Reset Complexity of Ideal Languages Over a Binary Alphabet

Abstract

We prove PSPACE-completeness of checking whether a given ideal language serves as the language of reset words for some automaton with at most four states over a binary alphabet. We compare the reset complexity and the state complexity for languages related to slowly synchronizing automata.

Synchronization of finite automata

“…For example, it can be verified that any DFA that recognizes the language Sync C 4 , where C 4 is the synchronizing DFA with four states presented in Example 1.1, has at least 12 states. Among the publications in this area we should mention [72], [88], [92], [93], [119]- [121], [139], and [146]. Now we turn back to the computational complexity of synchronizability recognition.…”