Semi-Algebraic Proofs, IPS Lower Bounds and the τ-Conjecture : Can a Natural Number be Negative?
- Submitting institution
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Royal Holloway and Bedford New College
- Unit of assessment
- 11 - Computer Science and Informatics
- Output identifier
- 36560484
- Type
- E - Conference contribution
- DOI
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10.1145/3357713.3384245
- Title of conference / published proceedings
- STOC 2020 : Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
- First page
- 54
- Volume
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- Issue
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- ISSN
- -
- Open access status
- -
- Month of publication
- June
- Year of publication
- 2020
- URL
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- Supplementary information
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- Request cross-referral to
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- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
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- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
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3
- Research group(s)
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- Citation count
- 0
- Proposed double-weighted
- No
- Reserve for an output with double weighting
- No
- Additional information
- Semi-algebraic reasoning is central in the development of approximation algorithms for hard computational problems. Published recently in the most prestigious conference in the theory of computing, this result is the first to characterise precisely the advantage of semi-algebraic reasoning over algebraic reasoning. The work provides the first known conditional impossibility result proved for a *strong* proof system: under conventional assumptions in complexity, even very simple instances require an exponential blow up to refute. Our impossibility result is fundamental as a basic hardness result in computational complexity, which underlie secure cryptography and derandomization of probabilistic algorithms.
- Author contribution statement
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- Non-English
- No
- English abstract
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