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- Seinosuke Toda
- SIAM J. Comput.
- 1991

In this paper, two interesting complexity classes, PP and P, are compared with PH, the polynomial-time hierarchy. It is shown that every set in PH is polynomial-time Turing reducible to a set in PP, and PH is included in BP. 0)P. As a consequence of the results, it follows that PP PH (or 03P___ PH) implies a collapse of PH. A stronger result is also shown:… (More)

- Zhi-Zhong Chen, Seinosuke Toda
- Structure in Complexity Theory Conference
- 1993

- Seinosuke Toda, Mitsunori Ogihara
- SIAM J. Comput.
- 1991

- Seinosuke Toda, Osamu Watanabe
- Theor. Comput. Sci.
- 1992

- Seinosuke Toda
- FOCS
- 1989

- Seinosuke Toda
- 1991

The main purpose of this paper is to exhibit non-algebraic problems that are computationally equivalent to computing the integer determinant. For this purpose, some graph-theoretic counting problems are shown to be equivalent to the integer determinant problem under suitable reducibilities. Those are the problems of counting the number of all paths between… (More)

- Ryuhei Uehara, Seinosuke Toda, Takayuki Nagoya
- Discrete Applied Mathematics
- 2005

This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipar-tite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded k. On the other side,… (More)

- Johannes Köbler, Seinosuke Toda
- Mathematical systems theory
- 1993

We investigate the computational power of the new counting class ModP which generalizes the classes Mod p P,p prime. We show that ModP is polynomialtime truth-table equivalent in power to #P and that ModP is contained in the class AmpMP. As a consequence, the classes PP, ModP, and AmpMP are all Turing equivalent, and thus AmpMP and ModP are not low for MP… (More)

- Seinosuke Toda
- FOCS
- 1990

- Johannes Köbler, Uwe Schöning, Seinosuke Toda, Jacobo Torán
- J. Comput. Syst. Sci.
- 1989