Rational series and their languages
Rational series and their languages
Complete systems of B -rational identities
Theoretical Computer Science
Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
Information and Computation
Automata, Languages, and Machines
Automata, Languages, and Machines
Theoretical Computer Science - Words, languages and combinatorics
Axiomatizing rational power series over natural numbers
Information and Computation
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Axiomatizing rational power series over natural numbers
Information and Computation
Cycle-Free Finite Automata in Partial Iterative Semirings
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
A Kleene-Schützenberger theorem for weighted timed automata
Theoretical Computer Science
A unifying Kleene theorem for weighted finite automata
Rainbow of computer science
Partial conway and iteration semiring-semimodule pairs
Algebraic Foundations in Computer Science
Kleene theorem in partial conway theories with applications
Algebraic Foundations in Computer Science
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
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A Conway semiring is a semiring S equipped with a unary operation *: S → S, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally important semirings, such as N or N$^{rat}$≪Σ≫ of rational power series of words on Σ with coefficients in N, cannot have a total star operation satisfying the Conway identities. We introduce here partial Conway semirings, which are semirings S which have a star operation defined only on an ideal of S; when the arguments are appropriate, the operation satisfies the above identities. We develop the general theory of partial Conway semirings and prove a Kleene theorem for this generalization.