Algorithmics of Posets Generated by Words Over Partially Commutative Alphabets (Extended)

It is natural to relate partially ordered sets (posets in short) and classes of equivalent words over partially commutative alphabets. Their common graphical representation are Hasse diagrams. We investigate this relation in detail and propose an efficient online algorithm that decompresses a concurrent word to its Hasse diagram. The lexicographically minimal representative of a trace (an equivalence class of words) is called its lexicographical normal form. We give an algorithm which enumerates, in the lexicographical order, all distinct traces identified by their lexicographical normal forms. The two presented algorithms are the main contribution of this paper.