The Kleene and the Parikh theorem in complete semirings
14th International Colloquium on Automata, languages and programming
Rational series and their languages
Rational series and their languages
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
Models of a K-rational identity system
Journal of Computer and System Sciences
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Selected papers of the second international colloquium on Words, languages and combinatorics
The equational logic of fixed points
Theoretical Computer Science
Information and Computation
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Communication and Concurrency
Automata, Languages, and Machines
Automata, Languages, and Machines
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Equational theories of tropical semirings
Theoretical Computer Science - Foundations of software science and computation structures
Partial Conway and Iteration Semirings
Fundamenta Informaticae
Handbook of Weighted Automata
On fixed point equations over commutative semirings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Conjugacy and equivalence of weighted automata and functional transducers
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
On the equivalence of Z-automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Partial Conway and Iteration Semirings
Fundamenta Informaticae
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
Sound and Complete Axiomatizations of Coalgebraic Language Equivalence
ACM Transactions on Computational Logic (TOCL)
A Connection Between Concurrency and Language Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
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Iteration semi-rings are Conway semi-rings satisfying Conway's group identities. We show that the semi-rings N^r^a^t of rational power series with coefficients in the semi-ring N of natural numbers are the free partial iteration semi-rings. Moreover, we characterize the semi-rings N"~"^"r"^"a"^"t as the free semi-rings in the variety of iteration semi-rings defined by three additional simple identities, where N"~ is the completion of N obtained by adding a point of infinity. We also show that this latter variety coincides with the variety generated by the complete, or continuous semirings. As a consequence of these results, we obtain that the semi-rings N"~^r^a^t, equipped with the sum order, are free in the class of symmetric inductive ^*-semi-rings. This characterization corresponds to Kozen's axiomatization of regular languages.