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.

References

1

This is a list of selected papers, from or related to this project, by University of Rochester authors. Links to essentially all Lane's conference and journal papers (and also his arXiv.org technical reports) can be found via the pointers from the related entries within Lane's entry at the DBLP project. Additionally, here is a link to Lane's complete publication list (note: that list does not itself have links to papers).

2

J. Abascal, L. Hemaspaandra, S. Maimon, and D. Rubery.
Closure and nonclosure properties of the compressible and rankable sets.
In Proceedings of the 13th International Conference on Language and Automata Theory and Applications, pages 177–189. Springer-Verlag Lecture Notes in Computer Science #11417, March 2019.

3

J. Abascal, L. Hemaspaandra, S. Maimon, and D. Rubery.
Closure and nonclosure properties of the classes of compressible and rankable sets.
Journal of Computer and System Sciences, 120:162–176, 2021.

4

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

5

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.

6

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

7

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

8

I. Caragiannis, E. Hemaspaandra, and L. Hemaspaandra.
Dodgson's Rule and Young's Rule.
In F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. Procaccia, editors, Handbook of Computational Social Choice, pages 103–126. Cambridge University Press, 2016.

9

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.

10

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.

11

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

12

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

13

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.

14

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

15

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.

16

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

17

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

18

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

19

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.

20

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.

21

Z. Fitzsimmons, E. Hemaspaandra, and L. Hemaspaandra.
Control in the presence of manipulators: Cooperative and competitive cases.
Autonomous Agents and Multi-Agent Systems, 34(2, Article 52):1–32, 2020.

22

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

23

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

24

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

25

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.

26

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

27

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) #20, February/March 2013.

28

E. Hemaspaandra, L. Hemaspaandra, and C. Menton.
Search versus decision for election manipulation problems.
ACM Transactions on Computation Theory, 12(#1, Article 3):1–42, 2020.

29

E. Hemaspaandra, L. Hemaspaandra, and J. Rothe.
The complexity of online bribery in sequential elections.
In Proceedings of the 17th Conference on Theoretical Aspects of Rationality and Knowledge, pages 233–251. Electronic Proceedings in Theoretical Computer Science #297, July 2019.

30

E. Hemaspaandra, L. Hemaspaandra, and J. Rothe.
The complexity of online bribery in sequential elections.
Journal of Computer and System Sciences, 127:66–90, 2022.

31

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.

32

E. Hemaspaandra, L. Hemaspaandra, H. Spakowski, and O. Watanabe.
The robustness of LWPP and WPP, with an application to graph reconstruction.
In Proceedings of the 43rd International Symposium on Mathematical Foundations of Computer Science, pages 51:1–51:14. Leibniz International Proceedings in Informatics (LIPIcs) #117, August 2018.

33

E. Hemaspaandra, L. Hemaspaandra, H. Spakowski, and O. Watanabe.
The robustness of LWPP and WPP, with an application to graph reconstruction.
Computational Complexity, 29(2, Article 7):1–49, 2020.

34

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

35

L. Hemaspaandra.
Complexity classes.
In K. Rosen, editor, Handbook of Discrete and Combinatorial Mathematics, pages 1308–1314. CRC Press, 2nd edition, 2018.

36

L. Hemaspaandra.
Computational social choice and computational complexity: BFFs?
In Proceedings of the 32nd AAAI Conference on Artificial Intelligence, pages 7971–7977. AAAI Press, February 2018.

37

L. Hemaspaandra.
That most important intersection.
In H.-J. Böckenhauer, D. Komm, and W. Unger, editors, Adventures Between Lower Bounds and Higher Altitudes: Essays Dedicated to Juraj Hromkovič on the Occasion of his 60th Birthday, pages 568–589. Springer, 2018.

38

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

39

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

40

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.

41

L. Hemaspaandra, M. Juvekar, A. Nadjimzadah, and P. Phillips.
Gaps, ambiguity, and establishing complexity-class containments via iterative constant-setting.
In Proceedings of the 47th International Symposium on Mathematical Foundations of Computer Science, pages 57:1–57:15. Leibniz International Proceedings in Informatics (LIPIcs) #241, August 2022.

42

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.

43

L. Hemaspaandra, R. Lavaee, and C. Menton.
Schulze and ranked-pairs voting are fixed-parameter tractable to bribe, manipulate, and control.
Annals of Mathematics and Artificial Intelligence, 77(3–4):191–223, 2016.

44

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.

45

L. Hemaspaandra and D. Narváez.
The opacity of backbones.
In Proceedings of the 31st AAAI Conference on Artificial Intelligence, pages 3900–3906. AAAI Press, February 2017.

46

L. Hemaspaandra and D. Narváez.
Existence versus exploitation: The opacity of backbones and backdoors under a weak assumption.
In Proceedings of the 45th International Conference on Current Trends in Theory and Practice of Computer Science, pages 247–259. Springer-Verlag Lecture Notes in Computer Science #11376, January 2019.

47

L. Hemaspaandra and D. Narváez.
Existence versus exploitation: The opacity of backdoors and backbones.
Progress in Artificial Intelligence, 10(3):297–308, 2021.

48

L. Hemaspaandra and D. Narváez.
The opacity of backbones.
Information and Computation, 281(Article 104772):1–10, 2021.

49

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

50

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.

51

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.

52

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.

53

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

54

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

55

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

56

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.

57

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.

58

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

59

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.

60

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 16, 2023.)