“closed semiring”的概念、定义、翻译、参考文献-科学参考

closed semiring

Computer

单词	closed semiring
释义	closed semiring Computer A semiring S with two additional properties: (a) if a₁,a₂,…,a_n,… is a countable sequence of elements of S then $a_{1} + a_{2} + \dots + a_{n} + \dots,$ exists and is unique; the order in which the various elements are added is irrelevant; (b) the operation • (see semiring) distributes over countably infinite sums as well as finite sums. A special unary operation called closure can be defined on closed semirings. Given an element a in S, powers can be defined in the expected manner: $\begin{array}{l} a^{0} = 1 \\ a^{n} = a • a^{n - 1} for all n > 0 \end{array}$ Then the closure a* can be defined as follows: $a^{} = 1 + a + a^{2} + \dots + a^{n} + \dots$ The properties of a semiring imply that $a^{} = 1 + a • a^{*}$ Closed semirings have applications in various branches of computing such as automata theory, the theory of grammars, the theory of recursion and fixed points, sequential machines, aspects of matrix manipulation, and various problems involving graphs, e.g. finding shortest-path algorithms within graphs.
随便看	oxidant oxidase oxidation oxidation number oxidation potential oxidation-reduction oxidation state oxidation–reduction oxidative burst oxidative coupling oxidative deamination oxidative decarboxylation oxidative phosphorylation oxide oxide masking oxides oxidizing acid oxidizing agent oxidoreductase oximes oxisol oxo- oxoacid oxonium ion oxo process