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A Turing machine is a mathematical model of computation describing an abstract ... The shift left and shift right operations may shift the tape head across the tape ...
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 simple generalization is the extension to Turing machines with m symbols instead of just 2 (0 and 1). [10] For example a trinary Turing machine with m = 3 symbols would have the symbols 0, 1, and 2. The generalization to Turing machines with n states and m symbols defines the following generalized busy beaver functions:
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."
A multi-tape Turing machine is a variant of the Turing machine that utilizes several tapes. Each tape has its own head for reading and writing. Each tape has its own head for reading and writing. Initially, the input appears on tape 1, and the others start out blank.
For example, the rules might convert (2,2A,0) to (2,1,0) and move the head left. Thus in this example, the machine acts like a 3-colour Turing machine with internal states A and B (represented by no letter). The case for a 2-headed Turing machine is very similar. Thus a 2-headed Turing machine can be Universal with 6 colours.
With a single infinite stack the model can parse (at least) any language that is computable by a Turing machine in linear time. [2] In particular, the language {a n b n c n } can be parsed by an algorithm which verifies first that there are the same number of a's and b's, then rewinds and verifies that there are the same number of b's and c's.
A Multitrack Turing machine is a specific type of multi-tape Turing machine. In a standard n-tape Turing machine, n heads move independently along n tracks. In a n-track Turing machine, one head reads and writes on all tracks simultaneously. A tape position in an n-track Turing Machine contains n symbols from the tape alphabet.