Łukasz Kaiser – Other Publications

Łukasz Kaiser – Other Publications

Papers on AI

  • Program Search as a Path to Artificial General Intelligence, Kaiser L., Artificial General Intelligence (Cognitive Technologies), B. Goertzel and C. Pennachin, Eds., To appear, Springer-Verlag, 2004.
  • MemeStorms: A Cellular Automaton for Pattern Recognition and Dynamic Fuzzy Calculus, Buller, A., Kaiser, L., Shimohara, K., Proceedings of The Seventh International Symposium on Artificial Life and Robotics (AROB 7th '02), pp. 528-531, 2002.
  • Para-evolutionary Paradigm of Reasoning, Buller, A., Kaiser, L, Shimohara, K. Knowledge-Based Intelligent Information Engineering Systems & Allied Technologies (KES'2001), Baba N, Jain LC, Howlett RJ (Eds.), Amsterdam: IOS Press, pp. 127-131, 2001.
  • MemeStorms: Cellular Working Memory and Dynamics of Judgments, Buller, A., Chodakowski, T., Kaiser, L., Nowak, A., Shimohara, K., Proceedings of The Sixth International Symposium on Artificial Life and Robotics (AROB 6th '01), pp 146-149, 2001.

Masters Theses

Confluence of Right Ground Term Rewriting Systems is Decidable, Masters Thesis in Computer Science under the supervision of professor Leszek Pacholski, Wroclaw, 2003. See the Publications Page for an abstract and a link to an improved version presented at FOSSACS'05.

On the extensions of approximative density, Masters Thesis in Mathematics under the supervision of professor Grzegorz Plebanek (in polish), Wroclaw, 2003.
Approximative density of a set of natural numbers A is defined as lim (n to infinity) |A intesection n| / n, if this limit exists. This concept is useful in number theory, it was also investigated how to extend this concept to an additive function defined on the power set of omega. It is known that such an extension can be defined by replacing the usual limit in the formula above with a limit taken on an ultrafilter. In this paper we define and describe the behavior of extensions of densities defined as limits on ultrafilters and convex combinations of such limits. The main result states that a linear combination of two different extensions of approximative density coming from limits on some ultrafilters can not be described as a limit on some ultrafilter. This result is a step towards the hypothesis that extensions of approximative density defined as limits on ultrafilters are in fact extremal points in the convex set of all additive extensions of approximative density.