The structure of reflexive regular splicing languages via Schützenberger constants

Bonizzoni, Paola; Felice, Clelia De; Zizza, Rosalba

doi:10.1016/j.tcs.2004.12.033

Cited by 23 publications

(44 citation statements)

References 17 publications

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“…This is the most commonly used definition for splicing in formal language theory. The notation we use has been employed in previous papers, see e. g., [2,9]. Throughout this section, a quadruplet of words…”

Section: The Case Of Classical Splicingmentioning

confidence: 99%

“…All investigations to date indicate that the class S does not coincide with another naturally defined language class. A characterization of reflexive splicing systems using Schützenberger constants has been given by Bonizzoni, de Felice, and Zizza [1][2][3]. A splicing system is reflexive if for all rules (u 1 , v 1 ; u 2 , v 2 ) in the system we have that (u 1 , v 1 ; u 1 , v 1 ) and (u 2 , v 2 ; u 2 , v 2 ) are rules in the system, too.…”

Section: Introductionmentioning

confidence: 99%

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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: The Case Of Classical Splicingmentioning

confidence: 99%

Section: Introductionmentioning

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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“…More precisely, not all regular languages can be generated by splicing and a characterization of the class of regular splicing languages is still unknown. This open question is related to several challenging issues concerning splicing theory and formal language theory that motivate a continuous development of the research in this direction [12,6]. Several progress have been made in the investigation of the generative power of finite splicing systems.…”

Section: Introductionmentioning

confidence: 99%

“…The first characterization of reflexive symmetric splicing languages has been given in [6] by using the concept of constant, introduced by Schützenberger [24]. Every language L in this class is constructed from a finite set of constants for L, as L is expressed by a finite union of constant languages and split languages, where a split language is a language obtained by a single iteration of a splicing operation over constant languages.…”

Section: Introductionmentioning

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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“…Intensive studies on linear splicing systems and variants have been carried out, in a formal language framework, aimed at proving the universality of splicing systems or closure properties of splicing languages generated under different restrictions on I and/or R [3,13,15,16,17]. While there have been many articles on linear splicing, relatively few works on circular splicing systems have been published.…”

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confidence: 99%

Marked Systems and Circular Splicing

Felice

Fici

Zizza

2007

Fundamentals of Computation Theory

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In 1987 Head introduced a new operation on strings, called splicing, as a formal model of certain cut and paste biochemical transformation processes of an initial collection of DNA strands under the simultaneous influence of enzymes [11]. Two strands of DNA are cut at specified substrings (sites) by restriction enzymes that recognize a pattern inside the molecule and then the fragments are pasted by ligase enzymes. Since 1987, his basic idea has been formalized in terms of generative mechanisms for formal languages, called splicing systems or, more recently, H systems. An H system is defined by giving an initial language I (initial set of DNA molecules) and a set of special words or rules R (enzymes). The set I is then transformed by repeated applications of the splicing operation. DNA occurs in both linear and circular form and, correspondingly, there are three definitions of linear splicing systems and three definitions of circular splicing systems, given by Head, Paun and Pixton respectively. Circular splicing deals with circular strings, a notion which has been intensively examined in formal language theory (see [1,2,9,14,19]). We recall that for a given word w ∈ A * , a circular word ∼ w is the equivalence class of w with respect to the conjugacy relation ∼ defined by xy ∼ yx, for x, y ∈ A * (see [14]). Let ∼ A * be the set of all circular words over A, i.e., the quotient of A * with respect to ∼. A subset C of ∼ A * is a circular language and every language L ⊆ A * such that ∼ L = { ∼ w | w ∈ L} = C is a linearization of C. Therefore, a circular language C is a regular (resp. context-free) circular language if C has a regular (resp. context-free) linearization [13]. We set Reg ∼ = {C ⊆ ∼ A * | ∃L ∈ Reg : ∼ L = C}. Our results deal with Paun circular splicing systems, defined below.Paun's definition [13,18]. A Paun circular splicing system is a triple SC P A = (A, I, R), where A is a finite alphabet, I is the initial circular language, with I ⊆ ∼ A * and R is the (finite) set of rules, with R ⊆ A * #A * $A * #A * and #, $ ∈ A. Then, given a rule r = u 1 #u 2 $u 3 #u 4 and two circular words ∼ u 2 hu 1 , ∼ u 4 ku 3 , the rule r cuts and linearizes the two circular strings, obtaining u 2 hu 1 , u 4 ku 3 , pastes them and circularizes, obtaining ∼ u 2 hu 1 u 4 ku 3 . We say that * Proceedings of the conference Automata: from Mathematics to Applications (AutoMathA 2007). Partially supported by MIUR Project "Automi e Linguaggi Formali: aspetti matematici e applicativi" (2005), by 60% Project "Linguaggi formali e codici: problemi classici e modelli innovativi" (University of Salerno, 2005) and by 60% Project "Linguaggi formali e codici a lunghezza variabile: proprietà strutturali e nuovi modelli di rappresentazione" (University of Salerno, 2006).

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The structure of reflexive regular splicing languages via Schützenberger constants

Cited by 23 publications

References 17 publications

Deciding whether a regular language is generated by a splicing system

Deciding whether a regular language is generated by a splicing system

Regular splicing languages and subclasses

Marked Systems and Circular Splicing

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