Behavioral Strengths and Weaknesses of Various Models of Limited Automata (2111.05000v1)

Abstract: We examine the behaviors of various models of $k$-limited automata, which naturally extend Hibbard's [Inf. Control, vol. 11, pp. 196--238, 1967] scan limited automata, each of which is a single-tape linear-bounded automaton satisfying the $k$-limitedness requirement that the content of each tape cell should be modified only during the first $k$ visits of a tape head. One central computation model is a probabilistic $k$-limited automaton (abbreviated as a $k$-lpa), which accepts an input exactly when its accepting states are reachable from its initial state with probability more than 1/2 within expected polynomial time. We also study the behaviors of one-sided-error and bounded-error variants of such $k$-lpa's as well as the deterministic, nondeterministic, and unambiguous models of $k$-limited automata, which can be viewed as natural restrictions of $k$-lpa's. We discuss fundamental properties of these machine models and obtain inclusions and separations among language families induced by them. In due course, we study special features -- the blank skipping property and the closure under reversal -- which are keys to the robustness of $k$-lpa's.