Authors:
Victor Mitrana
1
;
Andrei Păun
2
and
Mihaela Păun
3
Affiliations:
1
Department of Information Systems, Polytechnic University of Madrid, Crta. de Valencia km. 7 - 28031 Madrid, Spain, National Institute for Research and Development of Biological Sciences, Independentei Bd. 296, Bucharest and Romania
;
2
Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest and Romania
;
3
National Institute for Research and Development of Biological Sciences, Independentei Bd. 296, Bucharest and Romania
Keyword(s):
Splicing, Accepting Splicing System, Computational Complexity, Descriptional Complexity, 3-colorability Problem.
Related
Ontology
Subjects/Areas/Topics:
Bioinformatics
;
Biomedical Engineering
;
Biomedical Signal Processing
Abstract:
We define a variant of accepting splicing system that can be used as a problem solver. A condition for halting the computation on a given input as well as a condition for making a decision as soon as the computation has stopped is considered. An algorithm based on this accepting splicing system that solves a well-known NP-complete problem, namely the 3-colorability problem is presented. We discuss an efficient solution in terms of running time and additional resources (axioms, supplementary symbols, number of splicing rules. More precisely, for a given graph with n vertices and m edges, our solution runs in O(nm) time, and needs O(mn2) other resources. Two variants of this algorithm of a reduced time complexity at an exponential increase of the other resources are finally discussed.