On the emptiness problem for two-way NFA with one reversal-bounded counter

Abstract

We show that the emptiness problem for two-way nondeterministic finite automata augmented with one reversal-bounded counter (i.e., the counter alternates between nondecreasing and nonincreasing modes a fixed number of times) operating on bounded languages (i.e., subsets ofw*1⋯ w*k for some nonnull words w1,⋯, wk) is decidable, settling an open problem in [11,12]. The proof is a rather involved reduction to the solution of a special class of Diophantine systems of degree 2 via a class of programs called two-phase programs. The result has applications to verification of infinite state systems. © Springer-Verlag Berlin Heidelberg 2002.