On Simulation-Checking with Sequential Systems

• Authors: Antonín Kucera
• Venue: ASIAN '00 Proceedings of the 6th Asian Computing Science Conference on Advances in Computing Science
• Year: 2000

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 infinitestate 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 ϕ Ξ νX.[z]〈z〉X of the modal µ-calculus. Consequently, model-checking with ϕ 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.