ACM Transactions on Programming Languages and Systems (TOPLAS)
Canonical derivatives, partial derivatives and finite automaton constructions
Theoretical Computer Science
Kleene Algebra with Tests: Completeness and Decidability
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
The Complexity of Kleene Algebra with Tests
The Complexity of Kleene Algebra with Tests
Analytic Combinatorics
On the Average Size of Glushkov's Automata
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Regular expressions and the equivalence of programs
Journal of Computer and System Sciences
From Mirkin's Prebases to Antimirov's Word Partial Derivatives
Fundamenta Informaticae
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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 ($\mathcal{A}_{\mathsf{pos}}$), and a new construction based on the notion of prebase (equation automata, $\mathcal{A}_{\mathsf{eq}}$). 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 $\mathcal{A}_{{\mathsf{pos}}}$ is linear in the size of the KAT expression.