Closure Properties and Witness Reduction

Closure Properties and Witness Reduction

Witness reduction has played a crucial role in several recent results in complexity theory. These include Toda's result that PH BP P, the \collapsing" of PH into P with a high probability; Toda and Ogiwara's results which \collapses" PH into various counting classes with a high probability; and hard functions for various function classes studied by Ogiwara and Hemachandra. Ogiwara and Hemachand...

Closure, Properties and Closure Properties of Multirelations

The witness properties and the semantics of the Prolog cut

The semantics of the Prolog “cut” construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of responses to queries. A generalization of Prolog with negation as failure and cut is described, and shown not to have the witness properties. A restriction of the sys...

Basic Properties of Closure Spaces

This technical report summarized facts from the basic theory of generalized closure spaces and gives detailed proofs for them. Many of the results collected here are well known for various types of spaces. We have made no attempt to find the original proofs. 1. Set-Valued Set-Functions 1.1. Closure, Interior, Neighborhood, and Convergent. In this section, which in part generalizes the results o...

Orbit-closure Decompositions and Almost Periodic Properties

Let X be a metric space with metric p, let f(X)QX be a continuous mapping, and let h(X) ^X be a homeomorphism. For x&X, the s e t 23^-°o/(^) i called the semi-orbit of # under ƒ and the set n£XZh{x) is called the orbit of # under h. For # £ X , the closure of the semi-orbit of x under ƒ is called the semi-orbit-closure of x under ƒ and the closure of the orbit of x under h is called the orbit-c...