Synchronized finite automata and 2DFA reductions

Oscar H. Ibarra, Nicholas Q. Trân
1993 Theoretical Computer Science  
Ibarra, O.H. and N.Q. Trgn, Synchronized finite automata and 2DFA reductions, Theoretical Computer Science 115 (1993) 261-275. We establish a tight hierarchy of two-way synchronized finite automata with only universal states on the number of allowed processes (Y(ZSUFA(k-proc)) c Y(ZSUFA((k+ 1)-proc))) by studying the reduction functions made by two-way deterministic finite automata with a one-way write-only output tape. As corollaries, we show that, for every k> 1, Y(2SUFA(k-proc)) has a
more » ... e set under 2DFA reductions and is not closed under Boolean operations. In contrast, we show that the corresponding hierarchy collapses for unary alphabets; this follows from our characterization of U,^=, Y(2SUFA(k-proc)) to be exactly the class of unary regular languages. Note that, for binary alphabets, it was shown by Ibarra and Trln (1990) that Y(2DFA) c uz=, Y(2SUFA(k_proc)) c Y(2DFA(2_heads)). On the other hand, we show that synchronization dramatically enhances the power of pushdown automata. In fact, even under the severe restriction of the pushdown store to a counter making only one reversal, synchronized pushdown automata still recognize all recursively enumerable languages.
doi:10.1016/0304-3975(93)90119-e fatcat:modntx754za6jdaf6hypcngyvu