From Multi to Single Stack Automata
We investigate the issue of reducing the verification problem of multi-stack machines to the one for single-stack machines. For instance, elegant (and practically efficient) algorithms for bounded-context switch analysis of multi-pushdown systems have been recently defined based on reductions to the reachability problem of (single-stack) pushdown systems [10,18]. In this paper, we extend this view to both bounded-phase visibly pushdown automata (BVMPA)  and ordered multi-pushdown automata (OMPA)  by showing that each of their emptiness problem can be reduced to the one for a class of single-stack machines. For these reductions, we introduce effective generalized pushdown automata (EGPA) where operations on stacks are (1) pop the top symbol of the stack, and (2) push a word in some (effectively) given set of words L over the stack alphabet, assuming that L is in some class of languages for which checking whether L intersects regular languages is decidable. We show that the automata-based saturation procedure for computing the set of predecessors in standard pushdown automata can be extended to prove that for EGPA too the set of all predecessors of a regular set of configurations is an effectively constructible regular set. Our reductions from OMPA and BVMPA to EGPA, together with the reachability analysis procedure for EGPA, allow to provide conceptually simple algorithms for checking the emptiness problem for each of these models, and to significantly simplify the proofs for their 2ETIME upper bounds (matching their lower-bounds).
KeywordsRegular Language Concurrent Program State Automaton Input Alphabet Saturation Procedure
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