# Questions tagged [average-case-complexity]

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### definition of P-samplable distribution that allows non-binary fractions

Arora and Barak (in chapter 18, on average-case complexity) define a polynomial-time samplable (or P-samplable) distribution $D$ (actually a family $\{D_n\}$, for each output length $n$) as having an ...
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### Relationships between Descriptive Complexity and Average Case Complexity

Descriptive complexity gives one a logic or at least a logic to express languages in a complexity class. The PH can be defined as the union of all classes that can be expressed in Second order logic. ...
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### Hard-on-Average, Quasi-Polynomial-Time Problems

In a paper by Raphael Pass, he writes (page 162): ... most natural problems that we believe are hard on average for polynomial time are also believed hard for quasi-polynomial time. In another post ...
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### Fine-grained average-case derandomization

Many believe derandomization with polynomial overhead, $\mathsf{P} = \mathsf{BPP}$, because it follows from $2^{\Omega(n)}$ circuit lower bounds for $\mathsf{E}$ (IW97). Do we have any evidence for or ...
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### Avarage classes for PP (probabilistic polynomial time) and PPT machines running in expected polytime

i have some question concerning the class PP and PPT machines. PP is defined as the class of problems $L$ for wich exist a probabilistic turing machine running in polytime with error probability < ...
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### NP-hard problem which is easy on average

I have a feeling like I read somewhere that the Hamiltonian circuit problem is NP-hard, but it is easy on average, or easy for a random instance. However, I cannot find a reference for that, nor an ...
293 views

### Quantum computer versus Random 3-SAT?

It seems to be commonly believed that a quantum computer cannot efficiently solve NP-hard problems. What about problems that are challenging in the average-case, such as Planted Clique and Random 3-...
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### Worst to average case reductions for quantum complexity classes

I am studying worst to average case reductions for different complexity classes. Consider quantum complexity classes like QMA, QSZK, or QIP. Is it known or believed that these classes are amenable to ...
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### Hard instances in Impagliazzo's Heuristica

In Impagliazzo's imaginary world Heuristica, P ≠ NP but all NP problems are easy on average for any samplable probability distribution. In Impagliazzo's paper, he implies that if you do manage to ...
1 vote
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### Average case or beyond worse case analysis for non-convex optimization procedures?

I'm not sure if this is a well-formed question or not, but I thought I would ask to see if anyone is aware of related literature. It is known that global optimization of non-convex functions is NP-...
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### Worst-Case and Average-Case running-time equal with universal p-distribution with kolmogorov-complexity any applications of this theory?

at the moment I'm reading "Gems of Theoretical Computer Science" from Schöning and Pruim. In Chapter 8 the book defines a "universal probability distribution" in a way that the Average-Case running-...
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### Paradigms for complexity analysis of algorithms

Worst-case and average case analysis are well-known measures for the complexity of an algorithm. Recently smoothed analysis has emerged as another paradigm to explain why some algorithms which are ...
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### Average-case analysis of algorithms using the incompressibility method

I recently became very interested in Kolmogorov complexity and the incompressibility method especially in the context of average-case analysis. The "standard" book by Li & Vitanyi showcases many ...
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This question arose in the context of cryptography, but below I will present it in terms of complexity theory, since people here are more acquainted with the latter. This question is related to ...