M. Sipper, "Co-evolving Non-Uniform Cellular Automata to Perform Computations", Physica D, 92:  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Automata Unidimensional and bidimensional CA have been extensively studied [Wol94] Nowadays, the research area of CA encompasses theoretical studies, as well as applications in the so called hard and soft sciences. The hard CA science includes formal studies on computational properties of CA [Sip96, Sip99, ST99], extensions of the simple CA model [Sip96, LumN94, SchR99] and studies on the behavior of CA as complex dynamical systems [Wol94, Bar97] However, in most of these studies, CA were considered as synchronous and closed systems, for the sake of achieving determinism and predictability in CA s ....

....extensively studied [Wol94] Nowadays, the research area of CA encompasses theoretical studies, as well as applications in the so called hard and soft sciences. The hard CA science includes formal studies on computational properties of CA [Sip96, Sip99, ST99] extensions of the simple CA model [Sip96, LumN94, SchR99] and studies on the behavior of CA as complex dynamical systems [Wol94, Bar97] However, in most of these studies, CA were considered as synchronous and closed systems, for the sake of achieving determinism and predictability in CA s behavior. Although some work recognize the peculiar and ....

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M. Sipper, "Co-evolving Non-Uniform Cellular Automata to Perform Computations", Physica D, 92:

.... [18] Nuclear Instruments Methods in Physics Research A, 38] Nuclear Technology, 317] Parallel Computing, 65, 210, 67, 74, 75, 442, 76, 449, 77] Parallel Computing (Netherlands) 531] Parallel Processing Letters, 384] PARS Mitteilungen, 143] Pattern Recognition, 81, 332] Physica D, [12, 32, 37] Physical Review C, Nuclear Physics, 336, 337] Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 162] Scienti c Computing in Chemical Engineering, 249] Scienti c Computing World, 36] SIAM News, 502] SIGICE Bulletin, 127] Signal Processing, 555] Tech. Sci. Inform. France) ....

....295] Shida, Koichiro, 235] Shieber, Stuart, 418] Shimojima, Koji, 304] Shonkwiler, Ronald, 123, 490] Siegel, Howard Jay, 68] Siegmund, Frederik, 491] Silverman, H. 220] Simon k, Ivan, 185] Sims, Karl, 492] Singh, Kirti, 177] Singh, Montek, 332] Singru, A. 274] Sipper, Moshe, [30, 31, 32, 37, 38, 39] Sipper, M. 53] Sirtori, Enrico, 386, 387, 388] Sitko , N. 220] Siwak, P. 28] Skrlec, Davor, 266, 296] Sloot, P. M. A. 265, 329] Slootmaekers, Romain, 346] Smith, A. 220] Smith, D. G. 473] Smith, George D. 101, 403] Sonza Reorda, Matteo, 239, 280, 283, 493] Soraghan, J. J. ....

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Moshe Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 7(2):181{ 190, ? 1996. ga96cSipper.

....Anal Theory Methods Appl. 535] Nuclear Science and Engineering, 104, 349] Nucleic Acids Research, 335] Optics Letters, 237] Parallel Computing, 578] Pattern Recognition, 94, 588, 593] Pattern Recognition Letters, 137, 313, 762, 786] Phys. A Stat. Theor. Phys. 225] Physica D, [348, 856] Physical Review B, 202, 468] Polym. Compos. 734] Proc. CSEE (China) 459] Proc. Natl. Sci. Counc. Rep. China A, Phys. Sci. Eng. Taiwan) 756] Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering, 883] Prod. Plann Control, 466, ....

....Shuangxi, Zhou, 458] Shuwei, Fan, 459] Shuzi, Yang, 147, 301] Sidi, Moshe, 645] Sidorowich, John J. 215] Sikora, R. 460] Authors 31 Silva, Carlos, 161] Simon, Herbert A. 154] Simpson, Angus R. 652] Simpson, Marc T. 789] Singh, Jasbir, 205] Singh, R. 461] Sipper, Moshe, [790, 856] Siying, Zhang, 360] Sklansky, Jack, 462, 588] Skochinski, E. 585] Skomorokhov, A. O. 463] Small, Gary W. 24, 374] Smith, Alice E. 88, 622, 818] Smith, R. E. 329] So, Sung Sau, 428, 782] Sobieski, I. P. 660] Soh, Chee Kiong, 464, 791] Soloweij, James E. 205] Solterbeck, ....

