  We calculate how strongly one can constrain the alternative theories of
gravity with deci-Hz gravitational wave interferometers such as DECIGO and BBO.
Here we discuss Brans-Dicke theory and massive graviton theories as typical
examples. We consider the inspiral of compact binaries composed of a neutron
star (NS) and an intermediate mass black hole (IMBH) for Brans-Dicke (BD)
theory and those composed of a super massive black hole (SMBH) and a black hole
(SMBH) for massive graviton theories. Using the restricted 2PN waveforms
including spin effects and taking the spin precession into account, we perform
the Monte Carlo simulations of $10^4$ binaries to estimate the determination
accuracy of binary parameters including the Brans-Dicke parameter
$\omega_{\mathrm{BD}}$ and the graviton Compton length $\lambda_g$. Assuming a
$(1.4, 10)M_{\odot}$ NS/BH binary of SNR=$\sqrt{200}$, the constraint on
$\omega_{\mathrm{BD}}$ is obtained as $\omega_{\mathrm{BD}}>2.32\times 10^6$,
which is 300 times stronger than the estimated constraint from LISA
observation. Furthermore, we find that, due to the expected large merger rate
of NS/BH binaries of $O(10^4)$ yr$^{-1}$, a statistical analysis yields
$\omega_{\mathrm{BD}}>3.77\times10^8$, which is 4 orders of magnitude stronger
than the current strongest bound obtained from the solar system experiment. For
massive graviton theories, assuming a $(10^6, 10^5)M_{\odot}$ BH/BH binary at
3Gpc, one can put a constraint $\lambda_g>3.35\times10^{20}$cm, on average.
This is three orders of magnitude stronger than the one obtained from the solar
system experiment. From these results, it is understood that DECIGO/BBO is a
very powerful tool for constraining alternative theories of gravity, too.
