On aperiodic trace languages

Guaiana, Giovanna; Restivo, Antonio; Salemi, Sergio

doi:10.1007/bfb0020789

Cited by 9 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, we use a result from [9] stating that N is a finite union of Cartesian products of l ultimately periodic sets of naturals with periods in {0, 1} iff N is a star-free subset of N l , ie N can be obtained from finite subsets of N l using sum + and Boolean operations (union, intersection, complement). Finally, we can conclude using that (N l , +) is isomorphic to (M(A), ) and that over commutative monoids, star-free languages are precisely the recognizable and aperiodic ones [10].…”

Section: Sketch Of Proofmentioning

confidence: 91%

Automata and Logics for Unranked and Unordered Trees

Boneva

Talbot

2005

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. In this paper, we consider the monadic second order logic (MSO) and two of its extensions, namely Counting MSO (CMSO) and Presburger MSO (PMSO), interpreted over unranked and unordered trees. We survey classes of tree automata introduced for the logics PMSO and CMSO as well as other related formalisms; we gather results from the literature and sometimes clarify or fill the remaining gaps between those various formalisms. Finally, we complete our study by adapting these classes of automata for capturing precisely the expressiveness of the logic MSO.

show abstract

Section: Sketch Of Proofmentioning

confidence: 91%

Automata and Logics for Unranked and Unordered Trees

Boneva

Talbot

2005

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Syntactic characterizations are known for J [39] and for Pol(J ) [35]. The following theorem summarises the results of Guaiana, Restivo and Salemi [20,21], Bouajjani, Muscholl and Touili [2,3] and Cécé, Héam and Mainier [9,10].…”

Section: The Second Problemmentioning

confidence: 63%

“…The closure of a regular language under commutation or partial commutation has been extensively studied [37,25,1,17,18,19], notably in connection with regular model checking [2,3,9,10] or in the study of Mazurkiewicz traces, one of the models of parallelism [20,21,26,27,28,29,38]. We refer the reader to the book [16] and to the survey [15] for further references.…”

mentioning

confidence: 99%

Regular languages and partial commutations

Cano

Guaiana

2013

Information and Computation

View full text Add to dashboard Cite

The closure of a regular language under a [partial] commutation I has been extensively studied. We present new advances on two problems of this area: (1) When is the closure of a regular language under [partial] commutation still regular? (2) Are there any robust classes of languages closed under [partial] commutation? We show that the class Pol(G) of polynomials of group languages is closed under commutation, and under partial commutation when the complement of I in A 2 is a transitive relation. We also give a sufficient graph theoretic condition on I to ensure that the closure of a language of Pol(G) under I-commutation is regular. We exhibit a very robust class of languages W which is closed under commutation. This class contains Pol(G), is decidable and can be defined as the largest positive variety of languages not containing (ab) * . It is also closed under intersection, union, shuffle, concatenation, quotients, lengthdecreasing morphisms and inverses of morphisms. If I is transitive, we show that the closure of a language of W under I-commutation is regular. The proofs are nontrivial and combine several advanced techniques, including combinatorial Ramsey type arguments, algebraic properties of the syntactic monoid, finiteness conditions on semigroups and properties of insertion systems.The closure of a regular language under commutation or partial commutation has been extensively studied [37,25, 1,17,18,19], notably in connection with regular model checking [2, 3,9,10] or in the study of Mazurkiewicz traces, one of the models of parallelism [20,21,26,27,28,29,38]. We refer the reader to the book [16] and to the survey [15] for further references.In this paper, we present new advances on two problems of this area. The first problem is well-known and has a very precise statement. The second problem is more elusive, since it relies on the somewhat imprecise notion of robust class. By a robust class, we mean a class of regular languages closed under some of the usual operations on languages, such as Boolean operations, product, star, shuffle, morphisms, inverses of morphisms, quotients, etc. For instance, regular languages form a very robust class, commutative languages (languages whose syntactic monoid is commutative) also form a robust class. Finally, group languages (languages whose syntactic monoid is a finite group) form a semi-robust

show abstract

“…These languages are also called APC (Alphabetic Pattern Constraints) in [2], (4) the class Pol(Com) of polynomials of commutative languages. The following theorem summarises the results of Guaiana, Restivo and Salemi [14,15], Bouajjani, Muscholl and Touili [2,3] and Cécé, Héam and Mainier [7]. Theorem 1.2 Let I be any independence relation.…”

Section: The Second Problemmentioning

confidence: 85%

“…The closure of a regular language under commutation or partial commutation has been extensively studied [1,11,12,13], notably in connection with regular model checking [2,3,7] or in the study of Mazurkiewicz traces, one of the models of parallelism [14,15,16,22]. We refer the reader to the survey [10,9] or to the recent articles of Ochmański [17,18,19] for further references.…”

mentioning

confidence: 99%

When Does Partial Commutative Closure Preserve Regularity?

Gómez

Guaiana

2008

Automata, Languages and Programming

View full text Add to dashboard Cite

The closure of a regular language under commutation or partial commutation has been extensively studied [1,11,12,13], notably in connection with regular model checking [2,3,7] or in the study of Mazurkiewicz traces, one of the models of parallelism [14,15,16,22]. We refer the reader to the survey [10,9] or to the recent articles of Ochmański [17,18,19] for further references.In this paper, we present new advances on two problems of this area. The first problem is well-known and has a very precise statement. The second problem is more elusive, since it relies on the somewhat imprecise notion of robust class. By a robust class, we mean a class of regular languages closed under some of the usual operations on languages, such as Boolean operations, product, star, shuffle, morphisms, inverses of morphisms, residuals, etc. For instance, regular languages form a very robust class, commutative languages (languages whose syntactic monoid is commutative) also form a robust class. Finally, group languages (languages whose syntactic monoid is a finite group) form a semi-robust class: they are closed under Boolean operation, residuals and inverses of morphisms, but not under product, shuffle, morphisms or star.Here are the two problems: The classes considered in this paper are all closed under polynomial operations. Recall that, given a class L of regular languages, the polynomial languages of L are the finite unions of languages of the form L 0 a 1 L 1 · · · a k L k where a 1 , . . . , a k are letters and L 0 , . . . , L k are languages of L. Taking the polynomial closure usually increase robustness. For instance, the class Pol(G) of polynomials of group languages is closed under union, intersection, quotients, product, shuffle and inverses of morphisms. Let I be a partial commutation and let D be its complement in A × A. Our main results on Problems 1 and 2 can be summarized as follows:

show abstract

On aperiodic trace languages

Cited by 9 publications

References 4 publications

Automata and Logics for Unranked and Unordered Trees

Automata and Logics for Unranked and Unordered Trees

Regular languages and partial commutations

When Does Partial Commutative Closure Preserve Regularity?

Contact Info

Product

Resources

About