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Moshe Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 7(2):181-- 190, ? 1996. ga96cSipper.

....Commun. 668] Optical Engineering, 671, 890] Optics Communications, 802, 866] Optics Letters, 649, 653, 661, 691] Pattern Recognit. Image Anal. Russia) 327] Pharmaceutical Research, 322, 1035] Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. USA) 864] Physica D, [121, 122, 123, 125, 126, 130, 138, 143, 153, 154, 170, 173, 175, 180, 183] Physica Status Solidi (a) 905] Physical Review A, 283, 896, 181] Physical Review A General Physics, 174] Physical Review B, 135, 140, 868] Physical Review B: Condensed Matter Material Physics, 883] Physical Review C, Nuclear Physics, 150, 859] Physical Review E, 148, 864, 157, ....

....[571] Sidorovitch, D. V. 705, 751] Sidorowich, John J. 660] Sieber, I. 677] Siebert, Stefan, 289] Sikora, Riyaz, 253] Sileny, J. 572] Sim, Dong Joon, 467, 484] Simons, D. G. 29] Simpson, Marc T. 22, 23] Singh, Jasbir, 296] Singh, S. 833] Singher, Liviu, 671] Sipper, Moshe, [141, 143, 153, 155] Sizmann, R. 695, 696] Skaar, J. 678] Skochinski, E. 715] Skolnick, Je rey, 1004] Small, Gary W. 1113, 1117, 80] Smith, Howard, 328] Smith, Jim, 911, 1062] Smith, Lloyd M. 578] Smith, M. I. 669] Smith, R. G. 180] Smith, Richard W. 420] Smith, Roger, 76] Snellen, M. 29] ....

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Moshe Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 7(2):181{ 190, ? 1996. ga96cSipper.

....as well as the GKL or the Das rule. More recently, Paredis [74] described a coevolutionary approach to search the space of rules and showed the difficulty of coevolving consistently two populations toward continuous improvement. A coevolutionary approach has also been studied by Sipper [100] for the exploration of rules for non homogeneous CA. In that particular CA model, each cell has its own independent version of a rule. Capcarrere, Sipper and Tomassini [14] also reported that by changing the specification of the convergence pattern, from all 0 0 s or all 1 0 s to a pattern in ....

Moshe Sipper. Coevolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1994.

....to perform a particular computational task. However, computation requiring global coordination can be arduous for CAs [19] even if they are designed by evolutionary techniques. It has been suggested that better computational performance can be attained by using many CA rules or a non uniform CA [20]. Non uniform CAs are cellular automata with cells that may contain different transition rules [21] The evolvability of non uniform CAs has been studied in [22] where cellular programming algorithm has been employed to locate non uniform CAs for different computational tasks. It appears that the ....

....demes of cells where the computation of each deme arises from the interaction of all the cells belonging to the deme. Such a simple model is easily identifiable in many systems in nature capable of self organisation [27] The algorithm is a modification of cellular programming given by Sipper [20] and it is defined as follows: 1. Initialise the population of N cells at random with CA rules, uniformly distributed among different values (the percentage of all the entries in the rule table which map to non zero states) 28] and set N demes, each of which has size 1 (a single cell) 2. ....

M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

....Automata (NUCA) model proposed by Sipper in [12] seems a suitable framework for solving our problem, but it requires a slight modification proposed in the next section. Difficulty of designing CA to have a specific behavior or to perform a particular computational task was discussed in [9] and [13]. Both works concluded that such systems can be evolved rather than designed. This paper aims to give an idea about how much it is difficult to design CA for the proposed temporal binary sequence generation problem. This is done by reducing the problem to independent setcovering problems. Simply, ....

