Self-timed cellular automata and their computational ability

  • Authors:

  • F. Peper;T. Isokawa;N. Kouda;N. Matsui

  • Affiliations:

  • Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka-cho, Nishi-ku, Kobe 651-2492, Japan;Department of Computer Engineering, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan;Department of Computer Engineering, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan;Department of Computer Engineering, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan

  • Venue:
  • Future Generation Computer Systems - Cellular automata CA 2000 and ACRI 2000
  • Year:
  • 2002

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Abstract

This paper describes a novel type of Asynchronous Cellular Automata, in which transitions of cells only take place when triggered by transitions of their neighboring cells. Called Self-Timed Cellular Automaton (STCA), the model offers control over its cells' operations to the same degree as in Synchronous Cellular Automata, while at the same time offers the flexibility of its purely asynchronous counterparts. We implement some simple functionalities on STCA, like wires, crossings of wires, and NAND-gates, and show that a Synchronous Cellular Automaton with N states can be simulated by an STCA with O(N√N) states in linear time. This establishes the computational universality of STCA, since Synchronous Cellular Automata can, if properly designed, embed universal Turing Machines. The STCA model offers promise for the realization of Cellular Automaton-based computers with logic devices and wires on the molecular scale, a technology that is expected to take off in 10-15 years. In this context, self-timing is especially useful for its compatibility with the asynchronous behavior of molecules, and for avoiding delay problems associated with a central clock.