In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for superposition are drawn (only) from a set of positive unit c...

We analyze the achievable rate of the superposition of block Markov encoding (decode-and-forward) and side information encoding (compress-and-forward) for the three-node Gaussian relay channel. It is generally believed that the superposition can out perform decode-and-forward or compress-and-forward due to its generality. We prove that within the class of Gaussian distributions, this is not the...

The requirement that memory he superposition-free imposes a restrictive condition on the structure of neural models. A simple model which satisfies this condition consists of two levels of neurons, with primary level neurons tiring in response to external input and secondary (reference) neurons modifying activated primaries in such a way that they can later fire these primaries. Reference neuro...

Clipping is applied to superposition coding systems to reduce the peak-to-average power ratio (PAPR) of the transmitted signal. The performance limit is investigated through evaluating the mutual information driven by the induced peak-power-limited input signals. It is shown that the channel capacity can be approached by clipped superposition coding systems. To alleviate the performance degrada...

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of so...