SIPPER, M.: `Co-evolving Non-Uniform Cellular Automata To Perform Computations`, Physica D 92, 1996, pp. 193-208

....Hillis was able to evolve a nearly optimal sorting network with 61 exchanges, the best known designed solutions having 60 exchanges. Another highly parallel, local, co evolutionary algorithm has recently been used by Sipper for evolving non uniform cellular automata to perform computational tasks [14]. This model belongs to the cooperative class of co evolutionary algorithms, since the individual units must work in unison to attain a global goal. De Jong et al. 15] and Husbands [16] have proposed related co evolutionary models that are also based on species cooperation rather than ....

M. Sipper, Co-evolving Non-Uniform Cellular Automata to Perform Computations, Physica D, To appear, 1995.

....concentrating on the logic of life ) However, there is still no simple, principled way to program the transition table of a CA in such a way that all of these higher level phenomena can emerge. Some recent work has been published on evolving the transition tables in a non uniform CA [43], or, in other words, of automatically programming it. If we consider that Nidus is an aggregate system not too distantly related to a non uniform CA, then the emergence and selection of EOPs in Nidus can similarly be viewed as a process of (at least partially) evolving the transition tables. More ....

Moshe Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, (92):193--208, 1996.

....problem of scalability suffered by the gate level evolution, especially for EHW which would be used in industrial applications. 3. 3 Cellular Programming A research area closely related to EHW is cellular programming, i.e. evolving cellular automata (CA) by simulated evolution [66] Sipper et al. [66, 55, 67, 68] and Mitchell et al. 69, 70] have used EAs to evolve, rather than design by hand, CAs which display complex behaviours and perform complex computations. A hardware implementation was described in [55, 54] 3.4 Some Issues and Related Work in Adaptive EHW Although adaptive EHW might be accused ....

M. Sipper, "Co-evolving non-uniform cellular automata to perform computations," Physica D, vol. 92, pp. 193--208, 1996.

....a new rule set means reconfiguring the FPGA completely. This technique is unacceptably slow in the case of FPGAs and other programmable hardware devices, especially when 3D circuits become realizable[11] Another possibility to reduce the number of states in CAs is to use nonuniform CAs [8]. In non uniform CAs, different rule sets are used simultaneously, depending on the position of a cell in the CA space. This non uniformity can reduce the number of CA states, and hence the amount of information exchanged between CA cells. The reduction of CA state size causes a reduction in the ....

Sipper, M. 'Co-evolving Non-Uniform Cellular Automata to Perform Computations ', Physica D 92, 193-208 1996.

....bit has an equal chance of being 1 or 0 (see later) Likewise, the fitness of the CAs, as well as the empirical results were based on configurations generated in a similar way. According to this measure they found CAs that outperform the GKL rule (and two other slightly better hand generated CAs) Sipper (1996) introduced an elegant coevolutionary approach for evolving non uniform CAs for the density classification task, as well as for other tasks. In uniform CAs the same rules are used for each cell. This constraint is relaxed for non uniform CAs, allowing different rules for different cells. Where the ....

Sipper, M., (1996), Co-evolving Non-Uniform Cellular Automata to Perform Computations, Physica D, 92.

....process. Such experiments are needed to abstract the universal laws of evolution from the casual contingencies of the history of the earth. The first steps in this direction were the cellular automata (CA) of von Neumann [14] who only studied self replication. Among other, Langton [3] and Sipper [11] also addressed the question of evolution. Meanwhile Rasmussen et al. 7, 6] showed that a completely different model, inspired from computer architecture, could also be used in this domain. These ideas inspired T. Ray s Tierra simulator [8] providing the most spectacular simulations of evolution ....

Moshe Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

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M. Sipper, #Co-evolving non-uniform cellular automata to perform computations," Physica D92, 193 #1996#.

