Summary
Let L b = {w 1 *...* w 2b ¦w i is in {0,1}* and w i = w 2b+1−i for 1≦i≦2b for b≧1. We show that the language L b is not recognizable by any nondeterministic one-way k-head stack-counter automata if \(b > \left( {\begin{array}{*{20}c} k \\ 2 \\ \end{array} } \right)\). As a corollary, we show that k+1 heads are better than k for one-way multihead stack-counter automata.
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Miyano, S. A hierarchy theorem for multihead stack-counter automata. Acta Informatica 17, 63–67 (1982). https://doi.org/10.1007/BF00262976
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DOI: https://doi.org/10.1007/BF00262976