141k views
3 votes
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.

TRUE OR FALSE

User Abdesselam
by
7.8k points

1 Answer

2 votes

Final answer:

True, creating a halting C++ program that decides membership for all input strings and referencing the Church-Turing thesis can show a language is decidable.

Step-by-step explanation:

True, to show that a language is decidable, one can write a program in C++ (or any other Turing-complete language) that decides whether a string is in the language or not. This program must always halt, meaning it must always decide for every possible input string. By the Church-Turing thesis, which states that any computation can be performed by a Turing machine, if you provide such a program that halts for all inputs, you demonstrate that the language is decidable. Therefore, it concludes that the language can be decided by a mechanical computation process, such as a Turing machine, confirming its decidability.

User SilentKiller
by
7.1k points