This paper presents a novel analysis approach for bounded Petri nets. The net behavior is modeled by boolean functions, thus reducing reasoning about Petri nets to boolean calculation. The state explosion problem is managed by using Binary Decision Diagrams (BDDs), which are capable to represent large sets of markings in small data structures.The ability o f P etri nets to model systems, the exibility and generality of boolean algebras, and the e cient implementation of BDDs, provide a general environment to handle a large variety of problems. Examples are presented that show h o w all the reachable states (10 18 ) o f a P etri net can be e ciently calculated and represented with a small BDD (10 3 nodes). Properties requiring an exhaustive analysis of the state space can be veri ed in polynomial time in the size of the BDD. ? Supported by CYCIT TIC 91-1036 and Dept. d'Ensenyament de la Generalitat de CatalunyaPastor, E. [et al.]. Petri net analysis using boolean manipulation. Commutative Laws: a + b = b + a a b = b a 2. Distributive Laws: a + ( b c) = ( a + b) (a + c) a (b + c) = ( a b) + ( a c) 3. Identities: a + 0 = a a 1 = a 4. Complement. 8a 2 B 9a 0 2 B s u c h t h a t : a + a 0 = 1 a a 0 = 0As it is well known, the system (f0 1g + 0 1) , with + and de ned as the logic OR and logic AND operations respectively, is a boolean algebra (also known as the switching algebra). From now on, and since we will limit our scope to logic functions, w e w i l l a l w ays assume that B = f0 1g.

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This paper presents a methodology for the veri cation of speed-independent asynchronous circuits against a Petri net speci cation. The technique is based on symbolic reachability analysis, modeling both the speci cation and the gate-level network behavior by m e a n s of boolean functions. These functions are e ciently handled by u s i n g Binary Decision Diagrams. Algorithms for verifying the correctness of designs, as well as several circuit properties are proposed. Finally, t h e applicability o f o u r v eri cation method has been proven by c hecking the correctness of di erent b e n c hmarks. ? Work supported by CYCIT TIC 94-0531-E and Departament d'Ensenyament d e l a Generalitat de Catalunya.

AbstractÐThis work presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.

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