Behavioral Strengths and Weaknesses of Various Models of Limited Automata

TL;DR

This paper explores the behaviors and properties of various $k$-limited automata models, including probabilistic, deterministic, nondeterministic, and unambiguous variants, analyzing their language recognition capabilities and fundamental characteristics.

Contribution

It introduces and analyzes probabilistic $k$-limited automata and compares their computational power with other models, highlighting key properties and language class relationships.

Findings

Probabilistic $k$-limited automata accept languages with certain probabilistic bounds.

Inclusions and separations among language families are established.

Key features like blank skipping and reversal closure are examined for robustness.

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.