Space Complexity of Stack Automata Models

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.

Deterministic Real-Time Tree-Walking-Storage Automata

“…While the early studies of stack automata have extensively been done in relation with AFL theory as well as time and space complexity [11,14,15,22,25], more recent papers consider the computational power gained in generalizations by allowing the input head to jump [19], allowing multiple input heads, multiple stacks [18], and multiple reversal-bounded counters [17]. The stack size required to accept a language by stack automata has been considered as well [16]. In [20] the property of working input-driven has been imposed to stack automata, and their capacities as transducer are studied in [2].…”