Immerman and Vardi's theorem requires that order be present in the structure, so the logical reformulation captures only a restricted variant of P vs NP, not the general problem as standardly posed.

?Rate how convincing each reason is below to see the overall strength.

1 reason for

1 reason against

Reasons For

1 perspective

Reason for

1 perspective

Reason against

Based on where you are in your exploration

Immerman and Vardi(namesake of the theorem being discussed): Two computer scientists who proved an important theorem in the 1980s showing that certain logical systems can describe exactly the same problems as a famous computational complexity class.
Logical reformulation(how the theorem rewrites the P vs NP problem): Taking a problem and restating it using the formal rules and symbols of mathematical logic instead of plain language.
P vs NP(the general computational problem being restricted by the theorem): One of the most important unsolved problems in computer science asking whether two different classes of problems (those easy to solve and those easy to check) are actually the same.
Restricted variant(the theorem only works when order is present in the structure): A limited or simplified version of something that only applies under certain specific conditions.
Structure (in logic)(as used in mathematical logic): A mathematical object that shows how symbols and rules of a logical system relate to and apply to real things.
Theorem: A theorem is a statement that has been proven to be true through logical reasoning and evidence. It's a fact that mathematicians or scientists have carefully verified using step-by-step arguments, starting from things already known to be true. Once proven, theorems become reliable building blocks that others can use to prove even more complex ideas.

2 topics