A dynamical-systems-based model of computation is studied. We demonstrate the computational ability of nonlinear mappings. There exists a switching map system with two types of baker's map to emulate any Turing machine. Taking non-hyperbolic mappings with second-order nonlinearity (e.g., the...

We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. <p> We...</p>

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k1. For the Wiener measure occurring in many applications we have k=2. We want to...

We show that predicting the HPP or FHP III lattice gas for finite time is equivalent to calculating the output of an arbitrary Boolean circuit, and is therefore P-complete: that is, it is just as hard as any other problem solvable by a serial computer in polynomial time. <p> It is widely believed...</p>

A network is robust to the extent that it is not vulnerable to disconnection by removal of nodes. The minimum number of nodes that need be removed to disconnect a pair of other nodes is called the connectivity of the pair. It can be proved that the connectivity is also equal to the number of...