Erik Demaine
The Geometry of Glass Slippers
Cinderella is a tool for interactive geometry built at ETH Zurich. Its basic feature is to specify some input, then make a geometric construction (using essentially ruler and compass), with the ability to later modify the input. This sounds simple, but it is extremely useful for building geometric intuition, discovering geometric properties and theorems, and precise drawing. Such a system is also easy to implement poorly. Cinderella is "done right" in many ways; for example, changing the input *always* changes the output in a consistent and continuous way, preventing any unsuspected, annoying "jumps." Cinderella automatically discovers geometric relations between objects, using an intriguing and fast randomized theorem prover. This allows you to test, for example, whether a particular point really does lie on a particular line, or whether the appearance is just coincidence or the screen resolution. Cinderella also supports web applets (being written in Java), animations, accurate loci, etc. For more information, see http://www.cinderella.de/.
Algorithms and Complexity Group Seminar Wednesday, 23 August 2000 at 3:30PM DC1304 ------- Quantum Kolmogorov Complexity Wim van Dam University of California, Berkeley ABSTRACT We give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the string. We define the quantum Kolmogorov complexity of a string of qubits as the length of the shortest quantum input to a universal quantum Turing machine that produces the initial qubits with high fidelity. Joint work with Andre Berthiaume and Sophie Laplante, Proceedings of the 15th Conference on Computational Complexity, pages 240-249 (2000); quant-ph no. 0005018.