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The paper deals with the class RPk of sets of at most k regular patterns. A semantics of a set P of regular patterns is a union L(P) of languages defined by patterns in P. A set Q of regular patterns is said to be a more general than P, denoted by P ⊆ Q, if for any p ∈ P, there is a more general pattern q in Q than p. It is known that the syntactic containment P ⊆ Q for sets of regular patterns is efficiently computable. We prove that for any sets P and Q in RPk, (i) S2(P) ⊆ L(Q), (ii) the syntactic containment P ⊆ Q and (iii) the semantic containment L(P) ⊆ L(Q) are equivalent mutually, provided #Σ ≥ 2k - 1, where Sn(P) is the set of strings obtained from P by substituting strings with length at most n for each variable. The result means that S2 (P) is a characteristic set of L(P) within the language class for RPk under the condition above. Arimura et al. showed that the class RPk has compactness with respect to containment, if #Σ ≥ 2k+1. By the equivalency above, we prove that RPk has compactness if and only if #Σ ≥ 2k - 1. The results obtained enable us to design efficient learning algorithms of unions of regular pattern languages such as already presented by Arimura et al. under the assumption of compactness.