# General Pseudo-random Generators from Weaker Models of Computation

@inproceedings{Karakostas2009GeneralPG, title={General Pseudo-random Generators from Weaker Models of Computation}, author={George Karakostas}, booktitle={ISAAC}, year={2009} }

The construction of pseudo-random generators (PRGs) has been based on strong assumptions like the existence of one-way functions or exponential lower bounds for the circuit complexity of Boolean functions. Given our current lack of satisfactory progress towards proving these assumptions, we study the implications of constructing PRGs for weaker models of computation to the derandomization of general classes like BPP. More specifically, we show how PRGs that fool monotone circuits could lead to…

## 2 Citations

### On derandomization and average-case complexity of monotone functions

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2012

### Deterministic simulations and hierarchy theorems for randomized algorithms

- Computer Science, Mathematics
- 2010

It is shown that, in fact, any derandomization of randomized monotone computations would derandomize all randomized algorithms, whetherMonotone or not, and similar results are proved for pseudorandom generators and average-case hard functions.

## References

SHOWING 1-10 OF 21 REFERENCES

### Hardness vs Randomness

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1994

### How to generate cryptographically strong sequences of pseudo random bits

- Computer Science, Mathematics23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
- 1982

A more operative definition of Randomness should be pursued in the light of modern Complexity Theory.

### The complexity of Boolean functions

- Computer Science
- 1987

This chapter discusses Circuits and other Non-Uniform Computation Methods vs. Turing Machines and other Uniform Computation Models, and the Design of Efficient Circuits for Some Fundamental Functions.

### Near-optimal conversion of hardness into pseudo-randomness

- Computer Science, Mathematics40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
- 1999

These results are based on the NW (Nisan & Wigderson, 1997) generator and are able to obtain derandomization in almost optimal time using any lower bound functions s(n).

### Pseudorandom generators without the XOR Lemma

- MathematicsElectron. Colloquium Comput. Complex.
- 1998

Two different approaches are presented to proving the main result of Impagliazzo and Wigderson that if there exists a decision problem solvable in time 2/sup O(n)/ and having circuit complexity 2/Sup /spl Omega/(n)/ then P=BPP.

### Hard-core distributions for somewhat hard problems

- Mathematics, Computer ScienceProceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

It is shown that for any decision problem that cannot be 1-/spl delta/ approximated by circuits of a given size, there is a specific "hard core" set of inputs which is at least a /splDelta/ fraction of all inputs and on which no circuit of a slightly smaller size can get even a small advantage over a random guess.

### Pseudorandom generators without the XOR Lemma (extended abstract)

- Computer ScienceSTOC '99
- 1999

Two different approaches are presented to proving the main result of lmpagliazzo and Wigderso: the first construction of a pseudorandomgenerator that works with a mildly hard predicate without doing hardness amplification and a list-decoding algorithm that improves and simplifies a previous one by Arora and Sudan.

### P = BPP if E requires exponential circuits: derandomizing the XOR lemma

- MathematicsSTOC '97
- 1997

A pseudo-random generator which produces n instances of a problem for which the analog of the XOR lemma holds is given, and it is shown that if any problem in E = DTIAl E(2°t”j) has circuit complexity 2Q(”), then P = BPP.

### Separation of the Monotone NC Hierarchy

- Mathematics, Computer ScienceProceedings 38th Annual Symposium on Foundations of Computer Science
- 1997

A new class of communication complexity search problems is defined, referred to below as DART games, and a tight lower bound for the communication complexity of every member of this class is proved, and lower bounds for the monotone depth of many functions are got.

### The Potential of the Approximation Method

- Computer ScienceSIAM J. Comput.
- 2004

Developing certain techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph…