Uniform Generation in Trace Monoids

Samy Abbes (1) , Jean Mairesse (2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 APR - Algorithmes, Programmes et Résolution

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components—a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.

Mots clés: trace monoid; uniform generation; Möbius polynomial

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]; Théorie et langage formel [cs.FL]

Samy Abbes, Jean Mairesse. Uniform Generation in Trace Monoids. Mathematical Foundations of Computer Science 2015, Aug 2015, Milan, Italy. pp.63-75, ⟨10.1007/978-3-662-48057-1_5⟩. ⟨hal-01328454⟩