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Classes of automata. (Clicking on each layer gets an article on that subject) A Turing machine is a mathematical model of computation describing an abstract machine [ 1 ] that manipulates symbols on a strip of tape according to a table of rules. [ 2 ] Despite the model's simplicity, it is capable of implementing any computer algorithm.
An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".
Turing used seven symbols { A, C, D, R, L, N, ; } to encode each 5-tuple; as described in the article Turing machine, his 5-tuples are only of types N1, N2, and N3. The number of each "m ‑configuration" (instruction, state) is represented by "D" followed by a unary string of A's, e.g. "q3" = DAAA. In a similar manner, he encodes the symbols ...
A deterministic finite automaton M is a 5- tuple, (Q, Σ, δ, q0, F), consisting of. a finite set of states Q. a finite set of input symbols called the alphabet Σ. a transition function δ: Q × Σ → Q. an initial or start state q 0 ∈ Q {\displaystyle q_ {0}\in Q} a set of accept states F ⊆ Q {\displaystyle F\subseteq Q}
Some versions represent the positive integers as only a strings/stack of marks allowed in a "register" (i.e. left-ended tape), and a blank tape represented by the count "0". Minsky eliminated the PRINT instruction at the expense of providing his model with a mandatory single mark at the left-end of each tape.
A record is similar to a mathematical tuple, although a tuple may or may not be considered a record, and vice versa, depending on conventions and the programming language. In the same vein, a record type can be viewed as the computer language analog of the Cartesian product of two or more mathematical sets , or the implementation of an abstract ...
The rules for one 1-state Turing machine might be: In state 1, if the current symbol is 0, write a 1, move one space to the right, and transition to state 1; In state 1, if the current symbol is 1, write a 0, move one space to the right, and transition to HALT; This Turing machine would move to the right, swapping the value of all the bits it ...
One of the most common examples of an algebraic data type is the singly linked list. A list type is a sum type with two variants, Nil for an empty list and Cons x xs for the combination of a new element x with a list xs to create a new list. Here is an example of how a singly linked list would be declared in Haskell: