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Our main purpose is to present an algorithm which decides whether or not a condition C(X,Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This solves a problem stated in [4] and contains, as a very special case, the answer to case 4 left open in [6]. In an equally appealing form the result can be restated in the terminology of [7^10,15] » Every oi-game definable in sequential calculus Is determined. Moreover the player who has a winning strategy, in fact, has a winning finite state strategy, that is one which can effectively be played in a strong sense. The main proof, that of the central Theorem 1, will be presented at the end. We begin with a discussion of its consequences.

No abstract

Our main purpose is to present an algorithm which decides whether or not a condition &(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This solves a problem stated in [4] and contains, as a very special case, the answer to Case 4 left open in [6]. In an equally appealing form the result can be restated in the terminology of [7], [10], [15]: Every cu-game definable in sequential calculus is determined. Moreover the player who has a winning strategy, in fact, has a winning finite-state strategy, that is one which can effectively be played in a strong sense. The main proof, that of the central Theorem 1, will be presented at the end. We begin with a discussion of its consequences.

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Petri nets have been extensively studied because of their suitability as models for asynchronous computing Despite this effort, the mathematical properties of Petrl nets are not very well understood In this paper we investigate two unportant special types of Petn nets, the conflict-free nets and the persistent nets, the former being a proper subset of the latter. Our results completely characterize the sets of reachable markings attainable by such nets Reachabihty sets of persistent nets are shown to be semllmear A stronger result is obtamed for conflict-free nets which results m an exponential time algorithm for deciding boundedness of such nets The best known upper bound for deciding boundedness of arbitrary nets is exponential space We conclude with a proof that all reachablhty sets of Petri nets may be realized with a "small amount" of nonperslstence KEY WORDS AND PHRASES Petn nets, persistence, conflict-free, semdmear, computational complexity, reachabihty CR CATEGORIES 5 29

Scientific research has always relied on communication for gathering and providing access to data; for exchanging information; for holding discussions, meetings, and seminars; for collaborating with widely dispersed researchers; and for disseminating results. The pace and complexity of modern research, especially collaborations of researchers in different institutions, has dramatically increased scientists' communications needs. Scientists now need immediate access to data and information, to colleagues and collaborators, and to advanced computing and information services. Furthermore, to be really useful, communication facilities must be integrated with the scientist's normal day-to-day working environment. Scientists depend on computing and communications tools and are handicapped without them.