Tadao Murata

Petri nets: Properties, analysis and applications

Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

A method for stepwise refinement and abstraction of Petri nets

Abstract This paper is concerned with a method for expanding (or reducing) a Petri net representation to the desired level of detail using step-by-step refinement of transitions and places (or abstraction of subnets to transitions). In particular, we present conditions under which a subnet can be substituted for a single transition while preserving properties such as liveness and boundedness. The present method is general enough to include previously reported methods as special cases. The refinement technique can be used as a top-down approach for synthesizing Petri net models of concurrent systems, while the abstraction technique can be used as a “divide-and-conquer” approach to the analysis of Petri nets.

Detection of Ada static deadlocks using Petri net invariants

A method is presented for detecting deadlocks in Ada tasking programs using structural; and dynamic analysis of Petri nets. Algorithmic translation of the Ada programs into Petri nets which preserve control-flow and message-flow properties is described. Properties of these Petri nets are discussed, and algorithms are given to analyze the nets to obtain information about static deadlocks that can occur in the original programs. Petri net invariants are used by the algorithms to reduce the time and space complexities associated with dynamic Petri net analysis (i.e. reachability graph generation). >

A predicate-transition net model for parallel interpretation of logic programs

A predicate/transition net model for a subset of Horn clause logic programs is presented. The syntax, transformation procedure, semantics, and deduction process for the net model are discussed. A possible parallel implementation for the net model is described, which is based on the concepts of communicating processes and relations. The proposed net model offers a syntactical variant of Horn clause logic and has two distinctions from other existing schemes for the logic programs: representation formalism and the deduction method. The net model provides an approach towards the solutions of the separation of logic from control and the improvement of the execution efficiency through parallel processing for the logic programs. The abstract nature of the net model also lends itself to different implementation strategies. >

Circuit theoretic analysis and synthesis of marked graphs

Marked graphs are a graph model for representing and studying parallel computations and concurrent processes. This paper provides circuit theoretic concepts and methods for the analysis and synthesis of marked graphs. Among the results obtained, the reachability theorem developed in this paper is a generalization of known results in the sense that it does not require two hypotheses: the liveness of an initial marking and the strongly connectedness of marked graphs. A synthesis problem of marked graphs from prescribed markings is proposed, and is shown to be that of realizing cutset matrices as directed graphs.

Proof procedure and answer extraction in Petri net model of logic programs

A proof procedure and answer extraction in a high-level Petri net model of logic programs is discussed. The logic programs are restricted to the Horn clause subset of first-order predicate logic and finite problems. The logic program is modeled by a high-level Petri net and the execution of the logic program or the answer extraction process in predicate calculus corresponds to a firing sequence which fires the goal transition in the net. For the class of the programs described above, the goal transition is potentially firable if an only if there exists a nonnegative T-invariant which includes the goal transition in its support. This is the main result proved. Three examples are given to illustrate in detail the above results. >

Hierarchical reachability graph of bounded Petri nets for concurrent-software analysis

Petri nets have been proposed as a promising tool for modeling and analyzing concurrent-software systems such as Ada programs and communication protocol software. Among analysis techniques available for Petri nets, the most general approach is to generate all possible states (markings) of the system in a form of a so-called reachability graph. However, this conventional reachability graph approach is inefficient or intractable, even for a bounded Petri net, due to state explosion in many practical applications. To cope with this problem, this paper proposes a method for constructing a hierarchically organized state space called the hierarchical reachability graph (HRG). Using the HRG, we obtain necessary and sufficient conditions for reachability and deadlock, as well as algorithms to test whether a given state or marking is reachable from the initial state and whether there is a deadlock state (a state with no successor states). >

Temporal Uncertainty and Fuzzy-Timing High-Level Petri Nets

This paper discusses an approach to deal with temporal uncertainty and introduces fuzzy timing in a high-level Petri net model. The main features of the present model are the four fuzzy set theoretic functions of time called fuzzy timestamp, fuzzy enabling time, fuzzy occurrence time and fuzzy delay, all of which capture temporal uncertainty in a form not violating the axiom of measurement recently proposed by Dr. Petri. Fuzzy-timing nets are suitable for time-critical applications since fuzzy time functions can be computed very fast.

An application of Petri net reduction for Ada tasking deadlock analysis

As part of our continuing research on using Petri nets to support automated analysis of Ada tasking behavior, we have investigated the application of Petri net reduction for deadlock analysis. Although reachability analysis is an important method to detect deadlocks, it is in general inefficient or even intractable. Net reduction can aid the analysis by reducing the size of the net while preserving relevant properties. We introduce a number of reduction rules and show how they can be applied to Ada nets, which are automatically generated Petri net models of Ada tasking. We define a reduction process and a method by which a useful description of a detected deadlock state can be obtained from the reduced nets information. A reduction tool and experimental results from applying the reduction process are discussed.

A Petri net model for reasoning in the presence of inconsistency

Petri nets provide a promising framework for executing queries to logic programs. Petri net models for query processing in logic programming were initially developed by T. Murata and D. Zhang (IEEE Trans. Software Eng., vol.14, no.4, p.481-97, 1988). It is shown how this framework can be extended to be applicable to reasoning in the presence of inconsistency. This yields a Petri net model of programs that be inconsistent in classical logic. This is interesting because large expert systems may often contain inconsistent information. The Petri net method proposed suggests a robust way of preventing inconsistency from infecting a system and rendering it useless. >