We study the Ramsey theoretic properties of combinatorial configurations which are generated by infinite binary strings which are random in the sense of Kolmogorov-Chaitin. Introduction In this paper… (More)

In this paper we show the extent to wh ich a finite tree o f fixed height is a R a m s e y object m the class o f trees o f the same he igh t can be measu red by its s y m m e t r y group. @ I999… (More)

In the sequel, all the graphs, posets and other ordered structures referred to will be finite. In the 1970s and 1980s, largely due to the fundamental papers by Nes etr il and Ro dl [3, 4], remarkable… (More)

We investigate variations on the problem to construct a measure with a given support. The variations include the available information about the set, whether the support has to be precisely the given… (More)

Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown… (More)

We use recent results on the Fourier analysis of the zero sets of Brownian motion to explore the diophantine properties of an algorithmically random Brownian motion ( also known as a complex… (More)

The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of… (More)