Discrete state transition systems on continuous space-time: a theoretical model for amorphous computing

Authors:
Masami Hagiya
Affiliations:
Department of Computer Science, Graduate School of Information Science and Technology, University of Tokyo and NTT Communication Science Laboratories
Venue:
UC'05 Proceedings of the 4th international conference on Unconventional Computation
Year:
2005

Citing 3
Cited 3

The algorithmic analysis of hybrid systems

Theoretical Computer Science - Special issue on hybrid systems
Amorphous computing

Communications of the ACM
Transition Systems over Continuous Time-Space

Electronic Notes in Theoretical Computer Science (ENTCS)

Geometrical accumulations and computably enumerable real numbers

UC'11 Proceedings of the 10th international conference on Unconventional computation
Analytical identification of discrete objects

Automation and Remote Control
Abstract geometrical computation 7: geometrical accumulations and computably enumerable real numbers

Natural Computing: an international journal

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Abstract

This paper deals with a kind of hybrid system that is obtained by making cellular automata infinitely small. Each point on a continuous space is defined as a state transition system with a finite number of discrete states that changes its state according to its previous state and the states of its neighbors. Time is also defined as continuous, so that state transitions may propagate through the space continuously over time. Discrete state transitions can be made instantaneously, as in the case of ordinary hybrid systems. It turned out that even defining the global behaviors that satisfy local transition rules is not trivial. The framework that we propose here can be regarded as a framework for amorphous computing.