Deciding Whether a Regular Language Is Generated by a Splicing System
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.
KeywordsRegular Language Fourth Component Short Word Formal Language Theory Proper Subclass
Unable to display preview. Download preview PDF.
- 8.Goode, E.: Constants and Splicing Systems. PhD thesis, Binghamton University (1999)Google Scholar
- 11.Head, T.: Splicing languages generated with one sided context. In: Păun, G. (ed.) Computing With Bio-molecules: Theory and Experiments, pp. 269–282. Springer (1998)Google Scholar
- 12.Head, T., Pixton, D.: Splicing and Regularity. In: Ésik, Z., Martín-Vide, C., Mitrana, V. (eds.) Recent Advances in Formal Languages and Applications. SCI, pp. 119–147. Springer, Heidelberg (2006)Google Scholar
- 14.Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979)Google Scholar
- 15.Kari, L., Kopecki, S.: Deciding whether a regular language is generated by a splicing system. CoRR, abs/1112.4897 (2011)Google Scholar
- 18.Schützenberger, M.P.: Sur certaines opérations de fermeture dans le langages rationnels. Symposia Mathematica 15, 245–253 (1975)Google Scholar