Compositional semantics and behavioral equivalences for P Systems

Abstract

The aim of the paper is to give a compositional semantics in the style of the Structural Operational Semantics (SOS) and to study behavioral equivalence notions for P Systems. Firstly, we consider P Systems with maximal parallelism and without priorities. We define a process algebra, called P Algebra, whose terms model membranes, we equip the algebra with a Labeled Transition System (LTS) obtained through SOS transition rules, and we study how some equivalence notions defined over the LTS model apply in our case. Then, we consider P Systems with priorities and extend the introduced framework to deal with them. We prove that our compositional semantics reflects correctly maximal parallelism and priorities

An Overview on Operational Semantics in Membrane Computing

“…In this section we compare the operational semantics proposed in [4,7,9], adapted here to describe P systems defined as follows.…”

“…In subsections 3.1, 3.2 and 3.3 we recall the definitions of the semantics proposed in [9], [4] and [7], respectively. For reasons of space limitations we give only a brief description (by exploiting the toy example Π toy ) of the inference rules of the three semantics.…”

“…Configurations in this semantics (see [7]) are given by terms of an algebra, called P algebra. The abstract syntax of the P algebra is defined as follows.…”

“…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.…”

“…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. In [6] the latter semantics has also been used to define a notion of diagnosability for biological systems inspired by some notions from systems security.…”