Space Complexity of Stack Automata Models

TL;DR

This paper analyzes the space complexity of various stack automata models, providing a detailed characterization for checking stack automata and highlighting differences with non-erasing variants, including decidability results.

Contribution

It offers a comprehensive characterization of space complexity measures for checking stack automata and demonstrates decidability of these measures, contrasting with non-erasing automata.

Findings

Accept and strong space complexity are either bounded, linear, or unbounded for checking stack automata.

Non-erasing stack automata can have space complexity proportional to the square root of input length.

Decidability results are established for space complexity properties of these automata.

Abstract

This paper examines several measures of space complexity of variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept every word in the language of the automaton (weak measure), the maximum stack size used in any accepting computation on any accepted word (accept measure),and the maximum stack size used in any computation (strong measure). We give a detailed characterization of the accept and strong space complexity measures for checking stack automata. Exactly one of three cases can occur: the complexity is either bounded by a constant, behaves like a linear function, or it can not be bounded by any function of the length of the input word (and it is decidable which case occurs). However, this result does not hold for non-erasing stack automata; we provide an example where the space complexity grows proportionally to the square root of the length of the input. Furthermore, we study the complexity bounds of machines which accept a given language, and decidability of space complexity properties.