a) The Turing machine that accepts a string containing even number of b's is (see in attachments).
b) The Turing machine that accepts a string containing equal number of a’s and b’s is (see in attachments).
Turing machine:
The Turing machine is an abstract machine that manipulates symbols on a strip of tape in accordance with a set of rules. It is a mathematical model of computation. The paradigm is straightforward, but it can implement any computer algorithm. The machine runs on a never-ending tape of memory that is divided into distinct cells, each of which can store a single symbol selected from a limited range of symbols known as the machine's alphabet. It has a "head" that is always placed over one of these cells during operation, and it has a "state" chosen from a limited number of states. Turing machines demonstrated that mechanical computation's power has some fundamental limitations.
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