Final answer:
To show that a language is decidable, writing a program in C++ is not the only option. The Church-Turing thesis doesn't directly prove decidability.
Step-by-step explanation:
False
To show that a language is decidable, one could use other methods instead of writing a program in C++. The Church-Turing thesis doesn't directly prove decidability, but it suggests that any problem computable by a Turing machine is decidable. Additionally, halting is not the only criterion for decidability; a language can also be decidable if it is semidecidable or recursively enumerable.
To prove a language is decidable, one can write a C++ program that decides membership and shows it always halts in line with the Church-Turing thesis, which would be a true statement.
To determine whether a language is decidable, one must demonstrate that there is an algorithm (a computer program, for example) that can decide whether any given string belongs to the language within a finite amount of time, and it must always halt with a yes or no answer. If you can write a program in a language like C++ that decides membership in a language and can prove that it always halts, then you can argue that the language is decidable based on the Church-Turing thesis. The Church-Turing thesis states that any computation that can be done by a Turing machine can also be performed by a computer program. Therefore, writing such a program and demonstrating that it always halts for a particular language is a valid approach to proving that the language is decidable.