A W- semigroup is defined as a lattice - ordered semigroup with zero, the lattice of which is complete and in which multiplication is. completely distributive over joins. This paper discusses W-nets , i.e. finite directed graphs the edges of which are labeled by dements of a W - semigroup. It unifies and extends various results concerning switching nets, communication nets, edge sequences in finite graphs, finite - state languages, nondeterministic automata, and derivatives (quotients) of regular expressions.
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