Optimal 2DFA algorithms for one-way liveness on two and three symbols

Abstract

For all h, n≥ 2, the problem of one-way liveness for height h and length n captures the task of simulating one-way nondeterministic finite automata with h states on inputs with n- 2 symbols. We prove that the number of states in a smallest two-way deterministic finite automaton which decides this problem is Θ(h), if n= 2; and Θ(h2/ log h), if n= 3.