Stack languages and log n space

King, K. N.; Wrathall, Celia

doi:10.1016/0022-0000(78)90010-7

Cited by 6 publications

(2 citation statements)

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“…It is known that checking stack languages form a proper subset of non-erasing stack languages, which form a proper subset of stack languages [4], and those in turn form a proper subset of context-sensitive languages [8]. In terms of space complexity, it is possible to study the three space complexity measures (weak, accept, and strong) as the maximum stack size required for any input of length n. It is already known that every stack language can be accepted by some stack automaton which operates in linear space using the weak measure [8,12]. However, this does not imply that every stack automaton has this property.…”

Section: Introductionmentioning

confidence: 99%

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Space Complexity of Stack Automata Models

Ibarra

Jirásek

McQuillan

et al. 2021

Int. J. Found. Comput. Sci.

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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.

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Section: Introductionmentioning

confidence: 99%

“…Further results are known relating one-way and two-way versions of these machines to other models, and to space complexity classes of Turing machines, e.g. [3,10,12].…”

Section: Introductionmentioning

confidence: 99%