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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)

We introduce a measure for the computational complexity of mdiwdual instances of a decision problem and study some of Its properties. The instance complexity of a string ~ with respect to a set A and time bound t, ict(x : A). is defined as the size of the smallest special-case program for A that run> m time t,decides x correctly, and makes no mistakes on… (More)

- Berthold Ruf, Henry Markram, Pekka Orponen, Wulfram Gerstner, Ulrich Roth, Wolf Singer +1 other
- 1998

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 consider the complexity of combining bodies of evidence according to the rules of the Dempster{Shafer theory of evidence. We prove that, given as input a set of tables representing basic probability assignments m1; : : : ; mn over a frame of discernment , and a set A , the problem of computing the combined basic probability value (m1: : :mn)(A) is… (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)

- Pekka Orponen
- 1994

We survey some of the central results in the complexity theory of discrete neural networks, with pointers to the literature. Our main emphasis is on the computational power of various acyclic and cyclic network models, but we also discuss brieey the complexity aspects of synthesizing networks from examples of their behavior.