Alternating multihead finite automata

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Abstract

We define alternating multihead finite automata, a generalization of nondeterministic multihead finite automata based on the alternating Turing machine model introduced by Chandra, Kozen, and Stockmeyer (1981). We study the relationships between the classes of languages accepted by alternating multihead finite automata and the classes accepted by deterministic and nondeterministic multihead finite automata and pushdown automata. We also examine basic questions about alternating multihead finite automata (for example, are k + 1 heads better than k?). We conclude by placing upper bounds on the deterministic time and space complexity of the classes of languages accepted by alternating multihead finite automata. As corollaries to our results about alternating multihead finite automata, we obtain several facts about multihead pushdown automata, indicating that the study of alternating multihead finite automata may lead to useful results about nonalternating automata.

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A preliminary version of this paper appeared in the proceedings of the Eight Colloquium on Automata, Languages and Programming, Acre, July, 1981. A portion of this work appeared in the author's doctoral dissertation, completed at the University of California, Berkeley. The research was supported by NSF grants MCS 74-07636-A01, MCS 79-15763, and MCS 81-03608.