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# Questions tagged [descriptive-complexity]

Descriptive complexity classifies problems based on how hard it is to express the problem in some logical formalism.

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### Descriptive complexity characterization of TimeSpace classes

Are there descriptive complexity characterizations for TimeSpace complexity classes like $\mathsf{SC^i}= \mathsf{DTimeSpace}(n^{O(1)},O(\lg^i n))$?
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1 vote
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### Complexity class name for the class of languages that are $\Sigma^1_1$-definable over finite domains

Let ${\cal L}=\{Y_1,..., Y_k, X\}$ be a finite relational language such that $X$ is a unary relation name. Let $\phi(X,\bar{Y})\in{\cal L}$ be a first-order formula (the formula can have the equality ...
1 vote
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### Proof of SAT is complete for NP via first-order reductions

So I have been reading this: https://people.cs.umass.edu/~immerman/book/ch7.pdf I do not understand the proof of theorem 7.16, which says that SAT is complete for NP via first-order reductions. My ...
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1 vote
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### Do problems have to be statable in $\Pi_1$ to use Levin's universal search to find short proofs if P=NP

In If P=NP, could we obtain proofs of Goldbach's Conjecture etc.? it talks about the hypothetical world where P=NP and using the proof of it to prove a problem/theorem assuming that it has a short ...
• 21
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### Does Descriptive Complexity techniques have the naturalisation barrier?

I wished to know if the proof attempts at separation of complexity classes via the methods outlined by Descriptive Complexity theorists naturalise? By naturalise I'm talking about the Idea of Natural ...
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### Questions about the definition of the Quantum Turing Machine

I am trying to have a better understanding of the definition of the Quantum Turing Machine. My questions: If the output of a quantum program is the eigenvalue of the ground state of a Hamiltonian ...
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