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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)

- Seinosuke Toda
- FOCS
- 1989

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

In this paper, it is shown that many natural counting classes, such as PP, C=P, and MODkP, arc at least as computationally hard as PH (the polynomial-time hierarchy) in the following sense: for each K of the counting classes above, every set in K(PH) is polynomial-time randomized many-one reducible to a set in K with two-sided exponentially small error… (More)

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

- M H Bornstein, C S Tamis-LeMonda, +6 authors D Vardi
- Child development
- 1992

This study examines and compares prominent characteristics of maternal responsiveness to infant activity during home-based naturalistic interactions of mother-infant dyads in New York City, Paris, and Tokyo. Both culture-general and culture-specific patterns of responsiveness emerged. For example, in all 3 locales infants behaved similarly, mothers also… (More)

- 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)

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

- Seinosuke Toda
- Mathematical systems theory
- 1991

The existence of setsnot being ≤ tt P -reducible to low sets is investigated for several complexity classes such as UP, NP, the polynomial-time hierarchy, PSPACE, and EXPTIME. The p-selective sets are mainly considered as a class of low sets. Such investigations were done in many earlier works, but almost all of these have dealt withpositive reductions in… (More)

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

The intractability of the complexity class NP has motivated the study of subclasses that arise when certain restrictions on the definition of NP are imposed. For example, the study of sparse sets in NP [Ma82], the study of the probabilistic classes whithin NP [Gi77], and the study of low sets in NP for the classes in the polynomial time hierarchy [Sc83],… (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)