Banks, E. R. "Information Processing and Transmission in Cellular Automata". TR-81, M IT Project MAC,.]an. 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....bits, etc. to a memory, ceil, the proper tradeoff would be 2. F. ach element of an array of parallel processes need not be universal for the array to be universal, viz. Conway s LIFE game [38] or Fimnle tterative arrays [ tTJ. However, universality can be achieved with only . a few tens of gates [7], and is therefore relatively cheap. Actors in Hardware i Section 1.3 achieved. However, the protocol s in a content addressable. memory are too simpleto make efficient use of the communication bandwidth:of.the accetamg .me. hamsre. For only a few more gates, one can add a comp ete.micropr ....

Banks, E. R. "Information Processing and Transmission in Cellular Automata". TR-81, M IT Project MAC,.]an. 1971.

....evolutionary computation techniques rely upon sexual reproduction, motivated the introduction of such a feature also in the context of Enact. Although a number of cellular automata exhibiting the ability of self reproduction have been discovered for instance, von Neumann 1966] Codd 1968] [Banks 1971], Langton 1984] and [Byl 1989] no cellular automaton embedding a form of sexual reproduction has apparently been reported, other than the one in this thesis. The closest reference in the literature seems to be [Vitanyi 1973] where an abstract discussion is carried out on how to extend the ....

....for present purposes since they are the same for all cellular automata shown in the first five rows of the table. 13 Authors Year Number of Size of Initial Universal Universal States Configuration Computability Constructability von Neumann 1952 29 10 4 yes yes Codd 1968 8 10 4 yes yes Banks 1971 4 yes no Langton 1984 8 86 no no Byl 1989 6 11 no no Enact 1992 4 6 yes no Table 2.1: Cellular automata with ability for self reproduction, in a comparison with the sexual reproduction process embedded in Enact. cellular space that require initially special values. In the case of Enact, ....

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E. R. Banks. Information processing and transmission in cellular automata. PhD thesis, MIT, 1971.

....a general purpose computing structure within a cellular automaton, the most practical approach is to T. Toffoli, N. H. Margolus = Invertible Cellular Automata 6 start with a local map that directly supports logic gates and wires, and then build the appropriate logic circuits out of these primitives[4,77]. As explained in [70,19] in an invertible cellular automaton the gates will have to be invertible; because of this constraint, a complete, self contained logic design will have to explicitly provide, besides circuitry for the desired logic functions, additional circuitry for functions (analogous ....

Banks, Edwin, "Information Processing and Transmission in Cellular Automata," Tech. Rep. MAC TR81, MIT Project MAC (1971).

....process and wave localization. 1.2 Definition In order to give a definition of a cellular automaton, we first present a simple example. Although it is very basic, the rule we discuss here exhibits a surprisingly rich behavior. It has been proposed initially by Edward Fredkin in the 1970s [40] and is defined on a two dimensional square lattice. Each site of the lattice is a cell which is labeled by its position r = i; j) where i and j are the row and column indices. A function t ( r) is associated to the lattice to describe the state of each cell at iteration t. This quantity can ....

E. Banks. Information processing and transmission in cellular automata. Technical report, MIT, 1971. MAC TR-81.

....memory stack. Second, as far as we could understand it, it contains an error discussed in Section 3.3. Third, the author did not explain precisely what he means by universality . It could be at first sight considered as a minor problem since it is also the case for instance in the works of Banks [1], Nourai and Kashef [11] and Smith [7] As a matter of fact, all authors we could read on this topic did not defined what they meant by Turing universality. This point may seem of low interest since the definition is usually straightforward, but in the case of simulation by cellular automata, it ....

....of simulation presented in [14] The key point is that this definition is compatible with Turing universality: if a Turing universal cellular automaton is simulated by another cellular automaton, the latter is also Turing universal. This intrinsic universality is implicitly used by Banks in [1] but it seems that he did not get the relationship with Turing universality which he also proves in a different way. This author focuses on the problem of the difference between finite and infinite initial configurations, which is indeed the key point of the definition of Turing universality ....

E. R. Banks. Information processing and transmission in cellular automata. PhD thesis, Mass. Inst. of Tech., Cambridge, Mass, 1971. 21

....as well as more efficient. Indeed, if one wants to build a general purpose computing structure within a cellular automaton, the most practical approach is to start with a local map that directly supports logic gates and wires, and then build the appropriate logic circuits out of these primitives[4, 77]. As explained in [70, 19] in an invertible cellular automaton the gates will have to be invertible; because of this constraint, a complete, self contained logic design will have to explicitly provide, besides circuitry for the desired logic functions, additional circuitry for functions ....

Banks, Edwin, "Information Processing and Transmission in Cellular Automata," Tech. Rep. MAC TR-81, MIT Project MAC (1971). 25 More formally, the uniformity group of the structural description is a proper subgroup of that of the functional behavior.

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