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Galperin and Wigderson proposed a succinct representation for graphs, that uses number of bits that is logarithmic in the number of nodes. They proved complexity results for various decision problems on graph properties, when the graph is given in a succinct representation. Later, Papadimitriou and Yannakakis showed, that under the same succinct encoding(More)
We present a holography based optical architecture that computes Kronecker product of two given binary matrices in a single (configuration) step. We demonstrate the use of the holography capability to enlarge the input of size $$n$$ n into the size $$n^2$$ n 2 in one step, in contrast to the traditional optical copying techniques that duplicate the input by(More)
Finding a problem that is both hard to solve and hard to solve on many instances is a long standing issue in theoretical computer science. In this work we prove that the Succinct Permanent mod p is N EXP time hard in the worst case (via randomized polynomial time reduction). We find hard instance for any given heuristic, either by running the heuristic(More)
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