Model-Theoretic Characterization of Complexity Classes

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 kn...

A Model-Theoretic Characterization of Constant-Depth Arithmetic Circuits

We study the class #AC of functions computed by constantdepth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. No model-theoretic characterization for arithmetic circuit classes is known so far. Inspired by Immerman’s characterization of the Boolean class AC, we remedy this situation and develop such a characterization of #AC. Our characterization can b...

Ergodic Theoretic Characterization of Left Amenable Lau Algebras

Model-Theoretic Characterizations of Boolean and Arithmetic Circuit Classes of Small Depth

In this paper we give a characterization of both Boolean and arithmetic circuit classes of logarithmic depth in the vein of descriptive complexity theory, i.e., the Boolean classes NC1, SAC1 and AC1 as well as their arithmetic counterparts #NC1, #SAC1 and #AC1. We build on Immerman’s characterization of constant-depth polynomial-size circuits by formulae of first-order logic, i.e., AC0 = FO, an...

Multimetric continuous model theory

In this paper, we study metric structures with a nite number of metrics by extending the model theory developed by Ben Yaacov et al. in the monograph Model theory for metric structures. We rst de ne a metric structure with nitely many metrics, develop the theory of ultraproducts of multimetric structures, and prove some classical model-theoretic theorems about saturation for structures with mul...