The DOI matches its Crossref record.
Parity, circuits, and the polynomial-time hierarchy
Abstract
A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function. Introducing the notion of polynomial-size, constant-depth reduction, similar results are shown for the majority, multiplication, and transitive closure functions. Connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
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Citations
Cited by
Parity, circuits, and the polynomial-time hierarchy
Furst, M., Saxe, J. B., & Sipser, M. (1984) · Mathematical Systems Theory · doi:10.1007/bf01744431 · Cited by 938
Self-citationThreshold circuits of bounded depth
Hajnal, A., Maass, W., Pudlák, P., Szegedy, M., & Turán, G. (1993) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(93)90001-d · Cited by 237
Saturated Transformers are Constant-Depth Threshold Circuits
Merrill, W., Sabharwal, A., & Smith, N. A. (2022) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00493 · Cited by 25
Metadata
- Authors
- Furst, M., Saxe, J. B., & Sipser, M.
- Venue
- 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)
- Publisher
- IEEE
- Published
- 1981-10
- Pages
- 260-270
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2014850486
- Cited by
- 212
- References
- 0
- FWCI
- 10.47
- Type
- conference paper
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Parity, circuits, and the polynomial-time hierarchy. https://app.cochat.ai/papers/10.1109/sfcs.1981.35
- The paper
- Furst, M., Saxe, J. B., & Sipser, M. (1981). Parity, circuits, and the polynomial-time hierarchy. 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981). https://doi.org/10.1109/sfcs.1981.35
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
