We consider the problem of generating a large state-space in a distributed fashion. Unlike previously proposed solutions that partition the set of reachable states according to a hashing function provided by the user, we explore heuristic methods that completely automate the process. The rst step is an initial random walk through the state space to initialize a search tree, duplicated in each p...

In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the sense that they do not assume the differentiability or convexity of functions. Our proposed theo...

In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming 20 = 21 , there exists a normal absolutely star countable discrete clos...

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are themanifestation of the continuous space translational symmetry being spontaneously broken into a discrete one.We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the con...

We investigate the field theory of strings having as a target space an arbitrary discrete one-dimensional manifold. The existence of the continuum limit is guaranteed if the target space is a Dynkin diagram of a simply laced Lie algebra or its affine extension. In this case the theory can be mapped onto the theory of strings embedded in the infinite discrete line ZZ which is the target space of...

We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider different boundary conditions and show that the discrete-time Feynman path integral is well-defined for suitably smooth potentials.

The state space approach to the synthesis of a class of discrete linear control systems is given. Both time-optimal and quadratic-cost problems are considered and a comparison to classical methods is made via the technique of pole assignment.

In many pattern recognition applications, feature space expansion is a key step for improving the performance of the classifier. In this paper, we (i) expand the discrete feature space by generating all orderings of values of k discrete attributes exhaustively, (ii) modify the well-known decision tree and rule induction classifiers (ID3, Quilan, 1986 [1] and Ripper, Cohen, 1995 [2]) using these...

This paper proposes a novel algorithm for solving NP-hard constrained discrete minimization problems whose unconstrained versions are solvable in polynomial time such as constrained submodular function minimization. Applications of our algorithm include constrained MAP inference in Markov Random Fields, and energy minimization in various computer vision problems. Our algorithm assumes the exist...