Linear splicing and syntactic monoid

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

doi:10.1016/j.dam.2005.06.008

Cited by 8 publications

(28 citation statements)

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“…As for Head's result in [13], a relationship exists between reflexive splicing systems and the notion of a constant introduced by Schützenberger [24]. Furthermore, the above-mentioned marker languages are defined in [2] by means of a marker which is a set of constants. This explains why techniques introduced in [2] have been of great use when obtaining the results presented in this paper.…”

Section: Introductionmentioning

confidence: 96%

“…In the same papers, he designed an algorithm that, for a given regular language L and a given finite set of triples X, allows us to decide whether a language I ⊆ L exists such that L is generated by a finite Head splicing system with X being the set of the rules. As another result, in [2,3] the authors introduced a nontrivial class of languages (marker languages) and proved that these languages are generated by finite Paun systems. The authors also proved that we can decide whether a regular language is a marker language [2].…”

Section: Introductionmentioning

confidence: 98%

“…As another result, in [2,3] the authors introduced a nontrivial class of languages (marker languages) and proved that these languages are generated by finite Paun systems. The authors also proved that we can decide whether a regular language is a marker language [2].…”

Section: Introductionmentioning

confidence: 98%

“…Furthermore, the above-mentioned marker languages are defined in [2] by means of a marker which is a set of constants. This explains why techniques introduced in [2] have been of great use when obtaining the results presented in this paper. In addition, since finite Head splicing systems are all reflexive, as a byproduct of the results proved in this paper, we completely solve our main problem, i.e., the characterization of H, when Head's definition of splicing is taken into account (see [4] for further details).…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The structure of reflexive regular splicing languages via Schützenberger constants

Bonizzoni

Felice

Zizza

2005

Theoretical Computer Science

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“…For more details on codes the reader is referred to [1,8,20,24]. In [2], the authors have introduced a special type of regular languages using the syntactic congruence.…”

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confidence: 99%

The syntactic monoid of hairpin-free languages

2007

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The study of hairpin-free words has been initiated in the context of DNA computing. DNA strands that, theoretically speaking, are finite strings over the alphabet {A, G, C, T} are used in DNA computing to encode information. Due to the fact that A is complementary to T and G to C, DNA single strands that are complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: if some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper continues the theoretical study of hairpin-free languages. We study algebraic properties of hairpin-free words and hairpins. We also give a complete characterization of the syntactic monoid of the language consisting of all hairpin-free words over a given alphabet and illustrate it with an example using the DNA alphabet.

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A Decision Procedure for Reflexive Regular Splicing Languages

Bonizzoni

Mauri

2006

Developments in Language Theory

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Linear splicing and syntactic monoid

Cited by 8 publications

References 10 publications

The structure of reflexive regular splicing languages via Schützenberger constants

The structure of reflexive regular splicing languages via Schützenberger constants

The syntactic monoid of hairpin-free languages

A Decision Procedure for Reflexive Regular Splicing Languages

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