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Turing machines are similar to finite automata/finite state machines but have the advantage of unlimited memory. They are capable of simulating common computers; a problem that a common computer can solve (given enough memory) will also be solvable using a Turing machine, and vice versa.
Binary: 101. Unary: 11111. We prefer unary representation: easier to manipulate with Turing machines. Example: function may have many parameters: Addition function. f ( x , y ) = x + y.
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To use a Turing machine, you would write some input on its tape, start the machine, and let it compute until it halts. Whatever is written on the tape at that time is the output of the computation. Although the tape is infinite, only a finite number of cells can be non- blank at any given time.
Apr 5, 2013 · Summary. A GENERAL MODEL OF COMPUTATION. As is true for all our models of computation, a Turing machine also operates in discrete time. At each moment of time it is in a specific internal (memory) state, the number of all possible states being finite.
A function is computable if there is a Turing Machine such that: f M Initial configuration Final configuration w∈D Domain q0 w qf f (w) initial state accept state For all
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We’ll focus on functions f : N → N. For a computer program to compute f is for it to yield f(n) as output whenever it is given n as input (n ∈ N). Theorem: not every function is computable. (And I can give you examples!)
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Turing Machine Example Design a TM M2 that decides A = {02n|n≥0}, the language of all strings of 0s with length 2n. • Without designing it, do you think this can be done? Why? – Yes: we could write a program to do it and therefore we know a TM could do it since we said a TM can do anything a computer can do • How would you design it?
