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Article Dans Une Revue Algorithms Année : 2021

Efficient Construction of the Equation Automaton

Résumé

This paper describes a fast algorithm for constructing directly the equation automaton from the well-known Thompson automaton associated with a regular expression. Allauzen and Mohri have presented a unified construction of small automata and gave a construction of the equation automaton with time and space complexity in O(mlogm+m2), where m denotes the number of Thompson automaton transitions. It is based on two classical automata operations, namely epsilon-removal and Hopcroft’s algorithm for deterministic Finite Automata (DFA) minimization. Using the notion of c-continuation, Ziadi et al. presented a fast computation of the equation automaton in O(m2) time complexity. In this paper, we design an output-sensitive algorithm combining advantages of the previous algorithms and show that its computational complexity can be reduced to O(m×|Q≡e|), where |Q≡e| denotes the number of states of the equation automaton, by an epsilon-removal and Bubenzer minimization algorithm of an Acyclic Deterministic Finite Automata (ADFA).

Dates et versions

hal-03515718 , version 1 (06-01-2022)

Identifiants

Citer

Faissal Ouardi, Zineb Lotfi, Bilal Elghadyry. Efficient Construction of the Equation Automaton. Algorithms, 2021, 14 (8), pp.238. ⟨10.3390/a14080238⟩. ⟨hal-03515718⟩
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