Computational semantics of term rewriting systems
Algebraic methods in semantics
Advances in Petri nets 1986, part II on Petri nets: applications and relationships to other models of concurrency
Easy multiplications. I. The realm of Kleene's theorem
Information and Computation
Theoretical Computer Science
Recognizable closures and submonoids of free partially commutative monoids
Theoretical Computer Science
Recognizable languages in concurrency monoids
Theoretical Computer Science
Partial commutation and traces
Handbook of formal languages, vol. 3
Domains and lambda-calculi
Minimal and Optimal Computations of Recursive Programs
Journal of the ACM (JACM)
The Book of Traces
Computations, Residuals, and the POwer of Indeterminancy
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Divisibility Monoids: Presentation, Word Problem, and Rational Languages
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
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Kleene's theorem on recognizable languages in free monoids is considered to be of eminent importance in theoretical computer science. It has been generalized into various directions, including trace and rational monoids. Here, we investigate divisibility monoids which are defined by and capture algebraic properties sufficient to obtain a characterization of the recognizable languages by certain rational expressions as known from trace theory. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to our divisibility monoids. We obtain Ochmański's theorem on recognizable languages in free partially commutative monoids as a consequence.