Abstract
We present a general method for proving DP-hardness of equivalencechecking 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 onecounter 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).
This work was supported by the Grant Agency of the Czech Republic, Grant No. 201/00/0400.
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Jančar, P., Kučera, A., Moller, F., Sawa, Z. (2002). Equivalence-Checking with One-Counter Automata: A Generic Method for Proving Lower Bounds* . In: Nielsen, M., Engberg, U. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2002. Lecture Notes in Computer Science, vol 2303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45931-6_13
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DOI: https://doi.org/10.1007/3-540-45931-6_13
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