State Complexity of Simple Splicing

Kari, Lila; Ng, Timothy

doi:10.1007/978-3-030-23247-4_15

Cited by 3 publications

(13 citation statements)

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“…We will show in the following that this is necessary. This is in contrast to the lower bound witness for (1,3)-semi-simple systems from [9], which requires only three letters. We also note that the initial language used for this witness is the same as that for (1,3)-simple splicing systems from [9].…”

Section: ⊓ ⊔contrasting

confidence: 57%

“…To conclude this section, we observe, as noted in Section 4, that when the visible site is 4, as in (1,4)-and (2,4)-splicing systems, lower bound witnesses with finite initial languages must be defined over an alphabet that grows exponentially with the number of states in order to reach the upper bound. This is in contrast to (2,3)-semi-simple splicing systems, as in Section 5 and (1,3)semi-simple splicing systems, studied in [9]. In both of these cases, lower bound witnesses with a fixed size alphabet sufficed.…”

Section: ⊓ ⊔mentioning

confidence: 81%

“…We have studied the state complexity of several variants of semi-simple splicing systems. Our results are summarized in Table 1 and we include the state complexity of (1,3)-semi-simple and (1,3)-simple splicing systems from [9] for comparison. We observe that for all variants of semi-simple splicing systems, the state complexity bounds for splicing systems with regular initial languages are reached with simple splicing witnesses defined over a three-letter alphabet.…”

Section: Discussionmentioning

confidence: 99%

“…For simple splicing systems with finite initial languages, since (1,3)-and (2,4)-simple splicing systems are equivalent, the bound is reached by the same witness from [9]. The witness for (2,3)-simple splicing systems with a finite initial language is defined over a fixed alphabet of size 7, while the problem remains open for (1,4)-simple splicing systems.…”

Section: Discussionmentioning

confidence: 99%

“…It was also shown in [9] that if the initial language is finite, this upper bound is not reachable for (1,3)-simple and (1,3)-semi-simple splicing systems. This result holds for all variants of semi-simple splicing systems and the proof is exactly the same as in [9]. We state the result for semi-simple splicing systems and include the proof for completeness.…”

Section: Proposition 2 ([9]mentioning

confidence: 99%

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Descriptional Complexity of Semi-Simple Splicing Systems

Kari¹,

Ng²

2019

Preprint

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Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the "splicing operation", a cut-and-paste binary string operation defined by a set of "splicing rules" r = (α1, α2; α3, α4) where α1, α2, α3, α4 are words over an alphabet Σ. For two strings x = x1α1α2x2 and y = y1α3α4y2, applying the splicing rule r produces the string z = x1α1α4y2. In this paper we focus on a particular type of splicing systems, called (i, j) semi-simple splicing systems, i = 1, 2 and j = 3, 4, wherein all splicing rules have the property that the two strings in positions i and j are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called "axiom set", by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.1 Simple splicing language classes are pairwise incomparable except for the pair (1,3) and (2,4), which are equivalent [11]

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Section: ⊓ ⊔contrasting

confidence: 57%

Section: ⊓ ⊔mentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Proposition 2 ([9]mentioning

confidence: 99%

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Descriptional Complexity of Semi-Simple Splicing Systems

Kari¹,

Ng²

2019

Preprint

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Descriptional Complexity of Semi-simple Splicing Systems

Kari

2020

Developments in Language Theory

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Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the "splicing operation", a cut-and-paste binary string operation defined by a set of "splicing rules", quadruples r = (u1, u2; u3, u4) where u1, u2, u3, u4 are words over an alphabet Σ. For two strings x1u1u2y1 and x2u3u4y2, applying the splicing rule r produces the string x1u1u4y2. In this paper we focus on a particular type of splicing systems, called (i, j) semi-simple splicing systems, i = 1, 2 and j = 3, 4, wherein all splicing rules r have the property that the two strings in positions i and j in r are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called "axiom set", by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.

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Descriptional Complexity of Semi-Simple Splicing Systems

Kari

2021

Int. J. Found. Comput. Sci.

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Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the “splicing operation”, a cut-and-paste binary string operation defined by a set of “splicing rules”, quadruples [Formula: see text] where [Formula: see text] are words over an alphabet [Formula: see text]. For two strings [Formula: see text] and [Formula: see text], applying the splicing rule [Formula: see text] produces the string [Formula: see text]. In this paper we focus on a particular type of splicing systems, called [Formula: see text] semi-simple splicing systems, [Formula: see text] and [Formula: see text], wherein all splicing rules [Formula: see text] have the property that the two strings in positions [Formula: see text] and [Formula: see text] in [Formula: see text] are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called “axiom set”, by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.

show abstract

State Complexity of Simple Splicing

Cited by 3 publications

References 18 publications

Descriptional Complexity of Semi-Simple Splicing Systems

Descriptional Complexity of Semi-Simple Splicing Systems

Descriptional Complexity of Semi-simple Splicing Systems

Descriptional Complexity of Semi-Simple Splicing Systems

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