# Questions tagged [derandomization]

Every randomized algorithm can be simulated by a deterministic algorithm, at the expense of an exponential increase in running time. Derandomization is about converting randomized algorithms into efficient deterministic algorithms.

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### Derandomizing Valiant-Vazirani?

The Valiant-Vazirani theorem says that if there is a polynomial time algorithm (deterministic or randomized) for distinguishing between a SAT formula that has exactly one satisfying assignment, and an ...
2k views

### P vs. NP and Pseudorandom Bit Generators

According to an article on pseudorandom number generators (PRNG) by Jeff Lagarias, he states that trying to prove that a PRNG is unpredictable (secure) is just "as hard" as trying to prove ... 4k views

### Efficient and simple randomized algorithms where determinism is difficult

I often hear that for many problems we know very elegant randomized algorithms, but no, or only more complicated, deterministic solutions. However, I only know a few examples for this. Most ...
1k views

### Hierarchy for BPP vs derandomization

In one sentence: would the existence of a hierarchy for $\mathsf{BPTIME}$ imply any derandomization results? A related but vaguer question is: does the existence of a hierarchy for $\mathsf{BPTIME}$ ...
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### What specific evidence is there for P = RP?

RP is the class of problems decidable by a nondeterministic Turing machine that terminates in polynomial time, but that is also allowed one-sided error. P is the usual class of problems decidable by ...
807 views

### Does randomness buy us anything inside P?

Let $\mathsf{BPTIME}(f(n))$ be the class of the decision problems having a bounded two-sided error randomized algorithm running in time $O(f(n))$. Do we know of any problem $Q \in \mathsf{P}$ such ...
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### Is it known whether $BPP\cap NP\subseteq RP$?

The reverse inclusion is obvious, as is the fact that any self-reducible NP language in BPP is also in RP. Is this also known to hold for non-self-reducible NP languages?
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### More on PH in PP?

A recent question by Huck Bennett asking whether the class PH was contained in the class PP, received somewhat contradictory answers (all true, it seems). On one hand, several oracle results were ...
985 views

### Why does randomness have stronger effect on reductions than on algorithms?

It is conjectured that randomness does not extend the power of polynomial time algorithms, that is, ${\bf P}={\bf BPP}$ is conjectured to hold. On the other hand, randomness seems to have a quite ...
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### Problems in $\mathsf{BPP}$ not known to be in $\mathsf P$?

What problems are known to belong to $\mathsf{BPP}$ but not known to belong to $\mathsf P$? More precisely, I am interested in independent problems, that is whose derandomizations are not known to be ...
904 views

### Space efficient "industrial" unbalanced expanders

I am looking for unbalanced expanders that are "good" and "space-efficient". Specifically, a bipartite left-regular graph $G=(A,B,E)$, $|A|=n$, $|B|=m$, with left degree $d$ is a $(k,\epsilon)$-...
501 views

### Fine-grained complexity of BPP

If E does not have i.o.-$2^{o(n)}$ circuits, then P=BPP, but this does not tell us about the fine-grained containments between $\mathrm{Time}(n^a)$ and $\mathrm{BPTime}(n^b)$. Are there reasonable ...
While Adleman's theorem shows, that $\mathsf{BPP} \subseteq \mathsf{P}/\text{poly}$, I'm not aware of any literature investigating the possible inclusion of $\mathsf{BQP} \subseteq \mathsf{P}/\text{... 21 votes 1 answer 333 views ### A comparison of extractors in terms of tradeoffs between time, randomness and space ? Is there a good survey that compares different extractors, concentrators and superconcentrators and lays out the best methods in terms of the tradeoff between randomness, time and space ? 20 votes 4 answers 815 views ### Is there an equivalent to derandomization for quantum algorithms? With some randomized algorithms you can derandomize the algorithm, removing (at a possible cost in run time) the use of random bits and maximizing some lower bound on the objective (usually computed ... 18 votes 2 answers 2k views ### Beginner's Guide to Derandomization I found the book Pairwise Independence and Derandomization on the subject, but it's more research-oriented than tutorial oriented. I'm new to the subject of "Derandomization," and as such, I wanted ... 13 votes 1 answer 422 views ### Adleman's theorem over infinite semirings? Adleman has shown in 1978 that$\mathrm{BPP}\subseteq \mathrm{P/poly}$: if a boolean function$f$of$n$variables can be computed by a probabilistic boolean circuit of size$M$, then$f$can be also ... 12 votes 3 answers 477 views ### Streaming derandomization Stream algorithms require randomization for the most part to do anything nontrivial, and because of the small-space constraint, need PRGs that use little space. I know of two methods that have been ... 10 votes 1 answer 357 views ### Can we construct a k-wise independent permutation on [n] using only constant time and space? Let$k>0$be a fixed constant. Given an integer$n$, we want to construct a permutation$\sigma \in S_n$such that: The construction uses constant time and space (i.e. preprocessing takes constant ... 3 votes 1 answer 141 views ### Notion similar to k-wise independence I want to construct a family of functions$H:\{0,1\}^n \rightarrow \{0,1\}$with a property that is similar to k-wise independence. Specifically, I want$H$to satisfy the following property. Let$k$... 2 votes 1 answer 233 views ### Extractors in Practice: How to Determine the Min-Entropy in the Source Distribution One of the main parameters in the construction of extractors is$k$, the min-entropy of the source distribution. In practice, suppose we want to extract randomness from a given source$S\$. How do we ... 