Probably new Variable

Most Probably Intersecting Hypergraphs

The celebrated Erdős-Ko-Rado theorem shows that for n > 2k the largest intersecting k-uniform set family on [n] has size ( n−1 k−1 ) . It is natural to ask how far from intersecting larger set families must be. Katona, Katona and Katona introduced the notion of most probably intersecting families, which maximise the probability of random subfamilies being intersecting. We consider the most prob...

Program Analysis Probably Counts

Semantics-based program analysis uses an abstract semantics of programs/systems to statically determine run-time properties. Classic examples from compiler technology include analyses to support constant propagation and constant folding transformations and estimation of pointer values to prevent buffer overruns. More recent examples include the estimation of information flows (to enforce securi...

Probably Optimal Graph Motifs

We show an O∗(2k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute, and Min-Add. Moreover, we provide a piece of ...

Probably Approximately Correct Learning

This paper surveys some recent theoretical results on the efficiency of machine learning algorithms. The main tool described is the notion of Probably Approximately Correct (PAC) 1 earning, introduced by Valiant. We define this learning model and then look at sorne of the results obtained in it. We then consider some criticisms of the PAC model and the extensions proposed to address these criti...

What Will Probably Happen