From regular expressions to deterministic automata
Theoretical Computer Science
Regular expressions into finite automata
Theoretical Computer Science
Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
From regular expressions to DFA's using compressed NFA's
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Automata and Computability
Canonical derivatives, partial derivatives and finite automaton constructions
Theoretical Computer Science
A New Quadratic Algorithm to Convert a Regular Expression into an Automaton
WIA '96 Revised Papers from the First International Workshop on Implementing Automata
Constructing a finite automaton for a given regular expression
ACM SIGACT News
From Mirkin's Prebases to Antimirov's Word Partial Derivatives
Fundamenta Informaticae
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
Elements of Automata Theory
The complexity of regular(-like) expressions
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Deciding regular expressions (in-)equivalence in coq
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
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In this paper, the relation between the Glushkov automaton (Apos) and the partial derivative automaton (Apd) of a given regular expression, in terms of transition complexity, is studied. The average transition complexity of Apos was proved by Nicaud to be linear in the size of the corresponding expression. This result was obtained using an upper bound of the number of transitions of Apos. Here we present a new quadratic construction of Apos that leads to a more elegant and straightforward implementation, and that allows the exact counting of the number of transitions. Based on that, a better estimation of the average size is presented. Asymptotically, and as the alphabet size grows, the number of transitions per state is on average 2. Broda et al. computed an upper bound for the ratio of the number of states of Apd to the number of states of Apos, which is about 1/2 for large alphabet sizes. Here we show how to obtain an upper bound for the number of transitions in Apd, which we then use to get an average case approximation. Some experimental results are presented that illustrate the quality of our estimate.