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Show that A is Turing-recognizable AmATM

Short Answer

Expert verified

It is proved that A is Turing Recognizable.

Step by step solution

01

Introduction of Turing Recognizable

A language L is said to be Turing Recognizable if and only if there exist any Turing Machine (TM) which recognize it i.e., TM halt and accept strings belong to language L and will reject or not halt on the input strings that doesn鈥檛 belong to language L .

02

To show A is Turing recognizable

Before we proceed, we know that ATM is Turing Recognizable.

Let us assume that A is Turing Recognizable, this means we can construct a Turing Machine M for A , such that LM=A.

Assume f is Mapping Reduction Function which is defined as:
fw=M,w

So,wAif and only ifM,wATM.

So, if, AmATMthen A must be Turing Recognizable as ATM is Turing Recognizable

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