Abstract. We suggest a graph-theoretic approach to steganography based on the idea of exchanging rather than overwriting pixels. We construct a graph from the cover data and the secret message. Pixels that need to be modified are represented as vertices and possible partners of an exchange are connected by edges. An embedding is constructed by solving the combinatorial problem of calculating a maximum cardinality matching. The secret message is then embedded by exchanging those samples given by the matched edges. This embedding preserves first-order statistics. Additionally, the visual changes can be minimized by introducing edge weights.We have implemented an algorithm based on this approach with support for several types of image and audio files and we have conducted computational studies to evaluate the performance of the algorithm.

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AbstractWe consider the following problem: Given a proof of the Skolemization of a formulaF, what is the length of the shortest proof ofF? For the restriction of this question to cut-free proofs we prove corresponding exponential upper and lower bounds.

We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computing a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize such a compression. Finally, a proof using these cut-formulas is constructed. This method allows an exponential compression of proof length. It can be applied to the output of automated theorem provers, which typically produce analytic proofs. An implementation is available on the web and described in this paper.

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