We present the results of surveying [CI] $^3P_1-^3P_0$, $^{12}$CO $J=4-3$, and 630 $mu$m dust continuum emission for 36 nearby ultra/luminous infrared galaxies (U/LIRGs) using the Band 8 receiver mounted on the Atacama Compact Array (ACA) of the Atacama Large Millimeter/submillimeter Array. We describe the survey, observations, data reduction, and results; the main results are as follows. (i) We confirmed that [CI] $^3P_1-^3P_0$ has a linear relationship with both the $^{12}$CO $J=4-3$and 630 $mu$m continuum. (ii) In NGC 6052 and NGC 7679, $^{12}$CO $J=4-3$ was detected but [CI] $^3P_1-^3P_0$ was not detected with a [CI] $^3P_1-^3P_0$/ $^{12}$CO $J=4-3$ ratio of $lesssim0.08$. Two possible scenarios of weak [CI] $^3P_1-^3P_0$ emission are C$^0$-poor/CO-rich environments or an environment with an extremely large [CI] $^3P_1-^3P_0$ missing flux. (iii) There is no clear evidence showing that galaxy mergers, AGNs, and dust temperatures control the ratios of [CI] $^3P_1-^3P_0$/ $^{12}$CO $J=4-3$ and $L_{rm [CI](1-0)}/L_{rm 630mu m}$. (iv) We compare our nearby U/LIRGs with high-z galaxies, such as galaxies on the star formation main sequence (MS) at z$sim1$ and submillimeter galaxies (SMGs) at $z=2-4$. We found that the mean value for the [CII] $^3P_1$--$^3P_0$/ $^{12}$CO $J=4-3$ ratio of U/LIRGs is similar to that of SMGs but smaller than that of galaxies on the MS.
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