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We compute all synchronizing DFAs with 7 states and synchronization length >= 29. Furthermore, we compute alphabet size ranges for maximal, minimal and semi-minimal synchronizing DFAs with up to 7 states.
It was conjectured by v{C}erny in 1964 that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. In this paper, we investigate the ro
It was conjectured by v{C}erny in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs
In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained. It is shown that the transition complexity results for unio
We prove the following theorem. Suppose that $M$ is a trim DFA on the Boolean alphabet $0,1$. The language $L(M)$ is well-ordered by the lexicographic order $slex$ iff whenever the non sink states $q,q.0$ are in the same strong component, then $q.1$
We consider the problem {sc Max Sync Set} of finding a maximum synchronizing set of states in a given automaton. We show that the decision version of this problem is PSPACE-complete and investigate the approximability of {sc Max Sync Set} for binary