(Non)-Deterministic finite automata are one of the simplest models of computation studied in automata theory. Here we study them through the lens of succinct data structures. Towards this goal, we design a data structure for any deterministic automaton D having n states over a a-letter alphabet E using (cr - 1)n log n(1 + o(1)) bits, that determines, given a string x, whether D accepts x in optimal O(|x|) time. We also consider the case when there are N < an non-failure transitions, and obtain various time-space trade-offs. Here some of our results are better than the recent work of Cotumaccio and Prezza (SODA 2021). We also exhibit a data structure for non-deterministic automaton N using an2 + n bits that takes O(n2|x|) time for string membership checking. Finally, we also provide time and space efficient algorithms for performing several standard operations on the languages accepted by finite automata.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Succinct representation for (non)deterministic finite automata
Grossi, R;
2023-01-01
Abstract
(Non)-Deterministic finite automata are one of the simplest models of computation studied in automata theory. Here we study them through the lens of succinct data structures. Towards this goal, we design a data structure for any deterministic automaton D having n states over a a-letter alphabet E using (cr - 1)n log n(1 + o(1)) bits, that determines, given a string x, whether D accepts x in optimal O(|x|) time. We also consider the case when there are N < an non-failure transitions, and obtain various time-space trade-offs. Here some of our results are better than the recent work of Cotumaccio and Prezza (SODA 2021). We also exhibit a data structure for non-deterministic automaton N using an2 + n bits that takes O(n2|x|) time for string membership checking. Finally, we also provide time and space efficient algorithms for performing several standard operations on the languages accepted by finite automata.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
