Given a truncated portion of a band-limited image with known x and y bandwidths, the extrapolation problem is to determine the signal over all x and y. An iterative extrapolation algorithm, recently proposed by Gerchberg, requires only the repeated operations of Fourier transformation and truncation. A coherent optical processor is presented that implements Gerchberg's iterative extrapolation a...

We present a new algorithm that extends the techniques of the Pohlig-Hellman algorithm for discrete logarithm computation to the following situation: Given a nite abelian group and group elements h, g1; : : : ; g l , compute the least positive integer y and numbers x1 ; : : : ; x l such that h y = Q gi x i. This computational problem is important for computing the structure of a nite abelian gr...

We provide a knowledge compilation technique which deals with the computational intractability of first order reasoning problems. The notion of prime implicates is extended to theory prime implicates in first order case. We provide an algorithm to compute the theory prime implicates of a knowledge base X with respect to a knowledge base Y where both X and Y are assumed to be in Skolem Conjuncti...

In this article we provide an algorithm, where to escape from a local maximum y of convex function f over D, we (locally) solve piecewise convex maximization max{min{ f (x) − f (y), py(x)} | x ∈ D} with an additional convex function py(·). The last problem can be seen as a strictly convex improvement of the standard cutting plane technique for convex maximization. We report some computational r...

By increasing, the complexity of chips and the need to integrating more components into a chip has made network –on- chip known as an important infrastructure for network communications on the system, and is a good alternative to traditional ways and using the bus. By increasing the density of chips, the possibility of failure in the chip network increases and providing correction and fault tol...

We study the convergence properties of alternating proximal minimization algorithms for (nonconvex) functions of the following type: L(x, y) = f(x) + Q(x, y) + g(y) where f : R → R∪{+∞} and g : R → R∪{+∞} are proper lower semicontinuous functions and Q : R×R → R is a smooth C (finite valued) function which couples the variables x and y. The algorithm is defined by: (x0, y0) ∈ R n × R given, (xk...

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusive constraints. For the two input sequences X and Y of lengths n and m, and a set of d constraints P = {P1, · · · , Pd} of total length r, the problem is to find a common subsequence Z of X and Y excluding each of constraint string in P as a substring and the length of Z is maximized. A ve...

An algorithm based on consensus method to compute the set of prime implicates of a quantifier free first order formula X was presented in an earlier work. In this paper the notion of prime implicates is extended to theory prime implicates in the first order case. We provide an algorithm to compute the theory prime implicates of a Knowledge base X with respect to another knowledge base Y where b...

The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers, using joker states to represent clusters of configurations. The SP-y algorithm generalizes SP to work on the Max-SAT problem, but the cover interpretation of SP does not generalize to SP-y. Recently, a r...