Lindström Quantifiers and Leaf Language Definability

We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along the way we tighten the best up to now known leaf language characterization of the classes of the polynomial time hierarchy and give a new model-theoretic characterization of PSPACE

On sets Turing reducible to p-selective sets

We consider sets Turing reducible to p-selective sets under various resource bounds and restricted number of queries to the oracle. We show that there is a hierarchy among the sets polynomial-time Turing reducible to p-selective sets with respect to the degree of a polynomial bounding the number of adaptive queries used by a reduction. We give a characterization of EXP / poly in terms of exponential-time Turing reducibility to p-selective sets. Finally we show that EXP can not be reduced to the p-selective sets under 2 lin time reductions with at most n k queries for any fixed k element of N

Lindström Quantifiers and Leaf Language Definability

We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along the way we tighten the best up to now known leaf language characterization of the classes of the polynomial time hierarchy and give a new model-theoretic characterization of PSPACE

Comparing Counting Classes for Logspace, One-way Logspace, Logtime, and First-Order

We generalize the definition of first-order counting classes [SST92] to use !, SUCC, and + as linear orderings. It turns out that #\Pi2 [!] = #\Pi1[SUCC] = #\Pi1[+]. We introduce certain classes of logtime counting functions and show that the classes of first-order definable counting functions are subclasses of the corresponding logtime counting classes. These logtime counting classes are itself subclasses of the corresponding one-way logspace counting classes. These logspace counting classes form a strict hierachy within #P: F1L` = #1L` = span-1L` = #P: Using the logical characterization of #P we obtain a characterization of #P via universally branching logtime Turing machines. 1 Introduction An important open question in complexity theory is whether the two classes NL and NP are equal. Although in the case of computing partial multivalued functions nondeterministically the corresponding classes can be separated [Bur89], a solution for the class of decision problems is not in sight. ..