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.
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