Petri nets are a kind of formal language that are widely applied in concurrent systems associated with resource allocation due to their abilities of the natural description on resource allocation and the precise characterization on deadlock. Weighted System of Simple Sequential Processes with Resources (WS3PR) is an important subclass of Petri nets that can model many resource allocation systems in which 1) multiple processes may run in parallel and 2) each execution step of each process may use multiple units from a single resource type but cannot use multiple resource types. We first prove that the liveness problem of WS3PR is co-NP-hard on the basis of the partition problem. Furthermore, we present a necessary and sufficient condition for the liveness of WS3PR based on two new concepts called Structurally Circular Wait (SCW) and Blocking Marking (BM), i.e., a WS3PR is live iff each SCW has no BM. A sufficient condition is also proposed to guarantee that an SCW has no BM. Additionally, we show some advantages of using SCW to analyze the deadlock problem compared to other siphon-based ones, and discuss the relation between SCW and siphon. These results are valuable to the further research on the deadlock prevention or avoidance for WS3PR.

Generating state spaces is one of important and general methods in the analysis of Petri nets. There are two reasons why state spaces of Petri nets become so large. One is concurrent occurring of transitions, and the other is periodic occurring of firing sequences. This paper focuses on the second problem, and proposes a new algorithm for exploring state spaces of finite capacity Petri nets with large capacities. In the proposed algorithm, the state space is represented in the form of a tree such that a set of markings generated by periodic occurrences of firing sequences is associated with each node, and it is much smaller than the reachability graph.

In computer science, concepts of resource such as data consumption and of time such as execution time are very important. Logical systems which can treat them have been applied in that field. Linear logic has been called a resource conscious logic. The expressive power is enough to describe a dynamic change in process environments. However, linear logic is not enough to treat a dynamic change in environments with the passage of time since it does not include a concept of time directly. A typical example is the relation between linear logic and Petri nets. It is well known that the reachability problem for Petri nets is equivalent to the provability for the corresponding sequent of linear logic. But linear logic cannot naturally represent timed Petri nets which are extensions of ordinary Petri nets with respect to time concept. So we extend linear logic with respect to time concept in order to introduce a resource-conscious and time-dependent logical system, that is, temporal linear logic. This system has some temporal operators "" which means a resource usable only once at the next time, "" which means a resource usable only once at anytime, and a modal storage operator "!" which means a resource usable any times at anytime. We can show that the reachability problem for timed Petri nets is equivalent to the provability for the corresponding sequent of temporal linear logic. In this paper, we also represent the description of synchronous communication model by temporal linear logic. The expressive power of temporal linear logic will be applicable to various fields of computer science.

In a distributed concurrent system such as a computer communication network, the system components communicate with each other via communication links in order to accomplish a desired distributed application. If the links are dynamically established among the components, the system configuration as well as its behavior becomes complex. In this paper, we give formal specification of such a dynamically reconfigurable system in which the components are modeled by communicating finite state machines executed concurrently with the communication links which are dynamically established and disconnected. We also present an algorithm to validate the safety and link-related properties in the specified behavior. Finally, we design and implement a simulator and a validator that enables execution and validation of the given specification, respectively.

If a general Petri net N = (S, T, F, Mo) is transition-live under Mo, it is evident that each maximal structural deadlock SDL(D) in N as well as each minimal structural deadlock MSDL (ND) in each D is also transition-live under Mo. However, since the converse of the latter of the above is not always true, it is important to obtain the conditions for this converse to be true if we want to have a useful necessary and sufficient "initial-marking-based" or "structural" liveness condition for N. Up to now, usefull and well-known structural or initial-marking-based necessary and sufficient liveness conditions of Petri nets have only been those of an asymmetric choice (AC) net and its subclasses such as an EFC net, an FC net, an FCF net, MG, and SM. However, all the above subclasses are activated only by real or virtual deadlock-trap properties which are local liveness for each minimal deadlocks; in other words, the above topics of this paper are unconditionally satisfied in those subclasses because of their special structure of nets. In this paper, a necessary and sufficient structural liveness condition for a general Petri net N with globally structural live minimal structural deadlocks is presented as follows: The next () or () is satisfied. () N has no SDL D. () If N has at least one SDL D, () or () is satisfied under the condition that each MSDL ND in N is transition-live under Mo. () N has no singular MSDL (α) (i.e., (α-) and (α-)). () If N has at least one singular MSDL (α-)((α-), resp.), every semi-MDSL ()((), resp.) NDS = (SDS, TDS, FDS, MoDS with respect to each singular MSDL (α-)((α-), resp.), is transition-live under the MoDS under the condition of "the condition (**)", where the locally structural liveness for this NDS means (1) or (2)((3), resp.) of Lemma 4-4 and "the condition (**)" is defined in Lemma 4-7 of this paper. The relationship between the above results and the liveness problem for N is also shown.

The symbolic model checking algorithm was proposed for the efficient verification of sequential circuits. In this paper, we show that this algorithm is applicable to the verification of concurrent systems described by finite capacity Petri nets. In this algorithm, specifications of the system are given in the form of temporal logic formulas, and the algorithm checks whether these formulas hold in the state space. All logical operations are performed on Binary Decision Diagrams. Since the algorithm does not enumerating each state, the problem of state space explosion can be avoided in many cases.

State space explosion is a serious problem in analyzing discrete event systems that allow concurrent occurring of events. A new method is proposed for generating reduced state spaces of systems. This method is an improvement of Valmari's stubborn set method. The generated state space preserves liveness, livelocks, and terminal states of the ordinary state space. Petri nets are used as a model of systems, and a method is shown for generating a reduced state space from a given Petri net.

Net theory originated by Dr. Petri in 1962 is now indispensable key concept in the analysis and design of concurrent systems. In Japan, since late seventies the net theory has attracted attention among computer scientists. This paper reviews the historical aspect of the net theory developed in Japan during the last two decades.

This article discusses on PDM (Petri net based Development Methodology) which integrates approaches, modeling methods, design methods and analysis methods in a coherent manner. Although various development techniques based on Petri nets have demonstrated advantages over conventional techniques, those techniques are rather ad hoc and lack an overall picture on entire development process. PDM anticipates to provide a refernce process model to develop distributed systems with various Petri net based development methods. Behavioral properties of distrbuted systems can be an appropriate application domain of PDM.