Rational series and their languages
Rational series and their languages
Partial commutation and traces
Handbook of formal languages, vol. 3
The Kleene-Schützenberger theorem for formal power series in partially commuting variables
Information and Computation
The Book of Traces
Weighted asynchronous cellular automata
Theoretical Computer Science
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Expressiveness and Closure Properties for Quantitative Languages
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Weighted finite automata over strong bimonoids
Information Sciences: an International Journal
Handbook of Weighted Automata
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
DLT'10 Proceedings of the 14th international conference on Developments in language theory
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
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We study weighted trace automata with weights in strong bimonoids. Traces form a generalization of words that allow to model concurrency; strong bimonoids are algebraic structures that can be regarded as “semirings without distributivity”. A very important example for the latter are bounded lattices, especially non-distributive ones. We show that if both operations of the bimonoid are locally finite, then the classes of recognizable and mc-rational trace series coincide and, in general, are properly contained in the class of c-rational series. Moreover, if, in addition, in the bimonoid the addition is idempotent and the multiplication is commutative, then all three classes coincide.