The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
Open accessAbstract
Traditional hardness versus randomness results focus on time-efficient randomized decision procedures. We generalize these trade-offs to a much wider class of randomized processes. We work out various applications, most notably to derandomizing Arthur-Merlin games. We show that every language with a bounded round Arthur-Merlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomial-time hierarchy (and hence the polynomial-time hierarchy collapses). Since the graph nonisomorphism problem has a bounded round Arthur-Merlin game, this provides the first strong evidence that graph nonisomorphism has subexponential size proofs. We also establish hardness versus randomness trade-offs for space bounded computation.
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Cited by
Extractors and pseudorandom generators
(2001) · Journal of the ACM · doi:10.1145/502090.502099 · Cited by 324
Improving Exhaustive Search Implies Superpolynomial Lower Bounds
Williams, R. (2013) · SIAM Journal on Computing · doi:10.1137/10080703x · Cited by 157
Metadata
- Authors
- Klivans, A. R., & van Melkebeek, D.
- Venue
- SIAM Journal on Computing
- Published
- 2002-01
- Volume
- 31
- Issue
- 5
- Pages
- 1501-1526
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W1558847040
- Cited by
- 270
- References
- 33
- FWCI
- 11.43
- Type
- journal article
- Language
- en
- Open access
- bronze
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