On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Model checking
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
Memoryful Branching-Time Logic
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
FMCAD '07 Proceedings of the Formal Methods in Computer Aided Design
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
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Abstraction is a leading technique for coping with large state spaces. Abstraction over-approximates the transitions of the original system or the automaton that models it and may introduce nondeterminism. In applications where determinism is essential, we say that an abstraction function is helpful if, after determining and minimizing the abstract automaton, we end up with fewer states than the original automaton. We show that abstraction functions are not always helpful; in fact, they may introduce an exponential blow-up. We study the problem of deciding whether a given abstraction function is helpful for a given deterministic automaton and show that it is PSPACE-complete.