Causality in Membrane Systems

Abstract

Summary. P systems are a biologically inspired model introduced by Gheorghe Pȃun with the aim of representing the structure and the functioning of the cell. P systems are usually equipped with the maximal parallelism semantics; however, since their introduction, some alternative semantics have been proposed and investigated.We propose a semantics that describes the causal dependencies occurring between the reactions of a P system. We investigate the basic properties that are satisfied by such a semantics. The notion of causality turns out to be quite relevant for biological systems, as it permits to point out which events occurring in a biological pathway are necessary for another event to happen.

An Overview on Operational Semantics in Membrane Computing

“…It handles maximal parallelism with an exhaustive sequence of applications of evolution rules, and it has been used in [9,10] to study properties of the behaviour of P systems such as divergence and causality of events.…”

“…The SOS approach offers several advantages (see also [1]): it makes easier defining the semantics of a systems in terms of the semantics of its components, it makes easier proving properties of the semantics of a system by induction, and offers the possibility to prove some results on the semantics (such as congruence results for behavioural equivalences) simply by ensuring that the given inference rules satisfy some requirements (or formats). Operational semantics for P systems which follow the SOS approach have been defined in [3,4,12,9,10,7,8] with different aims. In [3,4,12] Andrei, Ciobanu and Lucanu proposed a semantics mainly aimed at developing a provably correct interpreter for P systems.…”

“…In [3,4,12] Andrei, Ciobanu and Lucanu proposed a semantics mainly aimed at developing a provably correct interpreter for P systems. The semantics in [9,10] was defined by Busi to study properties of the behaviour of P systems such as divergence and causality of events. In [7,8] the authors of the present paper have defined a compositional semantics aimed at studying behavioural equivalences for P systems.…”

Compositional semantics and behavioral equivalences for P Systems

“…Operational semantics for P Systems have been proposed in [8,9,11]. In [8] Catalytic P Systems without priorities are considered and their semantics is given as a Well-Structured Transition System.…”

“…The main purpose of the paper is to prove decidability of the divergence problem for the considered variant of P Systems. The semantics of [8] is extended in [9] to describe the causal dependencies occurring between reactions of a P System. In [11] a formal framework is proposed to describe a large number of variants of P Systems.…”