# Trading Group Theory for Randomness La ’ siszld

@inproceedings{Babai2007TradingGT, title={Trading Group Theory for Randomness La ’ siszld}, author={La’siszld Babai}, year={2007} }

la a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat& proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q’ oup,. The aim of this paper is t.o replace most of the (proven and unproven) group theory of IBS] by elementary combinatorial argumenls. The rev& we prove is that relative to a random oracle f3, tbc meutioned matrix… Expand

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#### References

SHOWING 1-10 OF 12 REFERENCES

On the Complexity of Matrix Group Problems I

- Mathematics, Computer Science
- FOCS
- 1984

A theory of black box groups is built, and it is proved that for such subgroups, membership and divisor of the order are in NPB, and under a plausible mathematical hypothesis on short presentations of finite simple groups, nom membership and exaact order will also be inNPB. Expand

Explicit Constructions of Linear-Sized Superconcentrators

- Computer Science
- J. Comput. Syst. Sci.
- 1981

A direct way to construct a family of l inear concentrators using Pinsker’s linear concentrators and disproved a conjecture that superconcentrators require more than a linear number of edges. Expand

Computational complexity and the classification of finite simple groups

- Mathematics, Computer Science
- 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
- 1983

It appears that unless there is another radical breakthrough in ISO, independent of the previous one, the simple groups classification is an indispensable tool for further developments. Expand

Universal Classes of Hash Functions

- Computer Science, Mathematics
- J. Comput. Syst. Sci.
- 1979

An input independent average linear time algorithm for storage and retrieval on keys that makes a random choice of hash function from a suitable class of hash functions. Expand

A Fast Monte-Carlo Test for Primality

- Mathematics, Computer Science
- SIAM J. Comput.
- 1977

A uniform distribution a from a uniform distribution on the set 1, 2, 3, 4, 5 is a random number and if a and n are relatively prime, compute the residue varepsilon. Expand

Computational complexity of probabilistic Turing machines

- Computer Science
- STOC '74
- 1974

It is shown how probabilisticlinear-bounded automata can simulate nondeterministic linear-bounding automata and an example is given of a function computable more quickly by Probabilistic Turing machines than by deterministic Turing machines. Expand

The knowledge complexity of interactive protocols

- in: Proc. 17th ACM Symp. Theory of Comp.,
- 1985

Lautrmann, E/‘/J and thr polynomial hierarchy, info

- Proc. Lett,crs 17,
- 1983

ErdGs, Representation of group c!ement,s as short products, in: Theory ant! Practice of Combinatorics (A

- Rosa et a!. eds.), Annals of Discr. Math
- 1982

Relative to a random oracle A, P’c#NP’#coNP

- SIAM J. Comp
- 1981