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We report results of a photometric survey with the WIYN telescope for carbonstars in the M 31 dwarf spheroidal (dSph) companions And III, And V, And VI,and And VII, as well as in the relatively isolated Local Group dSph Cetus. Wefind three carbon-star candidates in And VII and one carbon star in each And VIand Cetus. Comparing the carbon star content with other Local Group dwarfgalaxies, we argue against the presence of substantial intermediate-age stellarpopulations in the all of the galaxies surveyed with the exception of And VII.We discuss these results in the context of the origin of the Andromeda dSphsand conclude that these are ancient galaxies, most of which ceased starformation long before the main merger events in M31. The M31 dSphs thereforeshow less diversity in star formation histories than the Galactic dSphcompanions, or the M31 dE companions, as illustrated by NGC147 which wassurveyed as a calibration object. All of our dSph targets except And V havecandidate carbon stars below the tip of the RGB, which resemble CH stars foundin globular clusters. We estimate that 0.3% of stars in the dSphs are CH stars,presumably as a result of C pollution from a binary companion. Comparisons withCH star frequencies in globular clusters could constrain the impact of denseenvironments on the frequency of this form of binary star evolution.Comment: accepted for publication in A

WIYN Survey for Carbon Stars in the M31 and Cetus Dwarf Spheroidal Galaxies: Evolutionary Implications