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Das et al. have reported characterization of reachable/non-reachable CA states recently. Their scheme has only offered the characterization under a null boundary CA (NBCA). However, in hardware implementation, a periodic boundary CA (PBCA) is suitable for constructing cost-effective schemes such as a linear feedback shift register structure because of its circular property. Thus, this paper provides two decision algorithms for classification of reachable/non-reachable state and group/non-group CA based on periodic boundary condition. [ABSTRACT FROM AUTHOR]