Open Problems in Communication and Computation by Thomas M. Cover, B. Gopinath

By Thomas M. Cover, B. Gopinath

Thomas M. disguise and B. Gopinatb The papers during this quantity are the contributions to a different workshop on difficulties in communique and computation performed within the summers of 1984 and 1985 in Morristown, New Jersey, and the summer time of 1986 in Palo Alto. California. The constitution of this workshop was once special: no contemporary effects. no surveys. in its place. we requested for striking open prob~ lems within the box. there are lots of recognized open difficulties, together with the query P = NP?, the simplex conjecture in verbal exchange idea, the ability sector of the printed channel. and the two·helper challenge in details conception. past those well-defined difficulties are sure grand examine objectives. what's the basic thought of knowledge stream in stochastic networks? what's a entire thought of computational complexity? What a couple of unification of algorithmic complexity and computational complicated­ ity? Is there a idea of energy-free computation? And if this is the case, the place do details thought, communique thought, desktop technology, and physics meet on the atomic point? Is there a duality among computation and verbal exchange? ultimately. what's the final effect of algorithmic com­ plexity on chance concept? and what's its courting to info thought? the belief used to be to provide difficulties at the first day. try and resolve them at the moment day, and current the suggestions at the 3rd day. in general, just one challenge used to be solved in the course of the assembly -- El Gamal's prob· lem on noisy verbal exchange over a typical line.

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Then, the only possible interpretation of the third line is convex too. Rosenfeld et al. [1976] solved this labeling problem by formulating these local constraints and propagating them by an iterative application of the label discarding rule. Continuous relaxation labeling has been applied to the interpretation of small scale aerial images by Nevatia and Price [1982]. They described their images with lines (representing bridges) and regions (representing cities, airports, parks and water surfaces) and used relations like neighbours, above and part-of to describe the spatial relationships.

The noise characteristics of the channel can be modeled by the conditional probabilities of the transmitted symbols, given the received symbols. In an ideal channel there is a one to one correspondence between the symbols of the source alphabet and the symbols of the receiver alphabet. e. knowing the symbol that has been sent, one also knows the symbol that will be received and, vice versa, knowing the symbol that has been received, one also knows which symbol has been sent. If a source sends symbol ak over an ideal channel and the symbol bl is received, the conditional probabilities of the symbols of source alphabet A given that bt has been received is one for symbol ak and zero for all other symbols.

As a consequence, the inexact matching only uses so-called blind search methods. Although heuristics can improve their performance to a certain extent, more intelligent search methods certainly could bring a larger decrease in search time. In the next chapter we will elaborate on these problems and describe the contribution of this thesis in solving them. 4 Problem definition and contributions of the thesis Although relational matching nowadays is a widely applied technique, especially for object recognition tasks, only few attempts have been made to further develop the theory.

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