Computational Complexity of Determining Which Statements about Causality Hold in Different Space-Time Models

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

12-2007

Comments

Technical Report: UTEP-CS-07-34a

Published in Theoretical Computer Science, 2008, Vol. 405, No. 1-2, pp. 50-63.

Abstract

Causality is one of the most fundamental notions of physics. It is therefore important to be able to decide which statements about causality are correct in different models of space-time. In this paper, we analyze the computational complexity of the corresponding deciding problems. In particular, we show that: for Minkowski space-time, the deciding problem is as difficult as the Tarski's decision problem for elementary geometry, while for a natural model of primordial space-time, the corresponding decision problem is of the lowest possible complexity among all possible spacetime models.