Generating words in a context-free language uniformly at random
Information Processing Letters
Partial derivatives of regular expressions and finite automaton constructions
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
Information and Computation
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
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Elements of Automata Theory
Enumerating regular expressions and their languages
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Partial derivative automata formalized in Coq
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Partially ordered two-way büchi automata
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
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The partial derivative automaton (Apd) is usually smaller than other non-deterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptotic behaviour. This depends on the alphabet size, k, and its limit, as k goes to infinity, is 1/2. The lower bound corresponds exactly to consider the Apd automaton for the marked version of the regular expression, i.e. where all its letters are made different. Experimental results suggest that the average number of states of this automaton, and of the Apd automaton for the unmarked regular expression, are very close to each other.