Methods for Computing the Concurrency Degree of Commutation Monoids

Nasser Saheb () and Akka Zemmari ()
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Nasser Saheb: Université Bordeaux I, LaBRI
Akka Zemmari: Université Bordeaux I, LaBRI

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 731-742 from Springer

Abstract: 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.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_72

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