by Antonín Kučera, This is a full version of the paper accepted for ASIAN 2000. September 2000, 34 pages.
FIMU-RS-2000-05. Available as Postscript, PDF.
We present new complexity results for simulation-checking and model-checking with infinite-state systems generated by pushdown automata and their proper subclasses of one-counter automata and one-counter nets (one-counter nets are "weak" one-counter automata computationally equivalent to Petri nets with at most one unbounded place).
As for simulation-checking, we show the following: a) simulation equivalence between pushdown processes and finite-state processes is EXPTIME-complete; b) simulation equivalence between processes of one-counter automata and finite-state processes is coNP-hard; c) simulation equivalence between processes of one-counter nets and finite-state processes is in P (to the best of our knowledge, it is the first (and rather tight) polynomiality result for simulation with infinite-state processes).
As for model-checking, we prove that a) the problem of simulation-checking between processes of pushdown automata (or one-counter automata, or one-counter nets) and finite-state processes are polynomially reducible to the model-checking problem with a fixed formula F = nu X. [z]<z> X of the modal mu-calculus. Consequently, model-checking with F is EXPTIME-complete for pushdown processes and coNP-hard for processes of one-counter automata; b) model-checking with a fixed formula <>[a]<>[b]ff of the logic EF (a simple fragment of CTL) is NP-hard for processes of OC nets, and model-checking with another fixed formula []<a>[]<b>tt of EF is coNP-hard. Consequently, model-checking with any temporal logic which can express these simple formulae is computationally hard even for the (very simple) sequential processes of OC-nets.