Question

True and False for each. To show that a language is decidable, one could:

A. write a program in C++ for it, show that the program always halts, and use the Church-Turing thesis.

B. show that the language can be enumerated by a Turing machine.

C. show that the language is well-defined.

D. use closure properties.

E. describe a Turing machine for it and show it always halts.

Answer 1

To show that a language is decidable, one could write a program in C++ for it, show that the program always halts, and use the Church-Turing thesis.

Step-by-step explanation:

To show that a language is decidable, there are several approaches that can be taken:

1. Write a program in C++ for it, show that the program always halts, and use the Church-Turing thesis. This approach involves implementing a program in the C++ programming language that can determine whether a given input belongs to the language or not. By demonstrating that the program always halts and invoking the Church-Turing thesis, which states that any computable function can be calculated by a Turing machine, we can establish decidability.
2. Show that the language can be enumerated by a Turing machine. If a Turing machine can list or generate all the valid strings in the language, then the language is decidable.
3. Use closure properties. If we can prove that the language is closed under certain operations, such as union, intersection, or complement, then it is decidable.
4. Describe a Turing machine for it and show it always halts. By providing a detailed description of a Turing machine that recognizes the language and demonstrating that it always halts on any input, we can establish decidability.