New results concerning synchronized finite automata

Abstract

We establish a tight hierarchy of two-way synchronized finite automata having only universal states on the number of allowed processes, i.e. L(2SUFA(kproc)) $\subsetneq$ L(2SUFA(k + 1-proc)), by studying reduction functions made by two-way deterministic finite automata with a one-way write-only output tape. Consequently for every k > 1, L(2SUFA(k-proc)) has a complete set under 2DFA reductions and is not closed under union or intersection. In contrast, we show that the corresponding hierarchy collapses for unary alphabets. Next we study multihead synchronized finite automata having only universal states. We show that ∪ ^∞_k=1 L(2SUFA(k-heads)) = ∪ ^∞_k=1 L(2UFA(k-heads)) = NLOG, and ∪ ^∞_k=1 L(1SUFA(k- heads)) = ∪ ^∞_k=1 L(1UFA(k-heads)). As a result, we establish a tight hierarchy on the number of heads of the two-way machines, i.e. L(2SUFA(k-heads)) $\subsetneq$ L(2SUFA(k+l-heads)), and a weaker hierarchy of the one-way machines, i.e. L(1SUFA(k-heads)) $\subsetneq$ L(1SUFA(2k + 1heads)).

Finally, we show that any reasonable class of synchronized pushdown or counter machines accepts all r.e. languages.