取值于赋值幺半群的加权下推自动机的代数性质

Algebraic properties of weighted pushdown automata over valuation monoid

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。

By introducing the concepts of weighted pushdown automata and weighted normalized pushdown automata over valuation monoid, the equivalence of weighted pushdown automata and weigh- ted normalized pushdown automata over double unitary valuation monoid is proved. It is shown that the fact that weighted pushdown automata can accept the same formal power series by final states and by empty stack at the same time. The closed properties of weighted context-free languages under some regu- lar operations such as sum, concatenation and positive Kleene closure are dealt with as well. The main conclusions show that whether those properties of weighted pushdown automata are valid or not doesn＇t rely on the distributivity or associativity of valuation monoid.