Cellular automata models with complex valued transition functions

Authors

  • Alexander Makarenko Educational and Scientific Complex “Institute for Applied System Analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv https://orcid.org/0000-0001-6728-3058

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2020.4.11

Keywords:

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

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.

Author Biography

Alexander Makarenko, Educational and Scientific Complex “Institute for Applied System Analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv

Alexander S. Makarenko,

a professor, Doctor of Physical and Mathematical Sciences, the head of the Department of Applied Nonlinear Analysis of Educational and Scientific Complex “Institute for Applied System Analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine.

References

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Published

2020-12-29

Issue

Section

New methods in system analysis, computer science and theory of decision making