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
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Information and Computation
Automata, Languages, and Machines
Automata, Languages, and Machines
Theoretical Computer Science - Words, languages and combinatorics
Partial Conway and Iteration Semirings
Fundamenta Informaticae
Axiomatizing rational power series over natural numbers
Information and Computation
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A Conway semiring is a semiring S equipped with a unary operation *:S→S, called “star”, satisfying the sum star and product star identities. A Conway semiring-semimodule pair consists of a Conway semiring S and a left S-semimodule V together with a function ω: S→V, called “omega power”, subject to the sum omega and product omega identities. A Kleene type theorem holds in all Conway semiring-semimodule pairs that can be instantiated to give the equivalence of Büchi automata and regular languages over ω-words. However, sometimes the star and omega power operations cannot be defined in an appropriate manner on the whole semiring S. To handle this situation, we introduce partial Conway semiring-semimodule pairs and develop their basic theory in connection with automata. We prove a Kleene theorem, applicable to all partial Conway semiring-semimodule pairs.