Abstract
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).
Highlights
Introduction of the Equation AutomatonThe equation automaton was first introduced in Mirkin’s paper [1]
In [2], Antimirov introduced the notion of partial derivative of a regular expression, that lead to another definition and construction of the equation automaton
They proved that this automaton is isomorphic to the position automaton and that the equation automaton is its quotient for some equivalence relation
Summary
We introduce briefly the notion of finite automata. For further details on formal aspects of finite automata theory, we recommend reading classical books [14,15].
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