Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for complete systems, which are special finite circular splicing systems. We show that a circular language L is generated by a complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by complete systems. We can also decide whether the language generated by a complete system is regular. Finally, we point out that complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule is allowed. From our results on complete systems, it follows that finite simple systems generate a class of context-free languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems

Splicing Systems from Past to Future: Old and New Challenges

A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by P\u{a}un and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other author

1-splicing vs. 2-splicing: separating results

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A multi-objective optimization model for music styles

Style recognition is one of the problems mostly faced by Computational Intelligence techniques. Most of them were defined ad-hoc for a specific music genre and so not generalizable and applicable to any style. A music style, both of soloists performer and of musical collectives, is the result of aesthetic goals, i.e., experience and preferences, functional rules, i.e., rules used to produce music, and external influence, i.e., the choices depending by the simultaneous presence of other musicians. We propose a new model of style, defined in terms of a multi-objective problem, where the objective is to minimize the distance between the style of each musician and the stylistic features derived by other musicians. Such a model is general since it is applicable to any type of style. We also propose a new approach for both recognition and automatic composition of styles based on such a model, which exploits a machine learning recognizer and a splicing composer. To assess the effectiveness and the generalization capability of our system we performed several tests using a large set of Jazz transcriptions and a corpus of 4-voice music by J. S. Bach. We show that our classifier is able to achieve a recognition accuracy of 97.1%. With regard to the composition process, we measured the capability of our system to capture both aesthetic goals by collecting subjective perceptions from domain experts, and functional rules by computing the average percentage of (1) typical harmonic progressions in the Jazz music produced and (2) forbidden exceptions, which occur in the 4-voice music, produced

The structure of reflexive regular splicing languages via Schutzenberger constants

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