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Alternation
Open accessAbstract
Alternation is a generalization of nondeterminism in which existential and universal quantitiers can alternate during the course of a computation, whereas in a nondeterministic computation there are only existential quantifiers.Alternating Turing machines are defined and shown to accept precisely the recursively enumerable sets.Complexity classes of languages accepted by time-(space-) bounded alternating Turing machines are characterized in terms of complexity classes of languages accepted by space-(time-) bounded deterministic Turing machines.In particular, alternating polynomial time is equivalent to deterministic polynomial space and alternating polynomial space is equivalent to deterministic 'exponential time.Subrecursive quantifier hierarchies are defined in terms of time-or space-bounded alternating Tufing machines by bounding the number of alternations allowed during computations.Alternating finite-state automata are defined and shown to accept only regular languages, although, in general, 2 2 states are necessary and sufficient to simulate a k-state alternating finite automaton deterministically.Finally, it is shown that alternating pushdown automata are strictly more powerful than nondeterministic pushdown automata.
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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
The knowledge complexity of interactive proof systems
Goldwasser, S., Micali, S., & Rackoff, C. (1989) · SIAM Journal on Computing · doi:10.1137/0218012 · Cited by 3,285
Algorithms, games, and the internet
Papadimitriou, C. (2001) · Proceedings of the thirty-third annual ACM symposium on Theory of computing · doi:10.1145/380752.380883 · Cited by 1,085
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
Complexity and expressive power of logic programming
Dantsin, E., Eiter, T., Gottlob, G., & Voronkov, A. (2001) · ACM Computing Surveys · doi:10.1145/502807.502810 · Cited by 739
A calculus for access control in distributed systems
Abadi, M., Burrows, M., Lampson, B., & Plotkin, G. (1993) · ACM Transactions on Programming Languages and Systems · doi:10.1145/155183.155225 · Cited by 575
Metadata
- Authors
- Chandra, A. K., Kozen, D. C., & Stockmeyer, L. J.
- Venue
- Journal of the ACM
- Published
- 1981-01
- Volume
- 28
- Issue
- 1
- Pages
- 114-133
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W4241108585
- Cited by
- 1,221
- References
- 1
- FWCI
- 30.69
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Chandra, A. K., Kozen, D. C., & Stockmeyer, L. J. (1981). Alternation. Journal of the ACM. https://doi.org/10.1145/322234.322243
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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.
