The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Computational Complexity of Probabilistic Turing Machines
Abstract
A probabilistic Turing machine is a Turing machine with the ability to make decisions based on the outcomes of unbiased coin tosses. The partial function computed by a probabilistic machine is defined by assigning to each input the output which occurs with probability greater than $\frac{1}{2}$. With this definition, only partial recursive functions are probabilistically computable. The run time and tape of probabilistic machines are defined. A palindrome-like language is described that can be recognized faster by one-tape probabilistic Turing machines than by one-tape deterministic Turing machines. It is shown that every nondeterministic machine can be simulated in the same space by a probabilistic machine with small error probability. Several classes of languages recognized probabilistically in polynomial time are defined and compared with $NP$.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
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
Cited by
Learnability and the Vapnik-Chervonenkis dimension
Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. K. (1989) · Journal of the ACM · doi:10.1145/76359.76371 · Cited by 1,839
The complexity of stochastic games
Condon, A. (1992) · Information and Computation · doi:10.1016/0890-5401(92)90048-k · Cited by 517
Bennett, C. H., & Gill, J. (1981) · SIAM Journal on Computing · doi:10.1137/0210008 · Cited by 381
Bayesian estimation and the Kalman filter
Barker, A. L., Brown, D. E., & Martin, W. N. (1995) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(95)00156-s · Cited by 78
Metadata
- Authors
- Gill, J.
- Venue
- SIAM Journal on Computing
- Published
- 1977-12
- Volume
- 6
- Issue
- 4
- Pages
- 675-695
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2059442002
- Cited by
- 689
- References
- 1
- FWCI
- 5.89
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Computational Complexity of Probabilistic Turing Machines. https://app.cochat.ai/papers/10.1137/0206049
- The paper
- Gill, J. (1977). Computational Complexity of Probabilistic Turing Machines. SIAM Journal on Computing. https://doi.org/10.1137/0206049
Data sources
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.
