Three-valued logic gates in reaction–diffusion excitable media

It is well established now that excitable media are capable of implementing of a wide range of computational operations, from image processing to logical computation to navigation of robots. The findings published so far in the field of logical computation were concerned solely with realization of boolean logic. This imposed somewhat artificial limitations on a suitability of excitable media for logical reasoning and restricted a range of possible applications of these non-classical computational devices in the field of artificial intelligence. In the paper we go beyond binary logic and show how to implement three-valued logical operations in toy models of geometrically constrained excitable media. We realize several types of logical gates, including Łukasiewicz conjunction and disjunction, and Sobocinski conjunction in cellular automata and FitzHugh–Nagumo models of T-shaped excitable media.

[1]  Andrew Adamatzky,et al.  Molecular Computing , 2003 .

[2]  K. Showalter,et al.  Navigating Complex Labyrinths: Optimal Paths from Chemical Waves , 1995, Science.

[3]  Kenichi Yoshikawa,et al.  Different operations on a single circuit: Field computation on an excitable chemical system , 2003 .

[4]  Andrew Adamatzky,et al.  Computing with Waves in Chemical Media : Massively Parallel Reaction-Diffusion Processors( New System Paradigms for Integrated Electronics) , 2004 .

[5]  Tomohiko Yamaguchi,et al.  Finding the optimal path with the aid of chemical wave , 1997 .

[6]  N. G. Rambidi,et al.  Image processing using light-sensitive chemical waves , 2002 .

[7]  Kenichi Yoshikawa,et al.  Information operations with multiple pulses on an excitable field , 2003 .

[8]  Kenichi Yoshikawa,et al.  On Chemical Reactors That Can Count , 2003 .

[9]  Jerzy Gorecki,et al.  On the response of simple reactors to regular trains of pulses , 2002 .

[10]  Ángel Rodríguez-Vázquez,et al.  Reaction-diffusion navigation robot control: from chemical to VLSI analogic processors , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  M. Blunck,et al.  Online-Patentrecherchen — schnelle Antworten auf kritische Fragen , 1989, Naturwissenschaften.

[12]  K. Yoshikawa,et al.  Information operations with an excitable field. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Andrew Adamatzky,et al.  Collision-free path planning in the Belousov-Zhabotinsky medium assisted by a cellular automaton , 2002, Naturwissenschaften.

[14]  Andrew Adamatzky,et al.  Collision-based computing in Belousov–Zhabotinsky medium , 2004 .

[15]  Kenneth Showalter,et al.  Logic gates in excitable media , 1995 .

[16]  William H. Press,et al.  Numerical recipes in C , 2002 .

[17]  Andrew Adamatzky,et al.  Experimental implementation of mobile robot taxis with onboard Belousov-Zhabotinsky chemical medium , 2004 .

[18]  Andrew Adamatzky,et al.  Computing in nonlinear media and automata collectives , 2001 .

[19]  N G Rambidi,et al.  Finding paths in a labyrinth based on reaction-diffusion media. , 1999, Bio Systems.

[20]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[21]  K. Yoshikawa,et al.  Real-time memory on an excitable field. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  L. Kuhnert,et al.  Photochemische Manipulation von chemischen Wellen , 1986, Naturwissenschaften.

[23]  Andrew Adamatzky.  Programming Reaction-Diffusion Processors , 2004, UPP.