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.

Computational Properties of Two P Systems Solving the 3-colouring Problem

“…The 3-colouring problem is solved in maximum 2n + 3 steps by a simple kernel P system skΠ(n) given in [3]. We will consider again, only a restricted set of rules and a restricted alphabet that can be easily deduced from the rules.…”

“…COMPUTATIONAL PROPERTIES In [17] and [3] we analyzed the number of cells with the label 2 in different steps of computation for the P system Π(n) and respectively skΠ(n). In this section we will give, by comparison, some of their computational properties related to the number of symbols corresponding to the colours at different steps of the computation.…”

“…Many variants of P systems have been introduced and one of the most studied theoretical aspect about them is their capability to solve hard problems like NP-complete ones by a space-time trade-off. Introduced this year in [2], kernel P systems (kP systems), and its reduced variant [3] (skP systems) represent an unifying framework for P systems which integrates many features of existing P system variants into an elegant and yet powerful modeling formalism.…”

Foreword

“…Some papers deal with 'classic' theoretical issues, such as the power of symport-antiport systems [2] or the efficiency of cell division in solving hard problems [8], others deal with intricate ways of organizing the computation, such as the role of the clock [5] and the control of evolution by means of energy quanta associated with the rules [1]. Two papers propose new formalizations of P systems [3] or prove the usefulness of such new formalizations, specifically, of the recently introduced kernel P systems [4]. One paper is devoted to spiking neural P systems, a class of computer devices inspired from the brain organization and the way neurons cooperate by means of spikes [6].…”

An Integrated Model Checking Toolset for Kernel P Systems

“…The newly defined concept of kernel P systems (kP systems) has been introduced in order to provide a theoretical support for this language. A revised version of the model and the specification language can be found in [12] and its usage to specify the 3-colouring problem and a comparison to another solution provided in a similar context [8], is described in [14]. The kP systems have been also used to specify and analyse, through formal verification, synthetic biology systems, e.g.…”