Splicing semigroups of dominoes and DNA

Čulík, Karel; Harju, Tero

doi:10.1016/0166-218x(91)90054-z

Cited by 110 publications

(46 citation statements)

References 3 publications

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“…Note that L(I, R) is the smallest language which is closed under the splicing operator σ R and includes I. It is known that the language generated by a splicing system is regular, see [6,17]. A (regular) language L is called a splicing language if a splicing system (I, R) exists such that L = L(I, R).…”

Section: The Case Of Classical Splicingmentioning

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%

“…In this paper, by a splicing system we always mean a finite splicing system. Shortly after the introduction of splicing in formal language theory, Culik II and Harju [6] proved that splicing systems generate regular languages, only; see also [12,17]. Gatterdam [7] gave (aa)…”

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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“…An important result in splicing theory is the so-called Regularity Preserving Lemma proved first in [5], as a consequence of a more general result, and then in [19] by a direct argument. It states that GenS with a finite set of rules and a finite initial language, i.e.…”

Section: Word W E L(h) Is a Proper Word Of L(h) If It Is Generated Imentioning

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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“…An important result in splicing theory is the so-called Regularity Preserving Lemma proved first in [4], as a consequence of a more general result, and then in [16] by a direct argument. It states that GenSS with a finite set of rules and a finite initial language, i.e.…”

Section: ¿(Genss)mentioning

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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Splicing semigroups of dominoes and DNA

Cited by 110 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

Accepting splicing systems with permitting and forbidding words

Splicing Systems: Accepting Versus Generating

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