Structural complexity 1
Structural complexity 2
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
A uniform approach to define complexity classes
Theoretical Computer Science
Locally Definable Acceptance Types - The Three-Valued Case
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
On the Power of Parity Polynomial Time
STACS '89 Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science
Counting Classes: Thresholds, Parity, Mods, and Fewness
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Locally Definable Acceptance Types for Polynomial Time Machines
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
The Power of Local Self-Reductions
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Query Order and Self-Specifying Machines
Query Order and Self-Specifying Machines
Query Order in the Polynomial Hierarchy
Query Order in the Polynomial Hierarchy
Generalized Regular Counting Classes
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
A Generalized Quantifier Concept in Computational Complexity Theory
ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
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We study the power of transformation monoids, which are used as an acceptance mechanism of nondeterministic polynomial time machines. Focusing our attention on four types of transformation monoids (including the monoids of all transformations on k elements) we obtain exact characterizations of all investigated polynomial time classes. We apply these results to the cases of locally self reducible sets and of bottleneck Turing machines to obtain complete solutions to the formerly open problems related to these models. Especially, the complexity of k-locally self reducible sets for all numbers k, as well as the complexity of width-3 or width-4 bottleneck Turing machines are determined completely. Also for m-k-locally self reducible sets (i.e. k-locally self reducible sets, where the self reduction is given by a many-one reduction function) we determine the complexity exactly for all k.