Marius Zimand

An undergraduate track in computer security

To better prepare our graduates to face the challenges in computer and information security, in Fall 2002, Towson University launched an undergraduate track in computer security for the computer science majors. This paper describes the motivation behind this track and discusses its structure and requirements.

Is independence an exception

Abstract Godels incompleteness theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable statements of such a theory is dense and in many cases even corare.

Two sources are better than one for increasing the Kolmogorov complexity of infinite sequences

The randomness rate of an infinite binary sequence is characterized by the sequence of ratios between the Kolmogorov complexity and the length of the initial segments of the sequence. It is known that there is no uniform effective procedure that transforms one input sequence into another sequence with higher randomness rate. By contrast, we display such a uniform effective procedure having as input two independent sequences with positive but arbitrarily small constant randomness rate. Moreover the transformation is a truth-table reduction and the output has randomness rate arbitrarily close to 1.

Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence

An infinite binary sequence has randomness rate at least

Algorithmically independent sequences

\sigma

Short Lists with Short Programs in Short Time – A Short Proof

if, for almost every

Impossibility of independence amplification in Kolmogorov complexity theory

n

Almost-Everywhere Superiority for Quantum Polynomial Time

, the Kolmogorov complexity of its prefix of length

Linear List-Approximation for Short Programs (or the Power of a Few Random Bits)

n

Short Lists with Short Programs in Short Time

is at least