Regular splicing languages and subclasses

Bonizzoni, Paola; Mauri, Giancarlo

doi:10.1016/j.tcs.2005.03.035

Cited by 17 publications

(11 citation statements)

References 16 publications

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“…Relations between the computational power of splicing systems with 2-splicing and splicing systems with 1-splicing can be found in [20] (see also [25] for other results in this framework). An extension of the main result of this paper for splicing systems with 1-splicing can be found in a forthcoming paper [6]. Given a splicing system S PA = (A, I, R), let us consider a rule r = u 1 #u 2 $u 3 #u 4 ∈ R. Clearly r may be considered a word, so the reverse r R = u R 4 #u R 3 $u R 2 #u R 1 of r may also be defined.…”

Section: Linear Splicingmentioning

confidence: 84%

“…Another minor difference is that in this paper we have adopted the original definition of splicing operation given by Paun, where two words are generated by a splicing rule (2-splicing), whereas the definition in [9,10] assumes that only one word is produced by the application of a rule (1-splicing) (see Section 2.3 for the definitions). An extension of the main result of this paper to splicing languages generated by 1-splicing can be found in a forthcoming paper [6].…”

Section: Introductionmentioning

confidence: 88%

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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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Section: Linear Splicingmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 88%

The structure of reflexive regular splicing languages via Schützenberger constants

Bonizzoni

Felice

Zizza

2005

Theoretical Computer Science

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“…Several other works like [2], and the references therein, address two fundamental questions concerning splicing systems: recognition, which asks for an algorithm able to decide whether or not a given regular language is a splicing language, and synthesis, which asks for an effective procedure to construct a splicing system able to generate a given splicing language.…”

Section: Introductionmentioning

confidence: 99%

Accepting splicing systems with permitting and forbidding words

et al. 2012

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In this paper we propose a generalization of the accepting splicing systems introduced in Mitrana et al. (Theor Comput Sci 411:2414-2422, 2010. More precisely, the input word is accepted as soon as a permitting word is obtained provided that no forbidding word has been obtained so far, otherwise it is rejected. Note that in the new variant of accepting splicing system the input word is rejected if either no permitting word is ever generated (like in Mitrana et al. in Theor Comput Sci 411:2414-2422, 2010 or a forbidding word has been generated and no permitting word had been generated before. We investigate the computational power of the new variants of accepting splicing systems and the interrelationships among them. We show that the new condition strictly increases the computational power of accepting splicing systems. Although there are regular languages that cannot be accepted by any of the splicing systems considered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of (extended) finite splicing systems without additional restrictions. We also show that the smallest class of languages out of the four classes defined by accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediately derived from the proof of this result.

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“…Several other works like [1], and the references therein, address two fundamental questions concerning splicing systems: recognition, which asks for an algorithm able to decide whether or not a given regular language is a splicing language, and synthesis, which asks for an effective procedure to construct a splicing system able to generate a given splicing language.…”

Section: Introductionmentioning

confidence: 99%

Splicing Systems: Accepting Versus Generating

Castellanos

Mitrana

Santos

2011

Models of Computation in Context

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Abstract. In this paper we propose a condition for rejecting the input word by an accepting splicing system which is defined by a finite set of forbidding words. More precisely, the input word is accepted as soon as a permitting word is obtained provided that no forbidding word has been obtained so far, otherwise it is rejected. Note that in the new variant of accepting splicing system the input word can be rejected if either no permitting word is ever generated (like in [10]) or a forbidding word has been generated and no permitting word had been generated before. We investigate the computational power of the new variants of accepting splicing systems. We show that the new condition strictly increases the computational power of accepting splicing systems. Rather surprisingly, accepting splicing systems considered here can accept non-regular languages, a situation that has never occurred in the case of (extended) finite splicing systems without additional restrictions.

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Regular splicing languages and subclasses

Cited by 17 publications

References 16 publications

The structure of reflexive regular splicing languages via Schützenberger constants

The structure of reflexive regular splicing languages via Schützenberger constants

Accepting splicing systems with permitting and forbidding words

Splicing Systems: Accepting Versus Generating

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