The algorithm processes the set of xpaths and compiles three things : a set of states that the transition diagram might go through , the transition function to move from one state to another , and an indication of which states mark successful recognition of an xpath 该算法处理这组xpath ，并编译三样东西：转换图可能经过的一组状态，从一种状态迁移到另一种状态的转换函数，以及表明哪些状态成功地识别了xpath的标记。
Li in [ 41 ] has discussed the properties of transition functions on and obtained that a generally unlimited q - matrix q can generate a positive once integrated semigroup with contractions on up to now , it is the first time to apply the theories of integrated semigroups to ctmcs 上的性质，得出一般的无界q矩阵q在l 。上能生成正的一次压缩积分半群迄今为止，这是首次应用积分半群的理论来研究时间连续markov链
Then we also formulate the model of computing with values via lattice - valued finite state automata , as well as the state transition function of the model of computing with words via lattice - valued finite state automata and the language accepted by lattice - valued finite automata 然后,给出了基于格值有限状态自动机的数值计算的形式模型。同时,建立了输入是词的格值有限状态自动机的转移函数以及格值有限状态自动机所接收的语言的定义。
According to the theory of continuous - time markov chains , given a g - matrix q , it is possible that there exist infinite transition functions and therefore there maybe exist infinite positive contraction semigroups ( co semigroups ) on l1 derived from q - matrix q . but each positive contraction semigroup has and only has one infinitesimal generator 给定一个q -矩阵q ，可能存在无穷多个转移函数，从而在l1空间上可能有无穷多个正的压缩半群( c _ 0半群)与之对应，而每个正的压缩半群有且仅有一个无穷小生成元。
Chapter 5 is contributed to studying convergence rate of standard transition function and relation of all kinds of convergence rates . by revealing the close link among strong ergodicity , stochastically monotone , and the feller transition functions we are able to prove that a monotone ergodic transition function is strongly ergodic if and only if it is not a feller transition function 第五章讨论标准转移函数的收敛速度以及各种收敛速度之间的关系，通过找出强遍历、随机单调性和feller转移函数之间的紧密关系，我们证明了随机单调标准转移函数是强遍历的充要条件是它不是feller转移函数。
