Which of the following remarks the given statement?Statement: Any func...
The following conclusion is laid down from the Church-Turing thesis:
Any function whose values can be computed by an algorithm, can be computed by a Turing machine. If any real world computer can be simulated by a turing machine, it is Turing equivalent to a Turing Machine.
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Which of the following remarks the given statement?Statement: Any func...
Church-Turing Thesis:
The Church-Turing thesis is a hypothesis in computer science that suggests that any function that can be computed by an algorithm can also be computed by a Turing machine. The thesis is named after Alonzo Church and Alan Turing, who independently formulated similar ideas in the 1930s. It is a fundamental concept in computability theory and forms the basis for understanding the limits of computation.
Explanation:
The statement given in the question is directly related to the Church-Turing thesis. The thesis states that any function that can be computed by an algorithm can also be computed by a Turing machine. This means that if there exists a step-by-step procedure (algorithm) to compute the values of a function, then those values can also be computed by a Turing machine.
A Turing machine is a theoretical device that consists of an infinitely long tape divided into cells, a read/write head that can move along the tape, and a set of rules that dictate its behavior. It can perform basic operations such as reading and writing symbols on the tape, moving left or right, and changing its internal state based on the current symbol and state. Despite its simplicity, a Turing machine can simulate any algorithmic computation.
The Church-Turing thesis is widely accepted as a guiding principle in computer science. It suggests that any reasonable model of computation should be equivalent in power to a Turing machine. This means that if a function can be computed by one model (such as a computer program), it can also be computed by another model (such as a Turing machine).
The other options mentioned in the question, namely the Smn theorem and the Structured Program theorem, are not directly related to the given statement. These theorems deal with specific aspects of computability and program structure, but they do not address the general equivalence between algorithms and Turing machines.
In conclusion, the correct answer to the given statement is option 'C' - Church-Turing thesis. This thesis suggests that any function whose values can be computed by an algorithm can also be computed by a Turing machine.