Cellular automata models with complex valued transition functions

Abstract

The new class of mathematical models for computation theory is considered — namely cellular automata (CA) with branching complex-valued transition functions. The key point is possible multivaluedness of cell’s states with such transition functions. Different cases with complex-value transition functions had been considered. Dynamics CA on one branch and on different isolated branches are described. Also the case of transitions of states between branches is proposed. The case of continuous-valued CA and their finite-valued approximations are discussed. The problem of approximation of multivalued CA is stated.

Keywords

• cellular automata
• complex-valued transition functions
• Riemann surfaces
• continuous-valued CA
• branching
• approximation of multivaluedness