Inseparability and Strong Hypotheses for Disjoint NP Pairs

This paper investigates the existence of inseparable disjoint pairs of NP languages and related strong hypotheses in computational complexity. Our main theorem says that, if NP does not have measure 0 in EXP, then there exist disjoint pairs of NP languages that are P-inseparable, in fact TIME(2^(n^k))-inseparable. We also relate these conditions to strong hypotheses concerning randomness and genericity of disjoint pairs

On the existence of complete disjoint NP-pairs

Disjoint NP-pairs are an interesting model of computation with important applications in cryptography and proof complexity. The question whether there exists a complete disjoint NP-pair was posed by Razborov in 1994 and is one of the most important problems in the field. In this paper we prove that there exists a many-one hard disjoint NP-pair which is computed with access to a very weak oracle (a tally NP-oracle). In addition, we exhibit candidates for complete NP-pairs and apply our results to a recent line of research on the construction of hard tautologies from pseudorandom generators

Conservative Extensions and Satisfiability in Fragments of First-Order Logic : Complexity and Expressive Power

In this thesis, we investigate the decidability and computational complexity of (deductive) conservative extensions in expressive fragments of first-order logic, such as two-variable and guarded fragments. Moreover, we also investigate the complexity of (query) conservative extensions in Horn description logics with inverse roles. Aditionally, we investigate the computational complexity of the satisfiability problem in the unary negation fragment of first-order logic extended with regular path expressions. Besides complexity results, we also study the expressive power of relation-changing modal logics. In particular, we provide translations intto hybrid logic and compare their expressive power using appropriate notions of bisimulations

The Fekete-Szego theorem with Local Rationality Conditions on Curves

Let $K$ be a number field or a function field in one variable over a finite field, and let $K^{sep}$ be a separable closure of $K$. Let $C/K$ be a smooth, complete, connected curve. We prove a strong theorem of Fekete-Szego type for adelic sets $E = \prod_v E_v$ on $C$, showing that under appropriate conditions there are infinitely many points in $C(K^{sep})$ whose conjugates all belong to $E_v$ at each place $v$ of $K$. We give several variants of the theorem, including two for Berkovich curves, and provide examples illustrating the theorem on the projective line, and on elliptic curves, Fermat curves, and modular curves

A query-based approach to ontologies using the theory of institutions

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