On the Complexity of Semantic Equivalences for Pushdown Automata and BPA

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Authors	KUČERA Antonín MAYR Richard
Year of publication	2002
Type	Article in Proceedings
Conference	Proceedings of 27th International Symposium on Mathematical Foundations of Computer Science (MFCS 2002)
MU Faculty or unit	Faculty of Informatics
Citation
Field	Computer hardware and software
Keywords	verification; concurrency; weak bisimilarity; infinite-state systems
Description	We study the complexity of comparing pushdown automata (PDA) and context-free processes (BPA) to finite-state systems, w.r.t. strong and weak simulation preorder/equivalence and strong and weak bisimulation equivalence. We present a complete picture of the complexity of all these problems. In particular, we show that strong and weak simulation preorder (and hence simulation equivalence) is EXPTIME-complete between PDA/BPA and finite-state systems in both directions. For PDA the lower bound even holds if the finite-state system is fixed, while simulation-checking between BPA and any fixed finite-state system is already polynomial. Furthermore, we show that weak (and strong) bisimilarity between PDA and finite-state systems is PSPACE-complete, while strong (and weak) bisimilarity between two PDAs is EXPTIME-hard.
Related projects:	Infinite state concurrent systems - models and verification Non-sequential Models of Computing -- Quantum and Concurrent Distributed Models of Computing