Separating some splicing models

Bonizzoni, Paola; Ferretti, Claudio; Mauri, Giancarlo; Zizza, Rosalba

doi:10.1016/s0020-0190(01)00139-9

Cited by 22 publications

(22 citation statements)

References 3 publications

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“…However, for a triplet s = (u 1 , u 2 ; v) where v is not a concatenation of a prefix of u 1 and a suffix of u 2 , there is no quadruplet r that can be used for the same splicings. Moreover, the class of classical splicing languages is strictly included in the class of Pixton splicing languages; e. g., the language L = cx * ae + cx * be + dcx * bef over the alphabet {a, b, c, d, e, f, x} is a Pixton splicing language but not a classical splicing language, see [4]. For the rest of this section we focus on Pixton's splicing variant and by a rule we always mean a triplet.…”

Section: Pixton's Variant Of Splicingmentioning

confidence: 99%

Deciding whether a regular language is generated by a splicing system

Kari

Kopecki

2017

Journal of Computer and System Sciences

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Splicing as a binary word/language operation is inspired by the DNA recombination under the action of restriction enzymes and ligases, and was first introduced by Tom Head in 1987. Shortly thereafter, it was proven that the languages generated by (finite) splicing systems form a proper subclass of the class of regular languages. However, the question of whether or not one can decide if a given regular language is generated by a splicing system remained open. In this paper we give a positive answer to this question. Namely, we prove that, if a language is generated by a splicing system, then it is also generated by a splicing system whose size is a function of the size of the syntactic monoid of the input language, and which can be effectively constructed.

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Section: Pixton's Variant Of Splicingmentioning

confidence: 99%

Deciding whether a regular language is generated by a splicing system

Kari

Kopecki

2017

Journal of Computer and System Sciences

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“…This language has already been considered in [5], where the authors stated that L cannot be generated by a finite Paun splicing system. In the same paper it is proved that L is generated by the finite Pixton We can easily check that S PI is a reflexive splicing system, since each site of a rule in S PI is a constant for L. Indeed, thanks to Lemma 2.1, since a and dc are constants for L, then xa and dcx are also constants for L. In order to see that L is a PI-con-split language, it suffices to set …”

Section: Reflexive Pixton Splicing Languagesmentioning

confidence: 99%

“…When we restrict ourselves to finite splicing systems (i.e., splicing systems S = (A, I, R) with I and R being finite sets), we know that Pixton systems are more powerful than Paun systems, which in turn are more powerful than Head systems. The inclusions between the corresponding classes of languages are strict: there are languages which can be generated by finite Pixton splicing systems but not by finite Paun splicing systems, and there are languages which can be generated by finite Paun splicing systems but not by finite Head splicing systems [5]. Another parameter in the investigation of the computational power of splicing systems is the level in the Chomsky hierarchy I, R belong to.…”

Section: Introductionmentioning

confidence: 99%

The structure of reflexive regular splicing languages via Schützenberger constants

Bonizzoni

Felice

Zizza

2005

Theoretical Computer Science

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The splicing operation was introduced in 1987 by Head as a mathematical model of the recombination of DNA molecules under the influence of restriction and ligases enzymes. This operation allows us to define a computing (language generating) device, called a splicing system. Other variants of this original definition were also proposed by Paun and Pixton respectively. The computational power of splicing systems has been thoroughly investigated. Nevertheless, an interesting problem is still open, namely the characterization of the class of regular languages generated by finite splicing systems. In this paper, we will solve the problem for a special class of finite splicing systems, termed reflexive splicing systems, according to each of the definitions of splicing given by Paun and Pixton. This special class of systems contains, in perticular, finite Head splicing systems. The notion of a constant, given by Schützenberger, once again intervenes.

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“…These are known as Head and Pixton splicing operations, respectively. In [8] it has been shown that splicing systems based on Pixton splicing operation are more powerful than the ones based on the standard (Paun) splicing, and these systems are more powerful than Head splicing systems.…”

Section: Finite Splicing Systemsmentioning

confidence: 99%

Regular splicing languages and subclasses

Bonizzoni

Mauri

2005

Theoretical Computer Science

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Recent developments in the theory of finite splicing systems have revealed surprising connections between long-standing notions in the formal language theory and splicing operation. More precisely, the syntactic monoid and Schützenberger constant have strong interaction with the investigation of regular splicing languages. This paper surveys results of structural characterization of classes of regular splicing languages based on the above two notions and discusses basic questions that motivate further investigations in this field.In particular, we improve the result in [6] that provides a structural characterization of reflexive symmetric splicing languages by showing that it can be extended to the class of all reflexive splicing languages: this is the larger class for which a characterization is known.

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Separating some splicing models

Cited by 22 publications

References 3 publications

Deciding whether a regular language is generated by a splicing system

Deciding whether a regular language is generated by a splicing system

The structure of reflexive regular splicing languages via Schützenberger constants

Regular splicing languages and subclasses

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