Negotiation as concurrency primitive

Abstract

This paper introduces negotiations, a model of concurrency close to Petri nets, with multi-party negotiations as concurrency primitive. We study two fundamental analysis problems. The soundness problem consists of deciding if it is always possible for a negotiation to terminate successfully, whatever the current state is. Given a sound negotiation, the summarization problem aims at computing an equivalent one-step negotiation with the same input/output behavior. The soundness and summarization problems can be solved by means of simple algorithms acting on the state space of the negotiation, which however face the well-known state explosion problem. We study alternative algorithms that avoid the construction of the state space. In particular, we define reduction rules that simplify a negotiation while preserving the sound/non-sound character of the negotiation and its summary. In a first result we show that our rules are complete for the class of weakly deterministic acyclic negotiations, meaning that they reduce all sound negotiations in this class, and only them, to equivalent one-step negotiations. This provides algorithms for both the soundness and summarization problems that avoid the construction of the state space. We then study the class of deterministic negotiations. Our second main result shows that the rules are also complete for this class, even if the negotiation contains cycles. Moreover, we present an algorithm that completely reduces all sound deterministic negotiations, and only them, in polynomial time.

Timed Negotiations

“…A negotiation is deterministic iff all its processes are deterministic. It is weakly nondeterministic [9] (called weakly deterministic in [3]) iff, for every node n, one of the processes in P n is deterministic. Last, it is very weakly non-deterministic [9] (called weakly deterministic in [6]) iff, for every n, every p ∈ P n and every outcome r of n, there exists a deterministic process q such that q ∈ P n for every n ∈ X (n, p, r).…”

“…Semantics: A configuration [3] of a negotiation is a mapping M : P → 2 N . Intuitively, it tells for each process p the set M (p) of nodes p is ready to engage in.…”

“…For acyclic negotiations, it is in DP and co-NP-Hard [6]. Determining whether an acyclic weakly non-deterministic negotiation is sound is in PTIME [3,9]. Finally, deciding soundness for deterministic negotiations is NLOGSPACE-complete [9].…”

“…Step 2 : Before we introduce timing on N φ , we introduce a new outcome r at n 0 which takes all processes to n f . Now, the timing function γ associated with N φ is: γ(n 0 , r) = [2,2] and γ(n 0 , r ) = [3,3] and γ(n, r) = [0, 0], for all node n = n 0 and all r ∈ R n . Then, mintime(N φ ) ≤ 2 iff φ has a satisfiable assignment: if mintime(N φ ) ≤ 2, there is a run with decision r taken at n 0 which is final.…”

“…the original model, while preserving the property under analysis. In the context of negotiations, [7,3] proposed a sound and complete set of soundness-preserving reduction rules and algorithms to apply these rules efficiently. The question of soundness for deterministic negotiations was revisited in [9] and showed NLOGSPACEcomplete using anti patterns instead of reduction rules.…”