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Results tagged with computational-complexity
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user 9896
This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
5
votes
Abstract notion for energy complexity of computational problems?
The answer is no, energy cannot be considered a cost of computation.
Classical computations can be transformed, with only polynomial size blow-up, to reversible computations (computations which do no …
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3
votes
We know that a permutation of N bits {0, 1}^N --> {0,1}^N can be computed by circuits of siz...
Any function $f:V^n \rightarrow V^n$ can be computed with $O(n 2^n)$ gates as follows.
For each input $\langle v_1, \dots, v_n \rangle$, compute $t_v = x_1^{v_1} \wedge \dots \wedge x_n^{v_n}$ (where …
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1
vote
Accepted
Proof that any NP problem can be reduced (in P time) to any problem in NPC?
This is Cook-Levin theorem, look it up on Wikipedia.
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1
vote
0
answers
228
views
Inherent complexity of a language --- when does it exist?
For a language $L$, you can talk about the complexity of a Turing machine $M$ which decides $L$. Can you talk about the time complexity of the language $L$ itself, i.e. say $L$ has complexity $f(n)$ i …
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3
votes
0
answers
364
views
Amortized analysis of data structure via potential function
One common method for proving that a data structure supports an operation in $O(f(n))$ amortized time is to construct a potential function $\Phi: \mathcal S \rightarrow \mathbf R^{+}$, which associate …
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3
votes
2
answers
856
views
Formal verification in complexity theory
Reading books and papers on complexity theory, I am struck by the extreme degree to which proofs are stated in an intuitive, hand-wavy way. The alternative is to give a lot of details about the coding …
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6
votes
Is P=NP relevant to finding proofs of everyday mathematical propositions?
The point is that, if P=NP, there would exist a universal algorithm (applicable not just to specific theorems) that would find proofs in time polynomial in length of the proof. Most important results …
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14
votes
3
answers
3k
views
Definition of relativization of complexity class
Is there any general definition, for a class $C$ of languages, what is the relativized class $C^A$ for an oracle $A$?
Usually, these classes and their relativizations seem to be defined in an ad-hoc …
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