On store languages and applications

Abstract

The store language of a machine of some arbitrary type is the set of all store configurations (state plus store contents but not the input) that can appear in an accepting computation. New algorithms and characterizations of store languages are obtained, such as the result that any nondeterministic pushdown automaton augmented with reversal-bounded counters, where the pushdown can "flip" its contents up to a bounded number of times, can be accepted by a machine with only reversal-bounded counters. Then, connections are made between store languages and several model checking and reachability problems, such as accepting the set of all predecessor and successor configurations from a given set of configurations, and determining whether there are at least one, or infinitely many, common configurations between accepting computations of two machines. These are explored for a variety of different machine models often containing multiple parallel data stores. Many of the machine models studied can accept the set of predecessor configurations (of a regular set of configurations), the set of successor configurations, and the set of common configurations between two machines, with a machine model that is simpler than itself, with a decidable emptiness, infiniteness, and disjointness property. Store languages are key to showing these properties.

On store languages of language acceptors

“…Furthermore, this problem is also decidable for nondeterministic Turing machines with a one-way read-only input tape and a reversal-bounded worktape [30] (using Proposition 6 proven here). Also, certain applications to problems in the area of verification and model checking are presented in [6]. Another application is addressed here.…”

“…Standard one-way single-tape acceptors are a special case with only one input tape. Multi-tape inputs have been studied for NPDA [15], NCM [21], and NPCM [23].…”

“…In [19,23], the authors study the concept of a store language of a machine M for arbitrary types of automata, which is essentially a language description of all the store contents that can appear in any accepting computation of the machine. So, for a t-flip NPCM M = (Q, Σ, δ, q 0 , F ), the store language of M ,…”

“…, c k are new special symbols associated with the counters. In [23], the authors showed that the store language of every t-flip NPDA (resp. t-flip NPCM) is in fact a regular (resp.…”

“…Also, it was a key component to showing that it is decidable whether the set of all infixes (subwords) of the language accepted by a reversal-bounded 3 NPDA is equal to Σ * (i.e., is dense) [5]. Connections between store languages and the area of verification and model checking have also been recently explored [6].…”