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Fast Probabilistic Algorithms for Verification of Polynomial Identities
Open accessAbstract
The starthng success of the Rabm-Strassen-Solovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials.Ancdlary fast algorithms for calculating resultants and Sturm sequences are given.Probabilistlc calculatton in real anthmetlc, prewously considered by Davis, is justified ngorously, but only in a special case.Theorems of elementary geometry can be proved much more efficiently by the techmques presented than by any known arttficml-mtelhgence approach
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Cited by
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Property testing and its connection to learning and approximation
Goldreich, O., Goldwasser, S., & Ron, D. (1998) · Journal of the ACM · doi:10.1145/285055.285060 · Cited by 1,020
Checking computations in polylogarithmic time
Babai, L., Fortnow, L., Levin, L. A., & Szegedy, M. (1991) · Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91 · doi:10.1145/103418.103428 · Cited by 616
zkLLM: Zero Knowledge Proofs for Large Language Models
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Metadata
- Authors
- Schwartz, J. T.
- Venue
- Journal of the ACM
- Published
- 1980-10-01
- Volume
- 27
- Issue
- 4
- Pages
- 701-717
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2080132708
- Cited by
- 1,701
- References
- 0
- FWCI
- 3.94
- Type
- journal article
- Language
- en
- Open access
- bronze
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