Visit-Bounded Stack Automata

An automaton is k-visit-bounded if during any computation its work tape head visits each tape cell at most k times. In this paper we consider stack automata which are k-visit-bounded for some integer k. This restriction resets the visits when popping (unlike similarly defined Turing machine restrictions) which we show allows the model to accept a proper superset of context-free languages and also a proper superset of languages of visit-bounded Turing machines. We study two variants of visit-bounded stack automata: one where only instructions that move the stack head downwards increase the number of visits of the destination cell, and another where any transition increases the number of visits. We prove that the two types of automata recognize the same languages. We then show that all languages recognized by visit-bounded stack automata are effectively semilinear, and hence are letter-equivalent to regular languages, which can be used to show other properties.