Complexity results for POMSET languages

“…For arbitrary partial strings, the refinement ordering ⊑ from Definition 3.5 is different from the containment of two pomset languages, cf. [7]. For example, the languages of the partial strings (a; b) (a; b) and N(a, a, b, b) -as shown in Figure 2 and 3, respectively -are contained in each other but (a; b) (a; b) N(a, a, b, b), see also Pratt [21,p.…”

Section: Proposition 33 If the Alphabet γ And Universe Of Events E Is...mentioning

confidence: 99%

Concurrent Kleene Algebra of Partial Strings

Horn,

Alglave

2014

Preprint

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Concurrent Kleene Algebra (CKA) is a recently proposed algebraic structure by Hoare and collaborators that unifies the laws of concurrent programming. The unifying power of CKA rests largely on the so-called exchange law that describes how concurrent and sequential composition operators can be interchanged. Based on extensive theoretical work on true concurrency in the past, this paper extends Gischer's pomset model with least fixed point operators and formalizes the program refinement relation by Ésik's monotonic bijective morphisms to construct a partial order model of CKA. The existence of such a model is relevant when we want to prove and disprove properties about concurrent programs with loops. In particular, it gives a foundation for the analysis of programs that concurrently access relaxed memory as shown in subsequent work.

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“…Complexity While the complexity of the membership problem for pomset languages in general is NP-complete (Feigenbaum et al, 1993), by restricting the context sensitivity of the pomset grammars, polynomial time complexity is achievable. The complexity of the parsing of IDL graphs is O(n 3k ) (Nederhof and Satta, 2004) where k is the width of the graph, and the width is a measurement of the number of paths being traversed in parallel, i.e.…”

Section: Pomset Graphsmentioning

confidence: 99%