Succinct Representation for (Non)Deterministic Finite Automata - Archive ouverte HAL Access content directly
Conference Papers Year :

Succinct Representation for (Non)Deterministic Finite Automata

(1) , (2, 3) , (4) , (5)
1
2
3
4
5

Abstract

Deterministic finite automata are one of the simplest and most practical models of computation studied in automata theory. Their conceptual extension is the non-deterministic finite automata which also have plenty of applications. In this article, we study these models through the lens of succinct data structures where our ultimate goal is to encode these mathematical objects using information theoretically optimal number of bits along with supporting queries on them efficiently. Towards this goal, we first design a succinct data structure for representing any deterministic finite automaton D having n states over a σ-letter alphabet Σ using (σ−1)n log n+O(n log σ) bits of space, which can determine, given an input string x over Σ, whether D accepts x in O(|x| log σ) time, using constant words of working space. When the input deterministic finite automaton is acyclic, not only we can improve the above space bound significantly to (σ − 1)(n − 1) log n + 3n + O(log 2 σ) + o(n) bits, we also obtain optimal query time for string acceptance checking. More specifically, using our succinct representation, we can check if a given input string x can be accepted by the acyclic deterministic finite automaton using time proportional to the length of x, hence, the optimal query time. We also exhibit a succinct data structure for representing a non-deterministic finite automaton N having n states over a σ-letter alphabet Σ using σn 2 + n bits of space, such that given an input string x, we can decide whether N accepts x efficiently in O(n 2 |x|) time. Finally, we also provide time and space efficient algorithms for performing several standard operations such as union, intersection and complement on the languages accepted by deterministic finite automata.
Fichier principal
Vignette du fichier
1907.09271.pdf (800.6 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03498364 , version 1 (21-12-2021)

Identifiers

Cite

Sankardeep Chakraborty, Roberto Grossi, Kunihiko Sadakane, Srinivasa Rao Satti. Succinct Representation for (Non)Deterministic Finite Automata. LATA 2021 - 15th International Conference on Language and Automata Theory and Applications, Sep 2021, Milan, Italy. pp.55-67, ⟨10.1007/978-3-030-68195-1_5⟩. ⟨hal-03498364⟩

Collections

INRIA INRIA2
19 View
57 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More