The Role of Conceptual Structure in Designing Cellular Automata to Perform Collective Computation Manuel Marques-Pita 1,2,3 , Melanie Mitchell 3 , and Luis M. Rocha 1,2 1 Indiana University 2 Instituto Gulbenkian de Ciˆ encia 3 Portland State University Abstract. The notion of conceptual structure in CA rules that perform the density classification task (DCT) was introduced by [1]. Here we investigate the role of process-symmetry in CAs that solve the DCT, in particular the idea of conceptual similarity, which defines a novel search space for CA rules. We report on two new process-symmetric one- dimensional rules for the DCT which have the highest “balanced” per- formance observed to date on this task, as well as the highest-performing CA known to perform the DCT in two dimensions. Finally, we investigate the more general problem of assessing how different learning strategies (based on evolution and coevolution, with and without spatial distri- bution), previously compared by [2], are suited to exploit conceptual structure in learning CAs to perform collective computation. 1 Introduction The study of computation in cellular automata (CAs) and related cellular archi- tectures has lately garnered renewed interest due to advances in the related fields of reconfigurable hardware, sensor networks, and molecular-scale computing sys- tems. In particular, cellular array architectures are thought to be appropriate for constructing physical devices such as field configurable gate arrays for electron- ics, networks of robots for environmental sensing and nano-devices embedded in interconnect fabric used for fault tolerant nanoscale computing [3]. A current stumbling block for CA computing is the difficulty of programming CAs to per- form desired computations, due to the decentralized architectures and nonlinear behavior of these systems. One approach is to use genetic algorithms or other evolutionary computation methods to evolve cellular automata transition rules that will perform desired computations. However, this approach has problems of scaling, due to the large search spaces for non-elementary CAs—those with larger than nearest-neighbor cell communication or with multiple states per cell. In this paper we describe our investigation of reducing the dimensionality of these search spaces by using automatically-discovered conceptual structures of rule tables that are common to CAs likely to be successful for a particular computational task. We show that for one well-studied task—two-state density C.S. Calude et al. (Eds.): UC 2008, LNCS 5204, pp. 146–163, 2008. c  Springer-Verlag Berlin Heidelberg 2008