Refining nondeterminism below linear time

Authors:
Martin Kutrib
Affiliations:
Institute of Informatics, University of Giessen, Arndtstr. 2, D-35392 Giessen, Germany
Venue:
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Year:
2002

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Abstract

Multitape Turing machines with a restricted number of nondeterministic steps are investigated. Fischer and Kintala showed an infinite nondeterministic hierarchy of properly included real-time languages between the deterministic languages and the logbounded nondeterministic languages. This result is extended to time complexities in the range between real time and linear time, and is generalized to arbitrary dimensions.For fixed amounts of nondeterminism infinite proper dimension hierarchies are presented. The hierarchy results are established by counting arguments. For an equivalence relation and a family of witness languages the number of induced equivalence classes is compared to the number of equivalence classes distinguishable by the model in question. By contradiction the properness of the inclusions is proved.