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Weakly Continuation Closed Homomorphisms on Automata

A major limitation of system and program verification is the state space explosion problem. To avoid this problem, there exists several approaches to reduce the size of the system state space. Some methods try to keep the state space small during the verification run, other methods reduce the original state space prior to the verification. One of the later are abstraction homomorphisms. Weakly Continuation Closed homomorphisms are abstraction homomorphisms preserving exactly those properties of the original behaviour which are satisfied inherently fair [1]. However, the practical use of WCC homomorphisms is limited by the lack of a reasonably efficient algorithm, checking whether or not a homomorphism is WCC and performing reasonably well. This paper presents a result which allows to develop algorithms for WCC on automata.