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What are some examples of undecidable languages and how are they different from decidable languages?
Undecidable languages are languages for which there is no algorithm that can determine whether a given input string is in the language or not. Examples of undecidable languages include the Halting Problem and the Post Correspondence Problem. Decidable languages, on the other hand, are languages for which there exists an algorithm that can determine whether a given input string is in the language or not. Examples of decidable languages include regular languages and context-free languages. The key difference between undecidable and decidable languages is that decidable languages have algorithms that can always provide a definite answer, while undecidable languages do not have such algorithms.
Is the halting problem NP-hard?
Yes, the halting problem is not NP-hard, it is undecidable.
What is the decidable problem definition in computer science?
In computer science, a decidable problem is one that can be solved by an algorithm that always halts and gives a correct answer. This means that there is a clear and definite method to determine the solution to the problem.
Is the halting problem undecidable?
Yes, the halting problem is undecidable, meaning that there is no algorithm that can determine whether a given program will halt or run indefinitely.
Are decidable languages closed under any operations?
Yes, decidable languages are closed under operations such as union, intersection, concatenation, and complementation. This means that if a language is decidable, performing these operations on it will result in another decidable language.
