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Formal Languages and Automata Theory

Formal Languages and Automata Theory

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If a problem cannot be solved by a Turing machine, what does the Church–Turing Thesis imply?

It cannot be solved by any mechanical or algorithmic procedure.

It may still be solvable by some as-yet undiscovered algorithm.

It is NP-complete.

It can be solved using a faster computer.

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The Church–Turing Thesis informally states that:

Every polynomial-time problem is solvable by a Turing machine.

Every function is computable.

Every effectively computable function can be computed by a Turing machine.

All recursive functions are undecidable.

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The Halting Problem is recursively enumerable (RE) but not decidable. What does this imply?

There exists a polynomial-time algorithm for the halting problem.

There exists a Turing machine that can recognize halting instances but may not halt on non-halting ones.

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There exists a non-deterministic finite automaton that decides halting.

There exists a Turing machine that always halts and decides halting correctly.

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Problem A is NP-complete iff:

A is NP-hard.

Both a and b are true.

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A is in complexity class of NP.

A is NP.

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How many conditions have to be met if an NP-complete problem is polynomially reducible?

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