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A Turing machine is a mathematical model of computation describing an ... see state-table below (transition function). ... Turing built a digital (Boolean ...
Martin Davis makes a persuasive argument that Turing's conception of what is now known as "the stored-program computer", of placing the "action table"—the instructions for the machine—in the same "memory" as the input data, strongly influenced John von Neumann's conception of the first American discrete-symbol (as opposed to analog) computer—the EDVAC.
In the state-transition table, all possible inputs to the finite-state machine are enumerated across the columns of the table, while all possible states are enumerated across the rows. If the machine is in the state S 1 (the first row) and receives an input of 1 (second column), the machine will stay in the state S 1.
With regard to what actions the machine actually does, Turing (1936) [2] states the following: "This [example] table (and all succeeding tables of the same kind) is to be understood to mean that for a configuration described in the first two columns the operations in the third column are carried out successively, and the machine then goes over into the m-configuration in the final column."
As with Turing machines, the actions are specified by a state transition table listing the current internal state of the turmite and the color of the cell it is currently standing on. For example, the turmite shown in the image at the top of this page is specified by the following table:
Turing's a-machine model. Turing's a-machine (as he called it) was left-ended, right-end-infinite. He provided symbols əə to mark the left end. A finite number of tape symbols were permitted. The instructions (if a universal machine), and the "input" and "out" were written only on "F-squares", and markers were to appear on "E-squares".
A computation tree is a representation for the computation steps of a non-deterministic Turing machine on a specified input. [1] A computation tree is a rooted tree of nodes and edges. Each node in the tree represents a single computational state, while each edge represents a transition to the next possible computation.
Formally, we define a variant of Turing machines with a set of transitions of the form (,,,,) , where p,q are states, ab,cd are pairs of symbols and D is a direction. If D is left, then the head of a machine in state p above a tape symbol b preceded by a symbol a can be transitioned by moving the head left, changing the state to q and replacing the symbols a,b by c,d.