What does it mean for a Turing machine to accept a string?

M accepts a string w if it enters the accept state when run on w. ● M rejects a string w if it enters the reject state when run on w. ● M loops infinitely (or just loops) on a string w if when run on w it enters neither the accept or reject state.

Which of the following problem is undecidable?

Which of the following problems is undecidable? Deciding if a given context-free grammar is ambiguous. Deciding if a given string is generated by a given context-free grammar. Deciding if the language generated by a given context-free grammar is empty.

What makes a problem Undecidable?

An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.

What is undecidable problem in automata?

Undecidable Problems A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as ‘yes’ or ‘no’. An undecidable problem has no algorithm to determine the answer for a given input.

How does a Turing machine reject?

The Turing machine must halt with the reading head pointing to a 1 to accept the input, and must halt with the reading head point to a 0 to reject. The content of the tape in cells that are not being pointed to is irrelevant.

Which problem is undecidable Mcq?

Undecidable Problems MCQ Question 1 Detailed Solution According to Rice’s theorem, emptiness problem of Turing machine is undecidable.

Which of the following are undecidable theories?

3. Which among the following are undecidable theories? Explanation: Tarski and Mostowski in 1949, established that the first order theory of natural numbers with addition, multiplication, and equality is an undecidable theory.

What do you understand by undecidable problem prove that halting problem of Turing Machine is undecidable?

The Halting Problem is Undecidable: Proof Since there are no assumptions about the type of inputs we expect, the input D to a program P could itself be a program. Compilers and editors both take programs as inputs.

What do you understand by Undecidable problem prove that halting problem of Turing machine is undecidable?

In what ways might a logic be undecidable?

First-order logic is not decidable in general; in particular, the set of logical validities in any signature that includes equality and at least one other predicate with two or more arguments is not decidable. Logical systems extending first-order logic, such as second-order logic and type theory, are also undecidable.