The reachability problem for finite cellular automata

doi:10.1016/0020-0190(94)00169-Y

Information Processing Letters

Volume 53, Issue 1, 13 January 1995, Pages 27-31

https://doi.org/10.1016/0020-0190(94)00169-Y Get rights and content

Abstract

We investigate the complexity of the Configuration REachability Problem (CREP) for two classes of finite weakly predictable cellular automata: the invertible and the additive ones. In both cases we prove that CREP belongs to the “Arthur-Merlin” class CoAM[2]¹.

References (16)

R.B. Boppana et al.
Does co-NP have short interactive proofs?
Inform. Process. Lett.
(1987)
T. Toffoli et al.
Invertible cellular automata: A review
Phys. D
(1990)
L. Babai et al.
Arthur-Merlin games: a randomized proof system and a hierarchy of complexity classes
J. Comput. System Sci.
(1985)
S. Buss et al.
On the predictability of coupled automata: An allegory about chaos
A. Clementi
On the complexity of cellular automata
A. Clementi et al.
Graph theory and interactive protocols for reachability problems on finite cellular automata
K. Culik II and S. Yu, Undecidability of CA classification scheme, Complex Systems2, pp....
S. Goldwasser et al.
The knowledge complexity of interactive proof systems
SIAM J. Comput.
(1987)

There are more references available in the full text version of this article.

Cited by (4)

Reachability problem in non-uniform cellular automata
2021, Information Sciences
Citation Excerpt :
Primary focus of the non-uniform CA research was on the one-dimensional CAs, where the cells follow Wolfram’s CA rules [10]. Researchers already studied the reachability problem [4,3] for finite classical CAs. However, for non-linear non-uniform CAs, there is no method to deal with the reachability problem.
This paper deals with the CREP (Configuration REachability Problem) for non-uniform cellular automata (CAs). The cells of non-uniform CAs, we have considered here, can use different Wolfram’s rules to generate their next states. We report an algorithm which decides whether or not a configuration of a given (non-uniform) cellular automaton is reachable from another configuration. We develop a characterization tool, named Reachability tree, is used to develop theories and the decision algorithm for the CREP. Though the worst case complexity of the algorithm is exponential in time and space, but the average performance is very good.
Image Analysis and Computer Vision: 1995
1996, Computer Vision and Image Understanding
This paper presents a bibliography of over 1550 references related to computer vision and image analysis, arranged by subject matter. The topics covered include computational techniques; feature detection and segmentation; image and scene analysis; two-dimensional shape; pattern; color and texture; matching and stereo; three-dimensional recovery and analysis; three-dimensional shape; and motion. A few references are also given on related topics, including geometry and graphics, compression and processing, sensors and optics, visual perception, neural networks, artificial intelligence and pattern recognition, as well as on applications.
Reachability problem in non-uniform cellular automata
2019, arXiv
A Study of Chaos in Cellular Automata
2018, International Journal of Bifurcation and Chaos

¹: The result concerning the additive class has been first presented in [5].

View full text

The reachability problem for finite cellular automata

Abstract

Inform. Process. Lett.

Phys. D

Arthur-Merlin games: a randomized proof system and a hierarchy of complexity classes

J. Comput. System Sci.

On the predictability of coupled automata: An allegory about chaos

On the complexity of cellular automata

Graph theory and interactive protocols for reachability problems on finite cellular automata

The knowledge complexity of interactive proof systems

SIAM J. Comput.