13th International Conference on Membrane Computing - MTA Sztaki

<strong>13th</strong> <strong>International</strong> <strong>Conference</strong> on Membrane Computing, CMC13,
Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 455 - 458.
Simplifying Event-B Models of P Systems Using
Functions ∗
Adrian Ţurcanu, Florentin Ipate
Department of Computer Science, University of Pitesti
Abstract
Often modelling P systems in a language associated with a model
checker can be a difficult task due to its large size or the lack of automatic
methods. In this paper we present some initial results concerning the
simplification of Event-B models of P systems using functions, quantifiers
and non-deterministic assignments . We present some general ideas which
we then use to implement two P system models in the Rodin platform.
1 Introduction
Initiated by Gheorghe Păun [4], membrane computing studies computing devices,
called P systems, inspired by the functioning and structure of living cell.
Event-B [1] is a formal modelling language introduced about 10 years ago
by J.R. Abrial, used with a platform called Rodin for developing mathematical
models of complex systems which behave in a discrete fashion.
Event-B models are abstract state machines, made of several components.
Each component can be either a machine or a context. Contexts contain the
static structure of the system: sets, constants and axioms. Machines contain
the dynamic structure of the system: variables, invariants, and events.
An event is a state transition which is specified in terms of guards (necessary
conditions to be enabled) and actions (modifying variables of the machine). An
action might be either deterministic (using the assignment operator “:=”) or
non-deterministic (using the operators “:∈” or“:|”). An expression “x :| P (x)”
means that the variable x receives a value such that the predicate P is true.
The value of x after the assignment is denoted x ′ .
ProB is an animation and model checking tool integrated within the Rodin
platform. Unlike most model checking tools, ProB works on higher-level formalisms
and so it enables a more convenient modelling.
In this paper we propose a simplified way of modelling some P systems
using Event-B components like functions, quantifiers and non-deterministic assignments.
∗ ACKNOWLEDGMENT: This work was partially supported by the strategic grant POS-
DRU 88/1.5/S/52826, Project ID52826 (2009), co-financed by the European Social Fund -
Investing in People, within the Sectoral Operational Programme Human Resources Development
2007-2013 for Adrian Ţurcanu, and by UEFISCDI project MuVeT, code PN-II-ID-PCE-
2011-3-0688, no. 317/26.10.2011 for Florentin Ipate.
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