Let @math be a uniformly distributed random @math -SAT formula with @math variables and @math clauses. We present a polynomial time algorithm that finds a satisfying assignment of @math with high probability for constraint densities @math , where @math . Previously no efficient algorithm was known to find satisfying assignments with a nonvanishing probability beyond @math [A. Frieze and S. Suen, J. Algorithms, 20 (1996), pp. 312-355].
Montanari, Ricci-Tersenghi, and Semerjian @cite_9 provide evidence that Belief Propagation guided decimation may succeed up to density @math . This algorithm is based on a very different paradigm than the others mentioned in Table . The basic idea is to run a message passing algorithm ( Belief Propagation'') to compute for each variable the marginal probability that this variable takes the value true false in a uniformly random satisfying assignment. Then, the decimation step selects a variable, assigns it the value true false with the corresponding marginal probability, and simplifies the formula. Ideally, repeating this procedure will yield a satisfying assignment, provided that Belief Propagation keeps yielding the correct marginals. Proving (or disproving) this remains a major open problem.
@cite_9
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Index of refraction measurements are made by means of an optical device in which a coherent light beam is divided into an object beam and a reference beam, each of which is directed through a separate path in a common light transmitting medium. The object beam is also transmitted en route through a test volume that accommodates a substance to be tested. It is subsequently recombined with the reference beam to form a single output beam. The output beam is received by a photo detector and its intensity is measured. The intensity of the detected output beam is related to any phase shift between the object and reference beams. The phase shift in turn is a measure of the index of refraction of the test substance. Information relating to density, temperature and pressure of the test substance can be derived from measured index of refraction values by using conventional conversion formulas. An operating range control is provided by introducing a volume of pressurized gas into the paths of the object and reference beams. The operating range of the instrument is set by adjusting the pressure of the gas in the absence of a test substance.