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Counting Classes
This project studies counting classes.
The term ``counting classes''
has come to refer to a certain
collection of classes--such as #P, SPP,
probabilistic classes, parity-based classes, etc.--that
are defined in terms of the number of accepting paths of
nondeterministic machines. (We're also interested
in limited nondeterminism classes, such as
the levels of the beta hierarchy, since such classes
indirectly
limit the number of accepting--and indeed total--paths
of nondeterministic machines.)
Among the questions central to this project are:
- How powerful are counting classes?
- What are the properties of counting classes?
- How robust are the definitions of counting classes?
A more recent interest of this project is counting the frequency
with which heuristic algorithms can, and cannot (unless
shocking complexity class collapses occur) be correct
regarding concrete problems hard for complexity classes, most
especially problems related to elections.
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This is a list of selected journal (except when the work has not yet
appeared in journal/book form, plus in some cases some conference articles)
papers, from or related to this project, by University of Rochester authors.
Essentially all the papers listed below can be found, in their full technical
report versions, in the UR-CS Technical Report Archive's
theory section. Here is
Lane's complete publication
list
and links to
essentially all his conference and journal papers (and also his arXiv.org
technical reports) can be found via the ``EE'' (electronic edition) links at
Lane's entry at the DBLP
project.
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J. Cai and L. Hemachandra.
On the power of parity polynomial time.
Mathematical Systems Theory, 23(2):95-106, 1990.
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L. Hemachandra and S. Rudich.
On the complexity of ranking.
Journal of Computer and System Sciences, 41(2):251-271, 1990.
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R. Beigel, L. Hemachandra, and G. Wechsung.
Probabilistic polynomial time is closed under parity reductions.
Information Processing Letters, 37(2):91-94, 1991.
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J. Cai and L. Hemachandra.
A note on enumerative counting.
Information Processing Letters, 38(4):215-219, 1991.
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J. Goldsmith, L. Hemachandra, D. Joseph, and P. Young.
Near-testable sets.
SIAM Journal on Computing, 20(3):506-523, 1991.
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L. Hemachandra and A. Hoene.
On sets with efficient implicit membership tests.
SIAM Journal on Computing, 20(6):1148-1156, 1991.
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D. Eppstein, L. Hemachandra, J. Tisdall, and B. Yener.
Simultaneous strong separations of probabilistic and unambiguous
complexity classes.
Mathematical Systems Theory, 25(1):23-36, 1992.
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J. Goldsmith, L. Hemachandra, and K. Kunen.
Polynomial-time compression.
Computational Complexity, 2(1):18-39, 1992.
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L. Hemachandra and M. Ogiwara.
Is #P closed under subtraction?
In G. Rozenberg and A. Salomaa, editors, Current Trends in
Theoretical Computer Science: Essays and Tutorials, pages 523-536. World
Scientific, 1993.
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M. Ogiwara and L. Hemachandra.
A complexity theory for feasible closure properties.
Journal of Computer and System Sciences, 46(3):295-325, 1993.
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L. Hemaspaandra and H. Vollmer.
The Satanic notations: Counting classes beyond #P and other
definitional adventures.
SIGACT News, 26(1):2-13, 1995.
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L. Hemaspaandra, A. Naik, M. Ogihara, and A. Selman.
Computing solutions uniquely collapses the polynomial hierarchy.
SIAM Journal on Computing, 25(4):697-708, 1996.
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L. Hemaspaandra, M. Zaki, and M. Zimand.
Polynomial-time semi-rankable sets.
In Journal of Computing and Information, 2(1), Special
Issue: Proceedings of the 8th International Conference on Computing and
Information, pages 50-67. 1996.
CD-ROM ISSN 1201-8511/V2/#1.
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S. Fischer, L. Hemaspaandra, and L. Torenvliet.
Witness-isomorphic reductions and local search.
In A. Sorbi, editor, Complexity, Logic, and Recursion Theory,
pages 207-223. Marcel Dekker, Inc., 1997.
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L. Hemaspaandra and M. Ogihara.
Universally serializable computation.
Journal of Computer and System Sciences, 55(3):547-560, 1997.
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L. Hemaspaandra, H. Hempel, and G. Wechsung.
Self-specifying machines.
International Journal of Foundations of Computer Science,
10(3):263-276, 1999.
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B. Borchert, L. Hemaspaandra, and J. Rothe.
Restrictive acceptance suffices for equivalence problems.
London Mathematical Society Journal of Computation and
Mathematics, 3:86-95, 2000.
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L. Hemaspaandra and J. Rothe.
A second step towards complexity-theoretic analogs of Rice's
Theorem.
Theoretical Computer Science, 244(1-2):205-217, 2000.
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L. Hemaspaandra, M. Ogihara, and G. Wechsung.
Reducing the number of solutions of NP functions.
Journal of Computer and System Sciences, 64(2):311-328, 2002.
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L. Hemaspaandra and M. Thakur.
Lower bounds and the hardness of counting properties.
Theoretical Computer Science, 326(1-3):1-28, 2004.
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H. Spakowski, M. Thakur, and R. Tripathi.
Quantum and classical complexity classes: Separations, collapses,
and closure properties.
Information and Computation, 200(1):1-34, 2005.
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L. Hemaspaandra, M. Ogihara, M. Zaki, and M. Zimand.
The complexity of finding top-Toda-equivalence-class members.
Theory of Computing Systems, 39(5):669-684, 2006.
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L. Hemaspaandra, C. Homan, S. Kosub, and K. Wagner.
The complexity of computing the size of an interval.
SIAM Journal on Computing, 36(5):1264-1300, 2006-2007.
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L. Hemaspaandra, C. Homan, and S. Kosub.
Cluster computing and the power of edge recognition.
Information and Computation, 205(8):1274-1293, 2007.
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P. Faliszewski and L. Hemaspaandra.
The consequences of eliminating NP solutions.
Computer Science Review, 2(1):40-54, 2008.
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M. Zuckerman, P. Faliszewski, Y. Bachrach, and E. Elkind.
Manipulating quota value in weighted voting games.
In Proceedings of the 23rd AAAI Conference on Artificial
Intelligence, pages 215-220. AAAI Press, July 2008.
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G. Erdélyi, L. Hemaspaandra, J. Rothe, and H. Spakowski.
Frequency of correctness versus average polynomial time.
Information Processing Letters, 109(16):946-949, 2009.
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G. Erdélyi, L. Hemaspaandra, J. Rothe, and H. Spakowski.
Generalized juntas and NP-hard sets.
Theoretical Computer Science, 410(38-40):3995-4000, 2009.
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P. Faliszewski and L. Hemaspaandra.
The complexity of power-index comparison.
Theoretical Computer Science, 410(1):101-107, 2009.
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C. Homan and L. Hemaspaandra.
Guarantees for the success frequency of an algorithm for finding
Dodgson-election winners.
Journal of Heuristics, 15(4):403-423, 2009.
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P. Faliszewski, E. Hemaspaandra, and L. Hemaspaandra.
The complexity of manipulative attacks in nearly single-peaked
electorates.
In Proceedings of the 13th Conference on Theoretical Aspects of
Rationality and Knowledge, pages 228-237. ACM Digital Library, July 2011.
(Last modified: February 1, 2012.)
Lane A. Hemaspaandra
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