On Recognizable and Rational Formal Power Series in Partially Commuting Variables

@inproceedings{Droste1997OnRA,
  title={On Recognizable and Rational Formal Power Series in Partially Commuting Variables},
  author={Manfred Droste and Paul Gastin},
  booktitle={ICALP},
  year={1997}
}
We will describe the recognizable formal power series over arbitrary semirings and in partially commuting variables, i.e. over trace monoids. We prove that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to series for which the elements in the support all have the same connected alphabet. The converse is true if the underlying semi-ring is commutative… 
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References

SHOWING 1-10 OF 25 REFERENCES
Semirings and Formal Power Series: Their Relevance to Formal Languages and Automata
  • W. Kuich
  • Computer Science, Mathematics
    Handbook of Formal Languages
  • 1997
The purpose of Chapter 9 is to develop some classical results on formal languages and automata by an algebraic treatment using semirings, formal power series and matrices. The use of semirings,
Rational series and their languages
TLDR
This chapter discusses the development of Rational Series over a Principal Ring, a model based on the model developed in Chapter I, and its applications to Languages and Codes.
Automata-Theoretic Aspects of Formal Power Series
TLDR
The style has sometimes been characterized as austere or severe, but the author does expect the reader to be able to fill in the more obvious details and the author permits him to present the leading ideas in an uncluttered way.
Theory of Traces
Concurrent Program Schemes and their Interpretations
TLDR
It is shown that to each scheme corresponds a set of equations determining the result of the scheme; it is shown how these equations can be solved and that the solutions of these equations are regular trace languages.
Combinatorics on Traces
  • V. Diekert
  • Mathematics
    Lecture Notes in Computer Science
  • 1990
TLDR
Free partialy commutative monoids with full semi-thue systems and mobius functions and trace replacement systems are presented.
Partial Commutation and Traces
TLDR
Parallelism and concurrency are fundamental concepts in computer science and concerns the authors' daily life whether software written for distributed systems behaves correctly.
The Book of Traces
Organoaluminum compounds possessing a vinylic aluminaoxacyclopentane moiety are described. They are prepared by reacting a nonionic organoaluminum compound possessing an aluminacyclopentene moiety
Editors
  • Computer Science
    Brain Research Bulletin
  • 1986
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