Semirings, automata, languages
Semirings, automata, languages
Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Characterization of Glushkov automata
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Canonical derivatives, partial derivatives and finite automaton constructions
Theoretical Computer Science
Derivation of Rational Expressions with Multiplicity
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Brzozowski's Derivatives Extended to Multiplicities
CIAA '01 Revised Papers from the 6th International Conference on Implementation and Application of Automata
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
From Glushkov WFAs to rational expressions
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Fundamenta Informaticae
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
Regular expressions on average and in the long run
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Bisimulations for fuzzy automata
Fuzzy Sets and Systems
On the equivalence of Z-automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A unified construction of the glushkov, follow, and antimirov automata
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Valuations of weighted automata: doing it in a rational way
Algebraic Foundations in Computer Science
The language, the expression, and the (small) automaton
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
From Glushkov WFAs to \mathbb{K}-Expressions
Fundamenta Informaticae
An Efficient Computation of the Equation K-automaton of a Regular K-expression
Fundamenta Informaticae
Fundamenta Informaticae
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
The removal of weighted ε-transitions
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Nondeterministic automata: Equivalence, bisimulations, and uniform relations
Information Sciences: an International Journal
Hi-index | 5.23 |
This paper addresses the problem of turning a rational (i.e. regular) expression into a finite automaton. We formalize and generalize the idea of "partial derivatives" introduced in 1995 by Antimirov, in order to obtain a construction of an automaton with multiplicity from a rational expression describing a formal power series with coefficients in a semiring.We first define precisely what is such a rational expression with multiplicity and which hypothesis should be put on the semiring of coefficients in order to keep the usual identities.We then define the derivative of such a rational expression as a linear combination of expressions called derived terms and we show that all derivatives of a given expression are generated by a finite set of derived terms, that yields a finite automaton with multiplicity whose behaviour is the series denoted by the expression. We also prove that this automaton is a quotient of the standard (or Glushkov) automaton of the expression. Finally, we propose and discuss some possible modifications to our definition of derivation.