Let S = {w in {0,1}* | the length of w is a perfect square}.(A number x is said to be a perfect square if it can be written as x = y 2 , for some nonnegative integer y.) Design a Turing Machine to show that the language S is decidable. The only operations allowed to use are the addition (+) and multiplication (x) of integers, but you are not allowed to use square-root operations. Do not provide a DFA, NFA or PDA, only a Turing Machine (either diagram or described)

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Problems on Turing Machines

In the computational world, the Turing machine is a powerful computation engine. The invention of the Turing Machine is done by Alan Turing in 1936. A Turing Machine (TM) is a diagrammatic model of a fictional computer. It determines an output from a set of input variables using a pre-defined set of rules. It is used to get around the limitations of finite automata and pushdown automata.