Algebraic approaches to program semantics
Algebraic approaches to program semantics
The Kleene and the Parikh theorem in complete semirings
14th International Colloquium on Automata, languages and programming
Selected contributions on Trends, techniques, and problems in theoretical computer science. 4th International Meeting of Young Computer Scientists
On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Complete systems of B -rational identities
Theoretical Computer Science
The theory of semirings with applications in mathematics and theoretical computer science
The theory of semirings with applications in mathematics and 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
Continuous monoids and semirings
Theoretical Computer Science - Logic, semantics and theory of programming
*-μ-Semirings and *-μ-lamda;-semirings
Theoretical Computer Science
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Partial Conway and Iteration Semirings
Fundamenta Informaticae
A Mezei-Wright theorem for categorical algebras
Theoretical Computer Science
A semiring-semimodule generalization of transducers and abstract ω-families of power series
Journal of Automata, Languages and Combinatorics
A unifying Kleene theorem for weighted finite automata
Rainbow of computer science
Partial conway and iteration semiring-semimodule pairs
Algebraic Foundations in Computer Science
Partial Conway and Iteration Semirings
Fundamenta Informaticae
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One of the most well-known induction principles in computer science is the fixed point induction rule, or least pre-fixed point rule. Inductive *-semirings are partially ordered semirings equipped with a star operation satisfying the fixed point equation and the fixed point induction rule for linear terms. Inductive *-semirings are extensions of continuous semirings and the Kleene algebras of Conway and Kozen.We develop, in a systematic way, the rudiments of the theory of inductive *-semirings in relation to automata, languages and power series. In particular, we prove that if S is an inductive *-semiring, then so is the semiring of matrices Sn×n, for any integer n ≥ 0, and that if S is an inductive *-semiring, then so is any semiring of power series S«A*». As shown by Kozen, the dual of an inductive *-semiring may not be inductive. In contrast, we show that the dual of an iteration semiring is an iteration semiring. Kuich proved a general Kleene theorem for continuous semirings, and Bloom and Ésik proved a Kleene theorem for all Conway semirings. Since any inductive *-semiring is a Conway semiring and an iteration semiring, as we show, there results a Kleene theorem applicable to all inductive *-semirings. We also describe the structure of the initial inductive *-semiring and conjecture that any free inductive *-semiring may be given as a semiring of rational power series with coefficients in the initial inductive *-semiring. We relate this conjecture to recent axiomatization results on the equational theory of the regular sets.