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Counting Classes

UR-CS Participating Faculty: Lane A. Hemaspaandra (= Lane A. Hemachandra)

Project Description

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:

  1. How powerful are counting classes?
  2. What are the properties of counting classes?
  3. How robust are the definitions of counting classes?

More recent interests of this project are counting whether, and 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; and cases where in election attacks weighted (via binary-integer weights) vote counts are important.

Bibliography

1
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.

2
R. Beigel, L. Hemachandra, and G. Wechsung.
Probabilistic polynomial time is closed under parity reductions.
Information Processing Letters, 37(2):91-94, 1991.

3
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.

4
J. Cai and L. Hemachandra.
On the power of parity polynomial time.
Mathematical Systems Theory, 23(2):95-106, 1990.

5
J. Cai and L. Hemachandra.
A note on enumerative counting.
Information Processing Letters, 38(4):215-219, 1991.

6
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.

7
G. Erdélyi, E. Hemaspaandra, and L. Hemaspaandra.
More natural models of electoral control by partition.
In Proceedings of the 4th International Conference on Algorithmic Decision Theory, pages 396-413. Springer-Verlag Lecture Notes in Artificial Intelligence #9346, September 2015.

8
G. Erdélyi, L. Hemaspaandra, J. Rothe, and H. Spakowski.
Frequency of correctness versus average polynomial time.
Information Processing Letters, 109(16):946-949, 2009.

9
G. Erdélyi, L. Hemaspaandra, J. Rothe, and H. Spakowski.
Generalized juntas and NP-hard sets.
Theoretical Computer Science, 410(38-40):3995-4000, 2009.

10
P. Faliszewski, E. Hemaspaandra, and L. Hemaspaandra.
Weighted electoral control.
In Proceedings of the 12th International Conference on Autonomous Agents and Multiagent Systems, pages 367-374. International Foundation for Autonomous Agents and Multiagent Systems, May 2013.

11
P. Faliszewski, E. Hemaspaandra, and L. Hemaspaandra.
The complexity of manipulative attacks in nearly single-peaked electorates.
Artificial Intelligence, 207:69-99, 2014.

12
P. Faliszewski, E. Hemaspaandra, and L. Hemaspaandra.
The complexity of manipulative attacks in nearly single-peaked electorates.
In Proceedings of the 24th International Joint Conference on Artificial Intelligence, pages 4178-4182. AAAI Press, July/August 2015.

13
P. Faliszewski, E. Hemaspaandra, and L. Hemaspaandra.
Weighted electoral control.
Journal of Artificial Intelligence Research, 52:507-542, 2015.

14
P. Faliszewski and L. Hemaspaandra.
The consequences of eliminating NP solutions.
Computer Science Review, 2(1):40-54, 2008.

15
P. Faliszewski and L. Hemaspaandra.
The complexity of power-index comparison.
Theoretical Computer Science, 410(1):101-107, 2009.

16
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.

17
Z. Fitzsimmons, E. Hemaspaandra, and L. Hemaspaandra.
Control in the presence of manipulators: Cooperative and competitive cases.
In Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pages 113-119. AAAI Press, August 2013.

18
J. Goldsmith, L. Hemachandra, D. Joseph, and P. Young.
Near-testable sets.
SIAM Journal on Computing, 20(3):506-523, 1991.

19
J. Goldsmith, L. Hemachandra, and K. Kunen.
Polynomial-time compression.
Computational Complexity, 2(1):18-39, 1992.

20
L. Hemachandra and A. Hoene.
On sets with efficient implicit membership tests.
SIAM Journal on Computing, 20(6):1148-1156, 1991.

21
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.

22
L. Hemachandra and S. Rudich.
On the complexity of ranking.
Journal of Computer and System Sciences, 41(2):251-271, 1990.

23
E. Hemaspaandra, L. Hemaspaandra, and C. Menton.
Search versus decision for election manipulation problems.
In Proceedings of the 30th Annual Symposium on Theoretical Aspects of Computer Science, pages 377-388. Leibniz International Proceedings in Informatics (LIPIcs), February/March 2013.

24
E. Hemaspaandra, L. Hemaspaandra, and H. Schnoor.
A control dichotomy for pure scoring rules.
In Proceedings of the 28th AAAI Conference on Artificial Intelligence, pages 712-720. AAAI Press, July 2014.

25
L. Hemaspaandra.
Beautiful structures: An appreciation of the contributions of Alan Selman.
SIGACT News, 45(3):54-70, 2014.

26
L. Hemaspaandra, H. Hempel, and G. Wechsung.
Self-specifying machines.
International Journal of Foundations of Computer Science, 10(3):263-276, 1999.

27
L. Hemaspaandra, C. Homan, and S. Kosub.
Cluster computing and the power of edge recognition.
Information and Computation, 205(8):1274-1293, 2007.

28
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.

29
L. Hemaspaandra, R. Lavaee, and C. Menton.
Schulze and ranked-pairs voting are fixed-parameter tractable to bribe, manipulate, and control.
In Proceedings of the 12th International Conference on Autonomous Agents and Multiagent Systems, pages 1345-1346. International Foundation for Autonomous Agents and Multiagent Systems, May 2013.

30
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.

31
L. Hemaspaandra and M. Ogihara.
Universally serializable computation.
Journal of Computer and System Sciences, 55(3):547-560, 1997.

32
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.

33
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.

34
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.

35
L. Hemaspaandra and M. Thakur.
Lower bounds and the hardness of counting properties.
Theoretical Computer Science, 326(1-3):1-28, 2004.

36
L. Hemaspaandra and H. Vollmer.
The Satanic notations: Counting classes beyond #P and other definitional adventures.
SIGACT News, 26(1):2-13, 1995.

37
L. Hemaspaandra and R. Williams.
An atypical survey of typical-case heuristic algorithms.
SIGACT News, 43(4):71-89, 2012.

38
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.

39
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.

40
M. Ogiwara and L. Hemachandra.
A complexity theory for feasible closure properties.
Journal of Computer and System Sciences, 46(3):295-325, 1993.

41
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.

42
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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(Last modified: February 28, 2017.)


Lane A. Hemaspaandra