取值于赋值幺半群的加权下推自动机的代数性质

发布时间：2018-10-30 08:27

【摘要】：引入取值于赋值幺半群的加权下推自动机、标准型加权下推自动机的定义,证明了在双幺赋值幺半群框架下,加权下推自动机与标准型加权下推自动机相互等价,且以终态方式与以空栈方式识别语言的加权下推自动机能够识别相同的形式幂级数;在Cauchy双幺赋值幺半群上,加权上下文无关语言对于和、连接、正克林闭包运算封闭。结果表明加权下推自动机的诸多性质并不依赖于赋值幺半群的分配律和结合律。
[Abstract]:In this paper, we introduce the definition of weighted pushdown automaton and standard type weighted push-down automaton, and prove that the weighted push-down automata is equivalent to the canonical weighted push-down automaton under the framework of double-unvalued monoids. The weighted push-down automata, which uses the final state and the empty stack to recognize language, can recognize the same formal power series. On Cauchy doubly valued monoids, weighted context-independent language pairs are connected, and positive clinker closure operations are closed. The results show that many properties of weighted push-down automata do not depend on the distribution law and associative law of the assignment monoids.
【作者单位】：陕西师范大学数学与信息科学学院;
【基金】：国家自然科学基金(11401361,11226266) 中央高校基本科研业务费专项资金(GK201402002) 陕西省教育厅自然科学专项科研计划(16JK1373)
【分类号】：O152.7

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