Equivalence-Checking with One-Counter Automata: A Generic Method for Proving Lower Bounds

Petr Jancar, Antonin Kucera, Faron Moller, Zdenek Sawa

To appear at Foundations of Software Science and Computation Structures (FOSSACS02), Grenoble, France, 6-14 April, 2002


We present a general method for proving DP-hardness of equivalence-checking problems on one-counter automata. For this we show a reduction of the Sat-Unsat problem to the truth problem for a fragment of (Presburger) arithmetic. The fragment contains only special formulas with one free variable, and is particularly apt for transforming to simulation-like equivalences on one-counter automata. In this way we show that the membership problem for any relation subsuming bisimilarity and subsumed by simulation preorder is DP-hard (even) for one-counter nets (where the counter cannot be tested for zero). We also show DP-hardness for deciding simulation between one-counter automata and finite-state systems (in both directions).

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