This paper addresses the smallest grammar problem: What is the smallest context-free grammar that generates exactly one given string /spl sigma/? This is a natural question about a fundamental objectâ€¦ (More)

We address the network information flow problem, in which messages available to a set of sources must be passed through a network to a set of sinks with specified demands. This differs fromâ€¦ (More)

A problem in technology mapping is that quality of the final implementation depends significantly on the initially provided circuit structure. To resolve this problem, conventional techniquesâ€¦ (More)

The field of property testing studies algorithms that distinguish, using a small number of queries, between inputs which satisfy a given property, and those that are `far' from satisfying theâ€¦ (More)

We present a (randomized) test for monotonicity of Boolean functions. Namely, given the ability to query an unknown function f : f0; 1gn 7! f0; 1g at arguments of its choice, the test always acceptsâ€¦ (More)

We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f : Î£ 7â†’ Îž, where Î£ and Îž are finite ordered sets, the test always acceptsâ€¦ (More)

Several recently-proposed data compression algorithms are based on the idea of representing a string by a context-free grammar. Most of these algorithms are known to be asymptotically optimal withâ€¦ (More)

nodes that have working paths to the root. This lead s to the following lemma: Lemma 7.1 Suppose that d = (logN). With high probability, the fraction of abstract-tree leaves that have a working pat hâ€¦ (More)