Abstract
Kleene algebra with tests (KAT) is an equational system that extends Kleene algebra, the algebra of regular expressions, and that is specially suited to capture and verify properties of simple imperative programs. In this paper we study two constructions of automata from KAT expressions: the Glushkov automaton (Apos), and a new construction based on the notion of prebase (equation automata, Aeq). Contrary to other automata constructions from KAT expressions, these two constructions enjoy the same descriptional complexity behaviour as their counterparts for regular expressions, both in the worst-case as well as in the average-case. In particular, our main result is to show that, asymptotically and on average the number of transitions of the A pos is linear in the size of the KAT expression. © 2013 Springer-Verlag.
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CITATION STYLE
Broda, S., Machiavelo, A., Moreira, N., & Reis, R. (2013). On the average size of Glushkov and equation automata for KAT expressions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8070 LNCS, pp. 72–83). https://doi.org/10.1007/978-3-642-40164-0_10
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