We show that descriptive complexity’s result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we have a logical characterisation of ELEMENTARY. We also consider the expressivity of some fixed point operators and of monadic high order logic. Finally, we sh...

Abst rac t By applying descriptive set theory we get several facts on the fine structure of regular w-languages considered by K.Wagner. We present quite different, shorter proofs for main his results and get new results. Our description of the fine structure is new, very clear and automata-free. We prove also a closure property of the fine structure under Boolean operations. Our results demonst...

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic. Our approach is based on the novel notions of mimicking formulae and distance between formulae. The former are a weak versi...

This paper presents empirical evidence for five hypotheses about learning from large noisy domains: that trees built from very large training sets are larger and more accurate than trees built from even large subsets; that this increased accuracy is only in part due to the extra size of the trees; and that the extra training instances allow both better choices of attribute while building the tr...

Utilizing the connection between uniform constantdepth circuits and first-order logic with numerical predicates, we are able to provide a purely logical characterization of uniformity based on the intrinsic properties of these predicates. By requiring a numerical predicate R to satisfy a natural extensibility condition — that it can be translated to a polynomially magnified domain based on tupl...

AbstructWe combine pruned tree-structured vector quantization (pruned TSVQ) with Itoh’s universal noiseless coder. By combining pruned TSVQ with universal noiseless coding, we benefit from the “successive approximation” capabilities of TSVQ, thereby allowing progressive transmission of images, while retaining the ability to noiselessly encode images of unknown statistics in a provably asymptoti...

Typical reactive system languages are programmed by means of rules of the form if antecedent then consequent. However, despite their seemingly logical character, hardly any reactive system languages give such rules a logical interpretation. In this paper, we investigate a simplified reactive system language KELPS, in which rules are universally quantified material implications, and computation ...

We introduce a new framework for a descriptive complexity approach to arithmetic computations. We define a hierarchy of classes based on the idea of counting assignments to free function variables in first-order formulae. We completely determine the inclusion structure and show that #P and #AC0 appear as classes of this hierarchy. In this way, we unconditionally place #AC0 properly in a strict ...

We develop various aspects of the nite model theory of L k (9) and L k 1! (9). We establish the optimality of normal forms for L k 1! (9) over the class of nite structures and demonstrate separations among descriptive complexity classes within L k 1! (9). We establish negative results concerning preservation theorems for L k (9) and L k 1! (9). We introduce a generalized notion of preservation ...

Two graphs are co-spectral if their respective adjacency matrices have the same multi-set of eigenvalues. A graph is said to be determined by its spectrum if all graphs that are co-spectral with it are isomorphic to it. We consider these properties in relation to logical definability. We show that any pair of graphs that are elementarily equivalent with respect to the three-variable counting fi...