Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Markus Holzer; Martin Kutrib; Andreas Malcher

doi:10.4204/eptcs.1.9

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arXiv · 0906.3051

Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Markus Holzer·Martin Kutrib·Andreas Malcher

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Abstract

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature.

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Markus Holzer, Martin Kutrib, Andreas Malcher. 2009-06-17. Multi-Head Finite Automata: Characterizations, Concepts and Open Problems. https://doi.org/10.4204/eptcs.1.9

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