Atsushi Ohta

Reachability Problem of Marked Graphs with Batch Processing Arcs

Petri net is a mathematical model for discrete event systems. Batch processing arcs are suggested which moves all tokens in its input places by single firing of transition. This extension makes Petri net Turing machine equivalent, which means most of important analysis problems including reachability problem are undecidable. In this report, we study reachability problem of marked graphs with batch processing arcs. It is assumed that transitions are classified in two categories: for each transition, either all incident arcs are normal arcs or all incident arcs are batch processing arcs. Under this assumption, necessary and sufficient condition for reachability of marked graphs without batch processing arcs is shown to be extended to that with batch processing arcs.

Insufficiently marked siphon of Petri nets - extension of token-free siphon

Petri net is a mathematical model for concurrent systems. Liveness is one of important properties of Petri net. A live Petri net exhibits no local deadlocks. Siphon is a subset of places useful for liveness analysis. Token-free siphon implies non-liveness of Petri net. In this report, we suggest an insufficiently marked siphon as an extended token-free siphon. More general necessary condition for liveness is obtained using this new status of siphons. Two methods are proposed to obtain an insufficiently marked siphon.

POC net, a subclass of Petri nets, and its application to timed Petri nets

Abstract Liveness is one of the most important properties of the Petri net analysis. This property is concerned with a capability for firing of transitions. On the other hand, place-liveness is another notion related to liveness, which is concerned with a capability for having tokens in places. Concerning these liveness and place-liveness problems, this paper suggests a new subclass of Petri net, ‘POC nets’, as a superclass of AC nets and DC nets. For this subclass, the equivalence between liveness and place-liveness is shown and a sufficient condition for liveness for this POC net is derived. Then the results are extended to liveness problem of timed Petri nets which have transitions with finite firing durations and the earliest firing rule. Although liveness of a (non-timed) Petri net is neither necessary nor sufficient condition for liveness of a timed Petri net, it is shown that liveness is preserved if the net has POC structure. Furthermore, it is pointed out that if a POC net satisfies some addition...

Structural analysis of Petri nets with batch processing arcs

Petri net is an effective tool for concurrent systems. This paper studies analysis of batch Petri net, which is an extended Petri net with batch processing arcs. Intuitively, if a batch processing arc is connected from a place p to a transition t, then single firing of the transition t removes all tokens in p. In this paper, we show that batch Petri net with unity weighted arcs is Turing machine equivalent. Analysis using incidence matrices is studied to show P-invariant is as effective as in normal Petri net

On some analysis properties of colored Petri net using underlying net

Petri net is an effective tool to model and evaluate concurrent systems. Colored Petri net has been proposed to model large scale systems more effectively. Among analysis tools for colored Petri nets, such as reachability tree, to net invariants, to unfolded equivalent noncolored net, we use underlying noncolored Petri net. This method requires restriction on binding of the arc expression. In this report, some analysis properties of colored Petri net are studied using its underlying noncolored net. Sufficient conditions for boundedness and persistency are derived. Some restrictions on structure and binding are used to obtain a necessary condition for liveness.

Unfolding of Petri nets with semilinear reachability set

Petri net is an effective model for concurrent systems. The state space of a general Petri net is infinite. Even if it is finite, its size grows exponentially as the size of the net does. This problem, called state space explosion, makes Petri net analysis hard. Unfolding is suggested to give a compact description of the state space of a bounded Petri net. This is extended to an unbounded net using symbol /spl omega/ used in the coverability tree generating algorithm. However, using /spl omega/ causes lack of information. On the other hand, if the unbounded Petri net has a semilinear state space, it can be expressed without lack of information with an extended coverability tree. This paper suggests an extension of unfolding of Petri net with semilinear state space without lack of information.

Improvement of error reduction in fluidification of generalized stochastic Petri net

Behavior of stochastic Petri net can be approximated by difference equation resulting after fluidification. Vásquez et al. have introduced Gaussian noise to reduce approximation error. We suggest a method to reduce the number of additions of noise while keeping errors as small as Vasquezs method.

Decidability Analysis of Some Classes of Extended Function Petri Net

In this report, we study liveness and reach ability problem of extended function Petri net with some structural restriction. Petri net is a mathematical model for concurrent systems such as parallel computers, manufacturing system, communication protocol and so on. Liveness and reach ability are important problems of Petri net. The former is to verify whether the system has no local deadlocks. The latter is to verify whether the system can reach the target status from the initial one. Extended function Petri net, where each arc weight is a function of the marking, has wide range of application including system biology, communication protocol and so on. However, it is hard to obtain theoretical results for general extended Petri net. First, we show liveness criterion of extended Petri net with asymmetric choice structure and extended free choice structure with some restricted arc functions. Then reach ability and liveness of extended Petri net with asymmetric choice structure is shown to be undecidable.

Minimal time reachability problem of some subclasses of timed Petri nets

Timed Petri net is an effective tool to evaluate discrete event systems. This paper treats the reachability problem of timed Petri nets. The problem aims to find the firing sequence which drives the initial marking M/sub 0/ to the target marking M/sub f/ in minimal execution time. First, we consider the subclass in which non-delayed sequence gives the optimal solution. Then, an algorithm is proposed to solve the minimal time reachability problem of timed state machines.