Inspired by Fagin’s result that NP = Σ 1 , we have developed a partial framework to investigate expressibility inside Σ 1 so as to have a finer look into NP . The framework uses interesting combinatorics derived from second-order EhrenfeuchtFräıssé games and the notion of game types. Some of the results that have been proven within this framework are: (1) for any k, divisibility by k is not exp...

It is shown that the time needed by a concurrent read concurrent write parallel random access machine CRAM to check if an input has a certain property is the same as the minimal depth of a rst order inductive de nition of the property This in turn is equal to the number of iterations of a rst order sentence needed to express the property The second contribution of this paper is the introduction...

We formulate a formal syntax of approximate formulas for the logic with counting quantifiers, SOLP, studied by us in [1], where we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P andNL; (ii) weakening the ordering relation to an almost order (in the sense of [7]) we can separate meani...

Inspired by Fagin’s result that NP = Σ11, we have developed a partial framework to investigate expressibility inside Σ11 so as to have a finer look into NP . The framework uses interesting combinatorics derived from second-order Ehrenfeucht-Fräıssé games and the notion of game types. Some of the results that have been proven within this framework are: (1) for any k, divisibility by k is not exp...

Lindell, S., An analysis of fixed-point queries on binary trees, Theoretical Computer Science 85 (1991) 75-95. The presence of ordering appears to play an essential role in the logical expressibility of polynomialtime queries on finite structures. By examining the expressibility and complexity of inductive queries on the class of complete unordered binary trees, we are able to show that the abi...

We prove positive and negative results on the expressive power of the relational calculus augmented with linear constraints. We show non-expressibility of some properties expressed by polynomial constraints. We also show expressibility of some queries involving existence of lines, when the query output has a simple geometrical relation to the input. Finally, we compare the expressive power of l...

Existential positive queries are logical sentences built from conjunction, disjunction, and existential quantification, and are also known as select-project-join-union queries in database theory, where they are recognized as a basic and fundamental class of queries. It is known that the number of variables needed to express an existential positive query is the crucial parameter determining the ...