# How Complex is to Solve a Hard Problem with Accepting Splicing Systems

### Victor Mitrana, Andrei Păun, Mihaela Păun

#### 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.

Download#### Paper Citation

#### in Harvard Style

Mitrana V., Păun A. and Păun M. (2019). **How Complex is to Solve a Hard Problem with Accepting Splicing Systems**.In *Proceedings of the 4th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,* ISBN 978-989-758-366-7, pages 27-35. DOI: 10.5220/0007715900270035

#### in Bibtex Style

@conference{complexis19,

author={Victor Mitrana and Andrei Păun and Mihaela Păun},

title={How Complex is to Solve a Hard Problem with Accepting Splicing Systems},

booktitle={Proceedings of the 4th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,},

year={2019},

pages={27-35},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007715900270035},

isbn={978-989-758-366-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,

TI - How Complex is to Solve a Hard Problem with Accepting Splicing Systems

SN - 978-989-758-366-7

AU - Mitrana V.

AU - Păun A.

AU - Păun M.

PY - 2019

SP - 27

EP - 35

DO - 10.5220/0007715900270035