自动机

Now that the L-valued fuzzy state automata has such powerful computation capacity, it is necessary to traverse the algebraic properties such as transformation semigroups,products and covering relations in L-valued fuzzy automata in order to show the close correspondence between the algebraic properties and the latticeordered monoid.

既然格值自动机具有如此强大的计算能力，有必要对其从代数角度出发较详细地，较深入地研究此类自动机的变换半群，乘积和覆盖关系，揭示此类自动机的代数性质和格半群间的紧密联系。

At the same time , we discuss the determinism and nondeterminism of formula-clock automata and the closure propertied under Boolean operation of the language which is accepted by formula-clock automata. We also prove the expressive equivalence between the deterministic formula-clock automata and the nondeterministic formula-clock automata. This means that every nondeterministic formula-clock automata can be transformed to a deterministic formula-clock automata which exactly accept the timed language identified by the fomer.We also extend timed words to infiniteness and define the formula-clock Buchi automata and the formula-clock Muller automata. At last, we show its application in formal verification and modeling of real-time system.

然后讨论了公式时钟自动机的确定性和非确定性，公式时钟自动机识别的语言类在并、交、补运算下的封闭性；并证明了确定的公式时钟自动机和非确定的公式时钟自动机表达能力的等价性，这意味这每一个非确定的公式时钟自动机都能转换为一个与之识别相同时间语言的确定的公式时钟自动机；我们将时间字扩展为无穷的，从而定义了公式时钟Buchi自动机与公式时钟Muller自动机；最后给出了用它进行实时系统的形式化验证方面及对实时系统建模的应用。

In chapter three, we first give the definition of quadratic automata (3. 6 definition), then study their invertibility. 3. 10 theorem gives a sufficient and necessary conditions for weak inverse quadratic form finite automata, and a way to find the one whose weak inverse is quadratic form finite automata.

第三章首先构造了二次型有限自动机类（3.6定义），研究其上的可逆性理论。3.10定理给出了弱逆二次型有限自动机的充要条件及弱原逆的求法、3.12定理则给出了弱可逆二次型有限自动机的充要条件及弱逆的求法。

Then we found bijections between quadratic form finite automata and input memory linear automata which lead to a way to produce all weakly invertible or weak inverse quadratic form finite automata. In the last section of chapter three, we extend these results to a more general class of nonlinear finite automata (called qusi-quadratic form finite automata).

然后我们建立了建立全体二次型有限自动机与全体输入存储线性有限自动机之间的的一个一一对应L，由于L保持弱逆性（3.20定理），由此我们得到了产生全体可逆二次型有限自动机的方法：要产生一个具有某种可逆性的二次型有限自动机只需产生一个具有同种可逆性的输入存储线性有限自动机，然后作其二次型提升即可。

Establish integrated invertibility theory over it: By R〓R〓 transformation method, we solve the problem of deciding weakly invertibility and finding weak inverse, By founding the bijections between all quadratic form automata and input memory linear finite automata, we find a algorithm to produce all weak inverse quadratic form finite automata.

本文着眼于这些最基本问题，将有限域上的二次型和置换多项式理论引入有限自动机可逆性的研究，构造了一类由二次型构成的非线性有限自动机（3.6定义），称之为二次型有限自动机，我们在其上面建立了与线性有限自动机可逆性理论相对应的完整的可逆性理论：采用线性R〓R〓变换方法，解决了此类有限自动机的弱可逆性判定、求弱逆问题（3.10、3.12定理）、通过建立全体二次型有限自动机与全体输入存储线性有限自动机之间的保持弱逆性的一一对应，给出了产生全部可逆二次型有限自动机的方法。

In this project, we investigate the invertibility problem of finite automata, cryptosystems based on finite automata theory and security protocols. Some applications of the finite automata public key cryptosystem to internet are explored.

本项目研究有限自动机可逆性问题和基于自动机理论的密码算法与安全协议，探讨有限自动机公开钥密码在因特网环境的应用。

We have established some properties of languages of Lattice of Quantum Automata. For example, the definitions of Right-Linear Grammars of Lattice of Quantum, Regular Sets of Lattice of Quantum and Regular Expressions of Lattice of Quantum have been given.

我们证明了量子自动机格有一些重要的性质：它是分配格当且仅当自动机的基格是分配的；它是模格当且仅当自动机的基格是模格；它是完全格当且仅当自动机的基格是完全格。

And there is an approximate linear relationship between the momentum of the automatic mechanism and the length of the gas tube.

如β=〓与β=〓相比较（β角单位为弧度，其定义详见正文），前者与后者对应的气室最大压力之比可达65%，而对应的自动机动能之比可达60%；导气管内径对气室内气体压力冲量和自动机动能的影响存在极值点，且该极值点随导气孔的增大而有规律的增大；导气管长度对气室最大压力、压力冲量和自动机动能的影响呈单调递减规律，且自动机动量与管道长度之间近似符合一直线关系。

Firstly, the disadvantageous of the present system' in operation was analyzed and the relevant automaton state diagram was painted. Furthermore, according to the finite automaton is a useful model, the new automatic system, that is, the toll collector system by charging to the account was designed and the relevant automaton state diagram was painted.

首先分析了现行的自动收费站系统中的不足之处，画出了相应的自动机状态转移图，然后依据有穷自动机是一种具有离散输入输出系统的数学模型，提出了新的收费站自动机设计－记账式收费自动机的模型及相应的自动机状态转移图，进而给出了详细的分析和应用软件，并画出了相应的系统模块图。

Secondly, in a more generalized framestructrue--lattice-ordered monoids,the notion of lattice-valued Mealy-type automata is introduced,we traverse some algebraic properties of this automata and investigate the congruences and homomorphisms of this type automata.Our main results indicate that the algebraic properties of lattice-valued Mealy-type automata have Close links to the algebraic properties of lattice-ordered monoids which automata take values in.Futhermore we study the minimization of lattice-valued Mealy-type automata and provide an algorithm to achieve the minimal lattice-valued Mealy-type automata within finite steps.

其次，在更一般的框架—格半群意义下，提出具有输入和输出字符的自动机——格值Mealy自动机的概念，从代数角度出发较详细地研究了此类自动机具有的性质，同时研究了此类自动机的同余和同态，揭示了此类自动机的代数性质和格半群的紧密联系，最终研究了格值Mealy自动机的极小化问题，并给出了在有限步可实现此极小化的算法。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新