Information-preserving models of physics and computation: Final report

This research pertains to discrete dynamical systems, as embodied by cellular automata, reversible finite-difference equations, and reversible computation. The research has strengthened the cross-fertilization between physics, computer science and discrete mathematics. It has shown that methods and concepts of physics can be exported to computation. Conversely, fully discrete dynamical systems have been shown to be fruitful for representing physical phenomena usually described with differential equations - cellular automata for fluid dynamics has been the most noted example of such a representation. At the practical level, the fully discrete representation approach suggests innovative uses of computers for scientific computing. The originality of these uses lies in their non-numerical nature: they avoid the inaccuracies of floating-point arithmetic and bypass the need for numerical analysis. 38 refs