Two philosophical applications of the concept of program-size complexity are discussed. First, we consider the light program-size complexity sheds on whether mathematics is invent...
In this paper we consider the problem of theory patching, in which we are given a domain theory, some of whose components are indicated to be possibly awed, and a set of labeled t...
In 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A T 0 is nonlow2 if and only if A is prime bounding, i.e. for every complete atomic decidable theory T , there i...
The last two decades have seen enormous progress in the development of sublinear-time algorithms — i.e., algorithms that examine/reveal properties of “data” in less time tha...
We review the notion of hypertree width, a measure of the degree of cyclicity of hypergraphs that is useful for identifying and solving efficiently easy instances of hard problems...