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We continue our study of negotations, a concurrency model with multipartynegotiation as primitive. In a previous paper (arXiv:13072145) we have provideda correct and complete set of reduction rules for sound, acyclic, and (weakly)deterministic negotiations. In this paper we extend this result to alldeterministic negotiations, including cyclic ones. We also show that this setof rules allows one to decide soundness and to summarize negotiations inpolynomial time.

On Negotiation as Concurrency Primitive II: Deterministic Cyclic Negotiations