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.
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?
This is a list of selected journal (except when the work has not yet
appeared in journal/book form) 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. Lane
Hemaspaandra's complete publication list can always be found at
http://www.cs.rochester.edu/u/lane/publist.pdf.
E. Allender, R. Beals, and M. Ogihara.
The complexity of matrix rank and feasible systems of linear
equations.
Computational Complexity, 8(2):99-126, 1999.
R. Beigel, L. Hemachandra, and G. Wechsung.
Probabilistic polynomial time is closed under parity reductions.
Information Processing Letters, 37(2):91-94, 1991.
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.
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.
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.
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.
L. Hemaspaandra, C. Homan, and S. Kosub.
Cluster computing and the power of edge recognition.
In Proceedings of the 3rd Annual Conference on Computation and
Logic: Theory and Applications of Models of Computation. Springer-Verlag
Lecture Notes in Computer Science.
To appear, 2006.
L. Hemaspaandra, S. Kosub, and K. Wagner.
The complexity of computing the size of an interval.
In Proceedings of the 28th International Colloquium on Automata,
Languages, and Programming, pages 1040-1051. Springer-Verlag Lecture
Notes in Computer Science #2076, July 2001.
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.
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.
L. Hemaspaandra, M. Ogihara, M. Zaki, and M. Zimand.
The complexity of finding top-Toda-equivalence-class
members.
Theory of Computing Systems.
In press. Preliminary version available in Proceedings of 6th
Latin American Symposium on Theoretical Informatics (Springer-Verlag, 2004).
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.
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.
M. Liskiewicz, M. Ogihara, and S. Toda.
The complexity of counting self-avoiding walks in subgraphs of
two-dimensional grids and hypercubes.
Theoretical Computer Science, 304(1-3):129-156, 2003.
M. Ogiwara.
Generalized theorems on the relationships among reducibility notions
to certain complexity classes.
Mathematical Systems Theory, 27(3):189-200, 1994.
M. Ogiwara, T. Thierauf, S. Toda, and O. Watanabe.
On closure properties of #P in the context of PF#P.
Journal of Computer and System Sciences, 53(2):171-179, 1996.
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.