ACM Transactions on Database Systems (TODS)
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
The General Notion of a Dot-Operator
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Complexity and Expressive Power of Logic Programming
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Complexity bounds for the verification of real-time software
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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The concepts of succinct problem representation and of NP leaf languages were developed to characterize complexity classes above polynomial time. Here, we work out a descriptive complexity approach to succinctly represented problems, and prove a strictly stronger version of the Conversion Lemma which allows iterated application. Moreover, we prove that for every problem P its succinct version sP is complete under projection reductions for the leaf language it defines. Our main tool is a characterization of polynomial time Turing machines in terms of circuits which are constructed uniformly by quantifierfree formulas. Finally, we show that an alternative succinct representation model allows to obtain completeness results for all syntactic complexity classes even under monotone projection reductions. Thus, we positively answer a question by I.A.Stewart for a large number of complexity classes.