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Methods for Computing the Concurrency Degree of Commutation Monoids

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • Nasser Saheb

    (Université Bordeaux I, LaBRI)

  • Akka Zemmari

    (Université Bordeaux I, LaBRI)

Abstract

Mazurkiewicz proposed trace monoids to model syntactically concurrent processes. A commutation system is an action alphabet A together with a binary relation θ. Whenever (a, b) ∈ θ, the actions a and b are not causally related and, therefore, they are allowed to commute. Thus the elements of θ are pairs of letters (or actions) which may be performed simultaneously. The Foata normal form allows to maximize the rate of simultaneity for a word from A*. In [10], the concurrency degree for a non-empty word w is defined as the ratio between the length of the word and the number of its factors in the Foata normal form. It has been shown that each commutation monoid has a degree which is common to almost all infinite words. Here, we introduce new methods for an exact computation in a few cases and a method for its approximation in general.

Suggested Citation

  • Nasser Saheb & Akka Zemmari, 2000. "Methods for Computing the Concurrency Degree of Commutation Monoids," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 731-742, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_72
    DOI: 10.1007/978-3-662-04166-6_72
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