动态文法的随机过程语义
Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview
摘要：
我们定义了一类概率模型的随机过程的算子代数，并表示这一类随机参数化文法。语法的语法规范被映射到由运算符环给出的语义，因此语法组合对应于运算符加法或乘法。算子是随机过程时间演化的生成元。在这个建模框架内，可以表示数据聚类模型，逻辑程序，普通和随机微分方程，图形语法，和随机化学反应动力学。这个数学公式将这些看似遥远的场相互联系起来，并与量子场论和算子代数的数学方法联系起来。
英文摘要：
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatical composition corresponds to operator addition or multiplication. The operators are generators for the time-evolution of stochastic processes. Within this modeling framework one can express data clustering models, logic programs, ordinary and stochastic differential equations, graph grammars, and stochastic chemical reaction kinetics. This mathematical formulation connects these apparently distant fields to one another and to mathematical methods from quantum field theory and operator algebra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
