Time-Basic Petri nets, is a powerful formalism for modeling real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We introduce a technique for coverability analysis based on the building of a finite graph. This technique further exploits the time anonymous concept [5,6], in order to deal with topologically unbounded nets, exploits the concept of a coverage of TA tokens, i.e., a sort of anonymous timestamp. Such a coverability analysis technique is able to construct coverability trees graphs for unbounded Time-Basic Petri net models. The termination of the algorithm is guaranteed as long as, within the input model, tokens growing without limit, can be anonymized. This means that we are able to manage models that do not exhibit Zeno behavior and do not express actions depending on infinite past events. This is actually a reasonable limitation because, generally, real-world examples do not exhibit such a behavior.
We consider (unbounded) Timed Petri Nets (TPNs) where each token is equipped with a real-valued clock representing the "age" of the token. Each arc in the net is provided with a subinterval of the natural numbers, restricting the ages of the tokens travelling the arc. We apply a methodology developed in [AN00], based on the theory of better quasi orderings (BQOs), to derive an efficient constraint system for automatic verification of safety properties for TPNs. We have implemented a prototype based on our method and applied it for verification of a parametrized version of Fischer's protocol. To model the behavior of finite-state asynchronous real-time systems we propose the notion of timed Buchi automata (TBA). TBAs are Buchi automata coupled with a mechanism to express constant bounds on the timing delays between system events. These automata accept languages of timed traces, traces in which each event has an associated real-valued time of occurrence. We consider verification of safety properties for concurrent real-timed systems modelled as timed Petri nets by performing symbolic forward reachability analysis. We introduce a formalism, called region generators, for representing sets of markings of timed Petri nets. Region generators characterize downward closed sets of regions and provide exact abstractions of sets of reachable states with respect to safety properties. We show that the standard operations needed for performing symbolic reachability analysis are computable for region generators. Since forward reachability analysis is necessarily incomplete, we introduce an acceleration technique to make the procedure terminate more often on practical examples. We have implemented a prototype for analyzing timed Petri nets and used it to verify a parameterized version of Fischer's protocol, Lynch and Shavit's mutual exclusion protocol and a producer-consumer protocol. We also used the tool to extract finite-state abstractions of these protocols.