Concurrency measure in commutation monoids

AbstractThe phenomenon of concurrency is modelled by commutativity. We define for any nonempty word over the action alphabet its concurrency degree, a real number which measures the rate of simultaneousness, when the sequence of actions represented by the word is performed. We study this degree and we show, in particular, that when a word of length n is chosen at random, increases the degree tends with probability 1 to a fixed limit which is completely determined by the commutation system