Semirings, automata, languages
Semirings, automata, languages
Rational series and their languages
Rational series and their languages
Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Power Series, and Coinduction: Taking Input Derivatives Seriously
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Glushkov Construction for Multiplicities
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
New Finite Automaton Constructions Based on Canonical Derivatives
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
Derivatives of rational expressions with multiplicity
Theoretical Computer Science
An Efficient Computation of the Equation K-automaton of a Regular K-expression
Fundamenta Informaticae
An efficient computation of the equation K-automaton of a regular K-expression
DLT'07 Proceedings of the 11th international conference on Developments in language theory
An Efficient Computation of the Equation K-automaton of a Regular K-expression
Fundamenta Informaticae
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This paper introduces a generalization of the partial derivatives of rational expressions, due to Antimirov, to rational expressions with multiplicity. We define the derivation of a rational expression with multiplicity in such a way that the result is a polynomial of expressions. This amounts to interpreting the addition symbol at the upper level in the semiring of coefficients.Former results of Brzozowski and of Antimirov are then expressed in that framework that allows to deal with rational power series, and automata and expressions with multiplicity as well.