Negotiations: A Model for Tractable Concurrency.

并发理论投入了大量的精力来研究各种各样的通信原语，如共享变量、点对点FIFO通道、重传或可靠广播。特别是，验证问题的复杂性，通过这些原语的抽象机器通信是非常好的研究。不幸的是，在最坏情况下的复杂性的大小的系统是非常高的，范围从PSPACE困难的下界表示的指数，甚至非原始递归函数。我们最近开始研究一种新的沟通原语，称为谈判。谈判是同步和不确定性选择的结合（这个名字是因为在谈判中有许多方相遇--即，synchronize同步--to select选择one outof a number数of outcomes结果--即，为了进行我们的研究，我们引入了协商图，一个以原子协商为原语的并发模型。该模型接近于1-安全有色Petri网。我们的工作已经确定了一个子类的模型，称为deterministicnegotiation图，表现出非常好的属性。特别是，即使模型受到状态爆炸问题的影响，基本属性如可靠性（类似于没有死锁和活锁的属性）也可以在多项式时间内检查。我们还设计了一个小的编程语言，它可以准确地捕捉声音确定性谈判图。以确定性谈判图为出发点，我们建议研究越来越多的并发系统的表达模型，同时保持低于PSPACE的复杂性barrier.While这项工作的动机主要是理论，我们将使用的结果来设计一个小programminglanguage并行程序，连同一个简单的霍尔逻辑，和工具支持自动产生distributedimplementations的程序。

Concurrency theory has devoted much effort to thestudy of a large variety of communication primitives, likeshared variables, point-to-point FIFO channels, rendez-vous, or reliable broadcasts. In particular, the complexity of verification problems for abstract machines communicating by means of these primitives is very well studied. Unfortunately,the worst-case complexity in the size of the system is very high, ranging from PSPACE-hard to lower bounds expressed in terms oftower of exponentials, or even non-primitive recursive functions. We have recently initiated the study of a novel communication primitive, called negotiation. Negotiation is a combination of synchronization and nondeterministic choice(the name is due to the fact that in a negotiation a numberof parties meet--i.e., synchronize--in order to select one outof a number of outcomes--i.e., to conduct a nondeterministic choice).In order to conduct our study, we have introduced negotiation diagrams,a concurrency model with atomic negotiations as primitive. The modelis close to 1-safe colored Petri nets. Our work has identified a subclass of the model, called deterministicnegotiation diagrams, that exhibits exceptionally good properties. In particular, even though the model is subject tothe state-explosion problem, fundamental properties like soundness(a property similar to absence of deadlocks and livelocks) can be checked in polynomial time. We have alsodesigned a small programming language which captures exactly the sounddeterministic negotiation diagrams. Taking deterministic negotiation diagrams as starting point, we propose to study increasingly expressive models of concurrent systems,while at the same time remaining below the PSPACE complexity barrier.While the motivation of this work is mostly theoretical,we will use the results to design a small programminglanguage for parallel programs, together with a simple Hoare logic, and tool support to automatically produce distributedimplementations of programs.