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### $BPP$ type algorithms with slightly more capability

A language $L$ is in $BPP$ if and only if there exists a polynomial $p$ and deterministic Turing machine $M$, such that $M$ runs for polynomial time on all inputs For all $x$ in $L$, the fraction of ...
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### When is a problem specified on a TM contained in non-uniform classes such as P/poly? [closed]

In this paper by Gottesman and Irani: https://arxiv.org/abs/0905.2419 , they prove NEXP-hardness of tiling an $N\times N$ grid. They do so by encoding a TM in the tiles making up the grid. However, ...
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### What are examples of how non-uniformity can be useful?

I'm curious about ways in which you have seen non-uniformity be useful in computation. One way is randomness, as in $BPP \subseteq P/poly$, and another is look-up tables which are used to show that ...
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### Does the space hierarchy theorem generalize to non-uniform computation?

General Question Does the space hierarchy theorem generalize to non-uniform computation? Here are a few more specific questions: Is $L/poly \subsetneq PSPACE/poly$? For all space ...
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### What are the consequences of $P \subseteq L/poly$?

A language is in $L/poly$ if there exists a logspace Turing machine that decides the language with polynomial amount of advice. See here for more info: https://en.wikipedia.org/wiki/L/poly ...
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### Oracle separating $coNP$ and $NP/poly$

I'd like to prove that, with respect to some adversarial oracle $O$, $coNP^O \not\subseteq NP/poly^O$. I was thinking of using $\textsf{UNSAT}$ for this and to build my oracle as follows: $O$ will "...
639 views

### P/Poly vs Uniform Complexity Classes

It is not known whether NEXP is contained in P/poly. Indeed proving that NEXP is not in P/poly would have some applications in derandomization. What is the smallest uniform class C for which one can ...
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### Can a random oracle change which TFNP problems are strongly hard-on-average?

I've been thinking about the following question at various times since I saw this question on Cryptography. Question Let $R$ be a TFNP relation. ​ Can a random oracle help P/poly to break $R$ ...
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### Smallest Nonuniform Complexity Classes including uniform-P

As we know, studiyng differences between uniform complexity and nonuniform complexity class is crucial. For example, P/poly is defined as challenges to derive a separation between P and NP, because ...
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### Is Solomonoff Induction in $\mathsf{P/poly}$?

Consider any language $L$. Define $s(L) \in {\lbrace 0, 1 \rbrace}^\omega$ (an infinite sequence of bits) by the recursive formula $$s(L)_n=\chi_L(s(L)_{<n})$$ Here $\chi_L$ is the characteristic ...
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### Separation of space complexity classes: differeces between uniform class and nonuniform one as an analogy of circuit lower bounds project

Boolean circuit is used to measure time in a nonuniform way, which Pippenger showed the relation between a time complexity of uniform model (Turing Machines) and size complexity of boolean circuits. ...
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### Survey on the Power of Non-Uniformity

I know that BPP is in P/poly. I know that if NP is in P/poly then $PH = \Sigma^2_p$ Question: Is there a good survey on the power of non-uniformity? I'm basically looking for a list of known ...
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### Recommendation for a good book on first order logic w.r.t inductive logic programming

I have had 10 days to read up on Computational Logic but the books I am following are only succeeding in confusing me. I find most of text's ( Niehuys-Cheng & de Wolf 1997, De Raedt 2008, Lloyd ...
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### Beating Nonuniformity by Oracle Access

Informally, we say that a Turing machine $M(\cdot)$ approximates a function $f(\cdot)$ if their outputs on a series of inputs are indistinguishable. More formally, let $L$ be a language, $M(\cdot)$ ...
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### The Complexity of Advice in Computational Indistinguishability

One of the cornerstones of the modern cryptography is the definition of computational indistinguishability: It is used in definition of cryptosystems, pseudorandom generators, zero-knowledge, etc. ...
386 views

### Logarithmic advice language in P?

Is something like DTIME(poly(n))/log(n) in P? Can the log-length advice be somehow hardwired into a DTM for P?