an:02118423
Zbl 1078.68087
Jan??ar, Petr; Ku??era, Anton??n; Moller, Faron; Sawa, Zden??k
DP lower bounds for equivalence-checking and model-checking of one-counter automata
EN
Inf. Comput. 188, No. 1, 1-19 (2004).
00102492
2004
j
68Q45 68Q60
One-counter machines; Equivalence-checking; Model-checking
Summary: We present a general method for proving DP-hardness of problems related to formal verification of 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), and for the model-checking problem with one-counter nets and the branching-time temporal logic EF.