Lecture 7: Recursive saturation

Lecture 15 : Pseudorandomness for Logarithmic Space

In the last lecture, we discussed a recursive construction of a pseudorandom generator that is based on expanders: the INW generator. In this lecture we will show that the INW-generator with a suitable instantiation of an expander family produces pseudorandomness for machines that run in logarithmic space. We also introduce Nisan’s generator, which is a pseudorandom generator that has a recursi...

CS6180 Lecture 22 – Theory of Computability in CTT

This lecture will summarise core ideas in the theory of computing, including basic recursive function theory, using concepts from type theory. A fundamental concept is the type of partial recursive functions over the natural numbers and other types. The basic results include proofs that certain questions about partial functions are unsolvable, such as whether they converge on a specific input. ...

THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Expansions, omitting types, and standard systems

Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed. In this thesis we give further examples of variations of recursive saturation, all of which are connected with expandability properties similar to resplende...

Lecture Notes on Recursive Procedures

LECTURE NOTES ON Large sets of t-designs

Preface The method of partitionable sets for constructing large sets of t-designs have now been used for nearly a decade. The method has resulted in some powerful recursive constructions and also existence results especially for large sets of prime sizes. Perhaps the main feature of the approach is its simplicity. In these notes, we describe the method and show how it is employed to obtain larg...