A motivation for creating a Turing model for an individual element (e.g. Symbol) comes from the fact that the element is the only computational (”thinking”) part of model. That’s why all semantics, e.g., all intelligence (functionality) in SAM is deemed to be in an atom. The transition function,, being the only active part of the model, is the most important topic of the TM model of the atomistic element.

Each symbol in the symbolic atomistic model is Turing equivalent. See AHO and source code atom.

The states are inactive parts of the model containing branching conditions and calculations. Formulating an element can be done analytically by investigating the individual features of each Symbolic clause, one after another. In FIGURE the transition function  is in the middle of the model. Activation of the element is shown on the left of the figure. It uses the notation of the Symbolic clause containing input elements as atoms.

Turing_Equivalent_for_Symbol

The output of the block is described as  enabling a feedback into incoming input symbols. These are actually side effect elements in the symbolic model. There is no perfect compatibility to the Turing model’s right (R) and left (L), but selecting the next movement happens by specific movements in the state transition table Q. In FIGURE  a hypothesized state Q(i) is drawn as well as its predecessor Q(i-1) and successor Q(i+1).  In normal situations the atom selects the next state from the right to be executed. Loop is almost the only situation, where a backward movement is needed. Some forward movements are conditional like an if element or a switchcase element. There are some specialties for the sake of polymorphism and ambiguous calls that are are explained in the book.

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