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Extra resources for A Cellular Genetic Algorithm with Disturbances: Optimisation Using Dynamic Spatial Interactions
1 Turing and Wang formulations The operation of a Turing machine proceeds in discrete time steps. In a single step the following sequence of basic operations occurs: (1) D reads the symbol of the scanned square and sends it to A; (2) based on this input and its current state, A undergoes a state transition; (3) the output associated with this transition is decoded by D, which (a) writes a (not necessarily new) symbol in the scanned square and (b) moves along the tape one square to the left, or one square to the right, or not at all.
Well formed logical nets can be constructed by interconnecting our primitives subject to two constraints. The first is the familiar rule from McCulloch-Pitts nets: each input line can be identified with at most one output line. The second constraint avoids logical paradoxes that can result from the use of instantaneous primitives. What, for example, would be meant by a not unit which received its own output as a direct input? To avoid such situations we stipulate that every cycle in a logical net must contain at least one delay.
2b will cause the machine to find the leftmost binary digit and then proceed along the string to the right hand end, complementing each binary digit in turn. 2 can also be carried out by a finite state automaton, and a very simple one indeed. 2. (a) Example and (b) quintuples for binary complementation machine. 42 4: Turing machines string. Its (Moore type) state diagram has transitions to state 1 on 0 inputs and to state 0 on 1 inputs. 3 shows an initial tape configuration and quintuple table for a Turing machine which checks whether a set of nested parentheses is well formed, a computation which cannot be done by a finite state machine.