On Two-Way Nondeterministic Finite Automata 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 ¢¤£¥§¦¨¦¨¦©¢� £ � of for some nonnull ¢ ¥� � ¦¨¦¨ ¦ � ¢ � words) is decidable, resolving a problem left open in [4,7]. 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