable by a finite automaton, when they are represented in some integer base p 2. We show how to modify these characterizations, when integer bases p are replaced by linear numeration systems whose characteristic polynomial is the minimal polynomial of a Pisot number. We also prove some related interesting properties. 1 Introduction Since the work of [9], sets of integers recognizable by finite automata have been studied in numerous papers. One of the jewels in this topic is the famous Cobham's theorem [11]: the only sets of numbers recognizable by finite automata, independently of the base of representation, are those which are ultimately periodic. Other studies are concerned with computation models equivalent to finite automata in the recognition of sets of integers. The proposed models use firstorder logical formulae [9], uniform substitutions [12], algebraic formal series [10]. We refer the reader to the...
Fax: +810117067680An Efficient Matching Algorithm for Acyclic Regular Expressions with Bounded Depth
, 2010
"... Abstract. In this paper, we study the regular expression matching problem for a subclass of regular expressions of small depth. A regular expression is acyclic if it is over the basis Σ∪{·, }. By extending the SHIFTAND approach by Wu and Manber (JACM 39(2),1992), we present an efficient algorithm ..."
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Abstract. In this paper, we study the regular expression matching problem for a subclass of regular expressions of small depth. A regular expression is acyclic if it is over the basis Σ∪{·, }. By extending the SHIFTAND approach by Wu and Manber (JACM 39(2),1992), we present an efficient algorithm that solves the regular expression matching problem for acyclic regular expressions with length m and depth d and an input text of length n in O(nmd/w) time using O(md) preprocessing and O(md/w) space in words on unitcost RAM model with word length w. When the depth d is constant, typical in real applications, our algorithm runs in O(nm/w) time and O(m/w) space, while the algorithm by Bille (ICALP, 2006) runs in O(nm log w/w) time and O(m log w/w) space. Hence, this achieves O(log m) and O(log w) speedups in small automata (m ≤ w) and in large automata (m> w) cases, resp., still keeping O(m/w) space. 1