An Infinite Pebble Game and Applications

We generalize the well-known pebble game to infinite dag's, and we use this generalization to give new and shorter proofs of results in different areas of computer science (as diverse as "logic of programs" and "formal language theory"). Our applications here include a proof of a theorem due to Salomaa, asserting the existence of a context-free language with infinite index, and a proof of a theorem due to Tiuryn and Erimbetov, asserting that unbounded memory increases the power of logics of programs. The original proofs by Salomaa, Tiuryn, and Erimbetov, are fairly technical. The proofs by Tiuryn and Erimbetov also involve advanced techniques of model theory, namely, back-and-forth constructions based on a variant of Ehrenfeucht-Fraisse games. By contrast, our proofs are not only shorter, but also elementary. All we need is essentially finite induction and, in the case of the Tiuryn-Erimbetov result, the compactness and completeness of first-order logic.

Image Digestion and Relevance Feedback in the ImageRover WWW Search Engine

ImageRover is a search by image content navigation tool for the world wide web. The staggering size of the WWW dictates certain strategies and algorithms for image collection, digestion, indexing, and user interface. This paper describes two key components of the ImageRover strategy: image digestion and relevance feedback. Image digestion occurs during image collection; robots digest the images they find, computing image decompositions and indices, and storing this extracted information in vector form for searches based on image content. Relevance feedback occurs during index search; users can iteratively guide the search through the selection of relevant examples. ImageRover employs a novel relevance feedback algorithm to determine the weighted combination of image similarity metrics appropriate for a particular query. ImageRover is available and running on the web site.