Abstract not found

Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid

The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied

alone, giving better generalization for a fixed number of training examples. In this article, we consider the problem of learning a binary concept in the absence of noise. We describe a formalism for active concept learning called selective sampling and show how it may be approximately implemented by a

Consider the P-complete problem horn which asks whether a given set of Horn clauses is (un)satisfiable. To solve it one keeps a dynamic set of atoms that are forced to be true. Using the clauses one then adds atoms to this set until saturation is reached. It is easy to see that this dynamic set will in general more than constant size even if we allow to discard already proved atoms. Given that we need logarithmic space to store a single atom on a Turing machine tape this seems like a strong intuitive argument for the hypothesis that logarithmic space is different from polynomial time. We thus tried to find formal models of computation in which this intuitive argument can be made rigorous. Thus, we study computational models that can be simulated in logarithmic space and encompass logspace algorithms which manipulate a constant size of objects that require logarithmic space individually such as pointers or graph nodes. The hope is then to be able to show that such models are provably unable to solve P-complete problems. We report in this survey article on our partial results towards this goal as well as the state-of-the-art in general.

Abstract not found

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of semantic description, where the semantic load is spread more evenly throughout the lexicon. I argue that lexical decomposition is possible if it is performed generatively. Rather than assuming a fixed set of primitives, I will assume a fixed number of generative devices that can be seen as constructing

Abstract In this paper we consider an approach to solve the problem of existence of Hamiltonian alternating cycle with fixed number of color appearances. This approach is based on constructing logical models for the problem.

is important for problems such as optical flow or image restoration that have a large label set. A second technique makes it possible to obtain good results with a small fixed number of message passing iterations, independent of the size of the input images. Taken together these techniques speed up