The DOI matches its OpenAlex record; 12 of the 12 references it cites were found in a registry or an index.
Completeness Classes in Algebra
Open accessAbstract
In the theory of recursive functions and computational complexity it has been demonstrated repeatedly that the natural problems tend to cluster together in “completeness classes”. These are families of problems that (A) are computationally interreducible and (B) are the hardest members of some computationally defined class. The aim of this paper is to demonstrate that for both algebraic and combinatorial problems this phenomenon exists in a form that is purely algebraic in both of the respects (A) and (B). Such computational consequences as NP-completeness are particular manifestations of something more fundamental.
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Citations
Cites
Reducibility among Combinatorial Problems
Karp, R. M. (1972) · Complexity of Computer Computations · doi:10.1007/978-1-4684-2001-2_9 · Cited by 11,511
The Design and Analysis of Computer Algorithms
Aho, A. V., & Hopcroft, J. E. (1974) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,403
The complexity of theorem-proving procedures
Cook, S. A. (1971) · Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 · doi:10.1145/800157.805047 · Cited by 6,385
The Complexity of Enumeration and Reliability Problems
Valiant, L. G. (1979) · SIAM Journal on Computing · doi:10.1137/0208032 · Cited by 2,076
Self-citationSome simplified NP-complete problems
Garey, M. R., Johnson, D. S., & Stockmeyer, L. (1974) · Proceedings of the sixth annual ACM symposium on Theory of computing - STOC '74 · doi:10.1145/800119.803884 · Cited by 614
Statistical Mechanics of Dimers on a Plane Lattice
Fisher, M. E. (1961) · Physical Review · doi:10.1103/physrev.124.1664 · Cited by 605
Some NP-complete geometric problems
Garey, M. R., Graham, R. L., & Johnson, D. S. (1976) · Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76 · doi:10.1145/800113.803626 · Cited by 400
Fast Parallel Matrix Inversion Algorithms
Csanky, L. (1976) · SIAM Journal on Computing · doi:10.1137/0205040 · Cited by 397
THE COMPUTATIONAL COMPLEXITY OF ALGEBRAIC AND NUMERIC PROBLEMS.
Borodin, A., & Munro, I. (1975) · CERN Document Server (European Organization for Nuclear Research) · Cited by 396
Percolation Processes and Related Topics
Frisch, H. L., & Hammersley, J. M. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111066 · Cited by 266
Cited by
Computing Algebraic Formulas Using a Constant Number of Registers
Ben-Or, M., & Cleve, R. (1992) · SIAM Journal on Computing · doi:10.1137/0221006 · Cited by 139
Metadata
- Authors
- Valiant, L. G.
- Venue
- ACM eBooks
- Publisher
- Association for Computing Machinery
- Published
- 1979-01-01
- Pages
- 167-192
- OpenAlex
- W2170831059
- Cited by
- 465
- References
- 12
- FWCI
- 18.82
- Type
- book chapter
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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