Let Un,p be the random unary predicate and Tk the almost sure first-order theory of Un,p under the linear ordering, where k is a positive integer and n−1/k p(n) n−1/(k+1) . F...
We introduce high-level theories in analogy with high-level programming languages. The basic point is that even though one can define many theories via simple, low-level axiomatiza...
Blocks World (BW) has been one of the most popular model domains in AI history. However, there has not been serious work on axiomatizing the state constraints of BW and giving jus...
We describe a simple randomized construction for generating pairs of hash functions h1, h2 from a universe U to ranges V = [m] = {0, 1, . . . , m - 1} and W = [m] so that for ever...
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to po...