of constraints which does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition. We then investigate all the different possible forms of this algebraic closure property, and establish which of these are sufficient to ensure tractability. As examples, we show

Closure properties of pattern languages

The form--closure and force--closure properties of robotic grasping are investigated. Loosely speaking, these properties are related to the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, form--closure is considered as a purely

We study the closure properties of the function classes GapP and GapP+. We characterize the property of GapP+ being closed under decrement and of GapP being closed under maximum, minimum, median, or division by seemingly implausible collapses among complexity classes; thereby giving evidence

Abstract—We consider a specific class of combinatorial search or optimization problems where the search space gives rise to a closure operator and essentially the hulls are the only relevant subsets that must be checked in a brute force approach. We suggest that such a closure property can help

. In this note, we solve questions regarding closure properties of ordered languages. Especially, ordered languages form a full abstract family of recursive languages which is neither intersection- nor complementationclosed. 1 Introduction and Definitions Ordered languages (or equivalently

We classify the univariate functions that are relativizable closure properties of GapP, solving a problem posed by Hertrampf, Vollmer, and Wagner (Structures '95). We also give a simple proof of their classification of univariate functions that are relativizable closure properties of #P.

We generalize some of the central results in au-tomata theory to the abstraction level of coalgebras. In particular, we show that for any standard, weak pullback preserving functor F, the class of recogniz-able languages of F-coalgebras is closed under tak-ing unions, intersections and projections. Our main technical result concerns a construction which trans-forms a given alternating F-automaton into an equiv-alent non-deterministic one. 1.

Witness reduction has played a crucial role in several recent results in complexity theory. These include Toda's result that PH ` BP \Delta \PhiP, the "collapsing" of PH into \PhiP 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 Hemachandra's results establish a connection between functions being hard for #P and functions interacting with the class to effect witness reduction. In fact, we believe that the ability to achieve some form of witness reduction is what makes a function hard for a class of functions. To support our thesis we define new function classes and obtain results analogous to those of Ogiwara and Hemachandra. We also introduce the notion of randomly hard functions and obtain similar results.

The basic notions used for specifying languages are of algorithmic or operational character: automata (accepting devices) or grammars (generating devices). This duality reflects the original motivations coming from computer science or linguistics. A deeper theory and more involved proofs called for alternative definitional