Complexity of LTL Model-Checking for Safe Object Nets

Abstract

In this paper we present recently obtained results from [14] concerning the complexity of LTL model checking of safe Elementary Object Nets (Eos) in a novel and more algorithmic oriented way.Object nets are Petri nets which have Petri nets as tokens -an approach known as the nets-within-nets paradigm. Object nets are called elementary if the net system has a two levelled structure. Due to these two modelling levels object nets are very suited to model the mobility of e.g. active objects or agents. The well known p/t nets can be viewed as a special case of Eos.For p/t nets the concept of safeness means that there is at most one token on each place. Since object nets have nested markings there are different possibilities to generalise this idea for Eos. In this paper we concentrate on the variant of Eos safeness that guarantees the finiteness of state spaces and show that for safe Eos the LTL model checking problem is PSpace-complete. Model Checking for Object NetsIn the following we investigate the analysis of object nets using temporal logics. Object nets are Petri nets which have Petri nets as tokens -an approach which is called the nets-within-nets paradigm, proposed by Valk [22,24] for a two levelled structure and generalised in [11,12] for arbitrary nesting structures.1 The Petri nets that are used as tokens are called net-tokens. Net-tokens are tokens with internal structure and inner activity. Due to these two modelling levels object nets are very suited to model the mobility of active objects or agents (cf.[9] and [10]).In [12,8] we studied decidability properties of unbounded object nets. In this paper we repeat very recent results from [14] concerning bounded object nets and present them in a novel way. In particular we repeat the formalism of (safe) elementary object nets and sharpen the definitions in some points. We then prove that checking if a safe Eos satisfies a property expressed in LTL is PSpace-complete. This was first proved in [14]. We recapitulate the proof here, but take a more algorithmic oriented point of view and thus make the proof more elegant and easier to follow in several places. Throughout this paper we stress the relevance of the presented modelling formalism for the modelling of mobile objects and agents.The paper has the following structure: In Section 2 elementary object systems (Eos) are defined. In section 3 safe Eos are defined and in section 4 we discuss the complexity of LTL model checking these nets. The paper ends with a conclusion.In the following we assume basic knowledge of Petri nets, see e.g. [20].