Advances in Petri nets 1986, part II on Petri nets: applications and relationships to other models of concurrency
Easy multiplications. I. The realm of Kleene's theorem
Information and Computation
Combinatorics on traces
Easy multiplications. II. extensions of rational semigroups
Information and Computation
Recognizable languages in concurrency monoids
Theoretical Computer Science
Theoretical Computer Science
The Book of Traces
Word Processing in Groups
Stable Models of Typed lambda-Calculi
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
On Recognizable Languages in Divisibility Monoids
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Recognizable languages in divisibility monoids
Mathematical Structures in Computer Science
On relations defined by generalized finite automata
IBM Journal of Research and Development
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We present three results on divisibility monoids. These divisibility monoids were introduced in [11] as an algebraic generalization of Mazurkiewicz trace monoids. (1) We give a decidable class of presentations that gives rise precisely to all divisibility monoids. (2) We show that any divisibility monoid is an automatic monoid [5]. This implies that its word problem is solvable in quadratic time. (3) We investigate when a divisibility monoid satisfies Kleene's Theorem. It turns out that this is the case iff the divisibility monoid is a rational monoid [25] iff it is width-bounded. The two latter results rest on a normal form for the elements of a divisibility monoid that generalizes the Foata normal form known from the theory of Mazurkiewicz traces.