Learn More
A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfied clauses is known to be very effective: the time to solution(More)
We investigate the well-known anomalous diierences in the approximability properties of NP-complete optimization problems. We deene a notion of polynomial time reduction between optimization problems, and introduce conditions guaranteeing that such reductions preserve various types of approximate solutions. We then prove that a weighted version of the(More)
We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring(More)
Acknowledgments This thesis has benefited from several suggestions and ideas from numerous people. I am especially thankful to: Wolfgang Maass, my supervisor, who pointed me to the exciting subject of spik-ing neurons and who helped me in many discussions refining my ideas. His work provided the main framework of this thesis. Furthermore, Chapter 4 is the(More)
We survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classification include the architecture of the network (feedforward versus recurrent), time model (discrete versus continuous), state(More)