不确定自动机与JSL-dfas
Nondeterministic Automata and JSL-dfas
摘要：
我们介绍了依赖自动机的范畴。依赖自动机由两个非确定性有限自动机组成，它们的状态之间的关系满足条件。这个范畴等价于在联合半格中解释的确定性有限自动机，即JSL-dfas。接受$L$的规范依赖自动机相当于由“依赖关系”连接的$L$和$rev(L)$的状态最小dfa。我们描述了许多典型的JSL-dfas依赖自动机，并解释/扩展Brzozowski的算法。如果nfa的各个状态在左/右条件和集合论布尔运算下接受$\{L\}$闭包中的语言，则称其为“亚原子”。证明了nfa $N$是亚原子的当且仅当$rsc(rev(N))$的转移幺半群是句法的.
英文摘要：
We introduce the category of dependency automata. A dependency automaton consists of two nondeterministic finite automata, with a relation between their states satisfying conditions. This category is equivalent to deterministic finite automata interpreted in join-semilattices i.e. JSL-dfas. The canonical dependency automaton accepting $L$ amounts to the state-minimal dfas for $L$ and $rev(L)$ connected by the `dependency relation'. We describe many canonical JSL-dfas as dependency automata and also explain/extend Brzozowski's algorithm. Call an nfa `subatomic' if its individual states accept a language in the closure of $\{L\}$ under left/right quotients and set-theoretic boolean operations. We prove an nfa $N$ is subatomic iff $rsc(rev(N))$'s transition monoid is syntactic.
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