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首页> 外文期刊>IEEE Transactions on Automatic Control >A probabilistic language formalism for stochastic discrete-eventsystems
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A probabilistic language formalism for stochastic discrete-eventsystems

机译：随机离散事件系统的一种概率语言形式主义

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摘要

The formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete-event systems. A probabilistic language is a unit interval-valued map over the set of traces of the system satisfying certain consistency constraints. Regular language operators such as choice, concatenation, and Kleene-closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones. The set of probabilistic languages is closed under such operators, thus forming an algebra. It also is a complete partial order under a natural ordering in which the operators are continuous. Hence, recursive equations can be solved in this algebra. This is alternatively derived by using the contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space. The notion of regularity, i.e., finiteness of automata representation, of probabilistic languages has been defined and it is shown that regularity is preserved under choice, concatenation, and Kleene-closure. We show that this formalism is also useful in describing system performance measures such as completion time, reliability, etc., and present properties to aide their computation
机译：概率语言的形式主义已被引入，以对随机离散事件系统的定性行为进行建模。概率语言是满足某些一致性约束的系统跟踪集上的单位间隔值映射。在概率语言的设置中已经定义了诸如选择，连接和Kleene闭包之类的常规语言运算符，以允许根据较简单的系统对复杂的系统进行建模。概率语言集在此类运算符下是封闭的，因此形成了代数。在操作员连续的自然排序下，它也是一个完整的局部订单。因此，可以在该代数中求解递归方程。可替代地，这通过使用概率语言集合上的收缩映射定理来推导，该概率映射定理显示为一个完整的度量空间。已经定义了概率性语言的规则性概念，即自动机表示的有限性，并且表明规则性在选择，连接和Kleene闭包下得以保留。我们表明，这种形式主义在描述系统性能度量（例如完成时间，可靠性等）方面也很有用，并提供了一些属性来辅助其计算

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