关键词: 格半群, 确定型有限状态自动机, 等价关系, 商集, 最小化, 最小化算法

Abstract: The notion of deterministic lattice finite automata is proposed，and the definitions of effectual final states and reachable states are shown.Indicating that the key problem of implementing the minimization algorithm of DLFA is how to solve quotient set Q/R_k.At the base of effectual final states，the equivalence relations R_k，S_k and the quotient set Q/S_k are introduced，and R_k=R_k-1∩S_k is proved.The elements of Q/R_k are all nonempty intersections with each equivalence class belonging to Q/R_k-1 and each one belonging to Q/R_k.H_k is introduced，and it can solve Q/R_k，and therefore Q/R_k is solved using only set operations.A constructive minimization algorithm of DLFA easy to be implemented is presented based on the above discussion.

Key words: lattice-ordered monoid, deterministic lattice finite automata, equivalence relation, quotient set, minimization, minimization algorithm