Lenore Blum

A simple unpredictable pseudo random number generator

Two closely-related pseudo-random sequence generators are presented: The

Toward a mathematical theory of inductive inference

{1 / P}

Comparison of Two Pseudo-Random Number Generators

generator, with input P a prime, outputs the quotient digits obtained on dividing 1 by P. The

CS4HS: an outreach program for high school CS teachers

x^2 \bmod N

A model for high school computer science education: the four key elements that make it!

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On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines

Intelligence tests occasionally require the extrapolation of an effective sequence (e.g. 1661, 2552, 3663, …) that is produced by some easily discernible algorithm. In this paper, we investigate the theoretical capabilities and limitations of a computer to infer such sequences. We design Turing machines that in principle are extremely powerful for this purpose and place upper bounds on the capabilities of machines that would do better.

COMPLEXITY AND REAL COMPUTATION: A MANIFESTO

What do we want from a pseudo-random sequence generator? Ideally, we would like a pseudo-random sequence generator to quickly produce, from short seeds, long sequences (of bits) that appear in every way to be generated by successive flips of a fair coin.

Algebraic Settings for the Problem “P ≠ NP?”

In this paper, we describe a pilot summer workshop (CS4HS) held at Carnegie Mellon University in July 2006 for high school CS teachers to provide compelling material that the teachers can use in their classes to emphasize computational thinking and the many possibilities of computer science. Diversity and broadening participation was explicitly addressed throughout the workshop. We focused on broadening the image of what CS is -- and who computer scientists are -- since the reasons for under-representation in the field are very much the same as the reasons for the huge decline in interest. We describe the design of the workshop along with results from initial surveys and evaluations. Short-term evaluations show that this workshop was successful in changing the perception of CS for these teachers and giving them the impetus to include broader topics in their programming courses for the upcoming school year. Future surveys will track the long-term effect of this workshop.

The Evolving Culture of Computing: Similarity Is the Difference

This paper presents a model program for high school computer science education. It is based on an analysis of the structure of the Israeli high school computer science curriculum considered to be one of the leading curricula worldwide. The model consists of four key elements as well as interconnections between these elements. It is proposed that such a model be considered and/or adapted when a country wishes to implement a nation-wide program for high school computer science education.

Evaluating rational functions: infinite precision is finite cost and tractable on average

A model for computation over an arbitrary (ordered) ring R is presented. In this general setting, universal machines, partial recursive functions, and NP-complete problems are obtained. While the theory reflects of classical over Z (e.g. the computable functions are the recursive functions), it also reflects the special mathematical character of the underlying ring R (e.g. complements of Julia sets provide natural examples of recursively enumerable undecidable sets over the reals) and provides a natural setting for studying foundational issues concerning algorithms in numerical analysis.<<ETX>>