This paper examines several measures of space complexity on variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept any word in a language (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 (up to small technicalities explained in the paper) like a linear function, or it grows arbitrarily larger than the length of the input word. However, this result does not hold for non-erasing stack automata; we provide an example when the space complexity grows with the square root of the input length. Furthermore, an investigation is done regarding the best complexity of any machine accepting a given language, and on decidability of space complexity properties.
Space Complexity of Stack Automata Models / O.H. Ibarra, J. Jirasek, I. Mcquillan, L. Prigioniero (LECTURE NOTES IN ARTIFICIAL INTELLIGENCE). - In: Developments in Language Theory / [a cura di] N. Jonoska, D. Savchuk. - [s.l] : Springer, 2020. - ISBN 9783030485153. - pp. 137-149 (( Intervento presentato al 24. convegno International Conference on Developments in Language Theory tenutosi a Tampa nel 2020 [10.1007/978-3-030-48516-0_11].
Space Complexity of Stack Automata Models
L. Prigioniero
2020
Abstract
This paper examines several measures of space complexity on variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept any word in a language (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 (up to small technicalities explained in the paper) like a linear function, or it grows arbitrarily larger than the length of the input word. However, this result does not hold for non-erasing stack automata; we provide an example when the space complexity grows with the square root of the input length. Furthermore, an investigation is done regarding the best complexity of any machine accepting a given language, and on decidability of space complexity properties.File | Dimensione | Formato | |
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