3-Col problem modelling using simple kernel P systems

Abstract

This paper presents the newly introduced class of (simple) kernel P systems ((s)kP systems) and investigates through a 3-colouring problem case study the expressive power and efficiency of kernel P systems. It describes two skP systems that model the problem and analyses them in terms of efficiency and complexity. The skP models prove to be more succinct (in terms of number of rules, objects, number of cells and execution steps) than the corresponding tissue P system, available in the literature, that solves the same problem, at the expense of a greater length of the rules.

Keywords:

• membrane computing
• tissue P systems
• kernel P systems
• 3-colour problem
• formal verification

2010 AMS Subject Classifications:

• 68Q05
• 68Q10
• 68Q19
• 68Q45
• 68Q60

Acknowledgements

The authors thank the anonymous reviewers for their constructive comments and useful suggestions that significantly helped improving this paper. The work of FI, MG and RL was supported by a grant of the Romanian National Authority for Scientific Research, CNCS–UEFISCDI, project number PN-II-ID-PCE-2011-3-0688. The authors MPJ, LVC and MGQ acknowledge the support of the project TIN2009–13192 of the Ministerio de Ciencia e Innovación of Spain, cofinanced by FEDER funds, and the support of the Project of Excellence with Investigador de Reconocida Valía of the Junta de Andalucía, grant P08-TIC-04200. The author MGQ also acknowledges the support from the National FPU Grant Programme from the Spanish Ministry of Education.