Sebastiaan A. Terwijn

Nonapproximability of the normalized information distance

A water geyser assembly comprises an inner pressurizable container and an outer shell both formed from a glass fibre reinforced plastics material. A polyurethane foam material fills the void defined between the inner container and the shell. A fitting mounting land formed with a number of apertures is provided at one end of the inner container for receiving fittings in the form of a pair of flanged spigot portions which are externally threaded and which are bridged at the flange. The flange locates against an inner surface of the fitting mounting land via sealing rings, and lock nuts are screwed down over each of the threaded spigot portions which project through the apertures so as to form a pressure tight fit. The fittings are thus locked mechanically to the mounting land without being laid in glass fibre during manufacture. Water inlet and outlet conduits, a heating element assembly and a pressure relief valve are in turn mounted in communication with the spigot portions.

On the Learnability of Hidden Markov Models

A simple result is presented that links the learning of hidden Markov models to results in complexity theory about nonlearnability of finite automata under certain cryptographic assumptions. Rather than considering all probability distributions, or even just certain specific ones, the learning of a hidden Markov model takes place under a distribution induced by the model itself.

Notes on Sum-Tests and Independence Tests

AbstractWe study statistical sum-tests and independence tests, in particular for computably enumerable semimeasures on a discrete domain. Among other things, we prove that for universal semimeasures every

Linear Ramified Higher Type Recursion and Parallel Complexity

\Sigma ^{0}_{1}

Model theory of measure spaces and probability logic

-sum-test is bounded, but unbounded

The finite intervals of the Muchnik lattice

\Pi ^{0}_{1}

Counting Extensional Differences in BC-Learning

-sum-tests exist, and we study to what extent the latter can be universal. For universal semimeasures, in the unary case of sum-test we leave open whether universal

The Mathematical Foundations of Randomness

\Pi ^{0}_{1}

Covering the Recursive Sets

-sum-tests exist, whereas in the binary case of independence tests we prove that they do not exist.

On the Quantitative Structure of Δ 2 0

A typed lambda calculus with recursion in all finite types is defined such that the first order terms exactlyc haracterize the parallel complexityclass NC. This is achieved byuse of the appropriate forms of recursion (concatenation recursion and logarithmic recursion), a ramified type structure and imposing of a linearity constraint.