.... We have investigated an extension of the CA model termed non uniform cellular automata, in which cellular rules need not be identical [ Sipper, 1994, Sipper, 1995b, Sipper, 1995a ] Employing this model we found that high performance can be attained for the density task by means of co evolution [ Sipper, 1996 ] 1 . Non uniform CAs have also been investigated by [ Vichniac et al. 1986, Hartman and Vichniac, 1986 ] As noted by Mitchell et al. density is a global property and hence the task comprises a non trivial computation for a locally connected CA. Since the 1s can be distributed through 1 A ....

.... available on the best possible imperfect performance, attained to date by the Gacs Kurdyumov Levin (GKL) rule [ Gacs et al. 1978, Gonzaga de S a and Maes, 1992 ] Figure 1) Previous studies of the density task were conducted using locally connected, one dimensional grids [ Mitchell et al. 1994b, Sipper, 1996 ] The task can be extended in a straightforward manner to two dimensional grids, an investigation of which we have carried out, using the same number of local connections per cell as in the one dimensional case. We found that markedly higher performance is attained for the density task with ....

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M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

....two 75 cell blocks (# b = 2) CA is run for 665 time steps. The randomly generated initial configurations have a density of 1s greater than 0:5, and the CAs relax to a fixed pattern of all 1s, which is the correct solution. 4 Performance results for the synchronous case are reported, e.g. in [ Sipper, 1996a ] a) b) Figure 3: One dimensional synchronization task: Operation of a co evolved, asynchronous (model3) non uniform CA, with connectivity radius r = 1. CA size is N = 150, partitioned into 4 blocks (# b = 4) with updating order: block 1 block 2 block 0 block 3 block 1 block 2 ....

M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

....a cooperative or a competitive nature, the end result being a system displaying some global (worthwhile) functioning. An evolutionary component could also be added to such a system, increasing its adaptive capabilities, and allowing us to control or program its behavior [Mitchell et al. 1994, Sipper, 1996] Self reproducing, computing systems hold potential, both from an applicative standpoint as well as from a theoretical one. This work has shed light on the possibility of constructing such systems, and demonstrated the feasibility of their practical implementation. living organisms are ....

M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

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M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

....population genetics, studies of evolution and learning, and social Journal of Transfigural Mathematics, Vol.3.No.1. 1997 systems (Mitchell, 1996) An interesting line of research that has recently emerged upon the scene is that of evolving cellular automata (Mitchell et al. 1994; Mitchell, 1996; Sipper, 1996; Sipper, 1997a; Sipper, 1997b) In order to execute an evolutionary algorithm one creates, at random, a population of individuals. Each individual represents a possible solution to an a priori given problem, and is often represented by a simple string of characters. This initial population is ....

Sipper, M. 1996. Co-evolving non-uniform cellular automata to perform computations.

....evolved using genetic algorithms. We have investigated an extension of the CA model termed non uniform cellular automata, in which cellular rules need not be identical [14; 16; 15] Employing this model we found that high performance can be attained for the density task by means of co evolution [17]. As noted by Mitchell et al. density is a global property and hence the task comprises a non trivial computation for a locally connected CA. Since the 1s can be distributed throughout the grid, propagation of information must occur over large distances (i.e. O(N ) The computation involved ....

....cellular distance (see next Section) as the prime architectural parameter which linearly determines CA performance. Furthermore, we find that high performance architectures can be co evolved, concomitantly with the rules. This work extends our previous work on the co evolution of non uniform CAs [17] by studying evolving architectures. Our motivation stems from two primary sources: a) Finding more efficient CA architectures via evolution, b) The co evolution of architectures offers a promising approach for solving a general wiring problem for a set of distributed processors, subject to ....

M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193--208, 1996.

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Sipper, M. 'Co-evolving Non-Uniform Cellular Automata to Perform Computations ', Physica D 92, 193-208 1996.

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Sipper, M. (To appear). Co-evolving non-uniform cellular automata to perform computations. To appear in Physica D. Smith, A. R. III (1971). Simple computation-universal cellular spaces. Journal of the Association for Computing Machinery, 18, 339--353.

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