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The Shortest Common Supersequence problem (SCS for short) consists in findinga shortest common supersequence of a finite set of words on a fixed alphabetSigma. It is well-known that its decision version denoted [SR8] in [Garey andJohnson] is NP-complete. Many variants have been studied in the literature. Inthis paper we settle the complexity of two such variants of SCS where inputs donot contain identical consecutive letters. We prove that those variants denoted\varphi SCS and MSCS both have a decision version which remains NP-completewhen |\Sigma| is at least 3. Note that it was known for MSCS when |\Sigma| isat least 4 [Fleisher and Woeginger] and we discuss how [Darte] states a similarresult for |\Sigma| at least 3.

The complexity of Shortest Common Supersequence for inputs with no identical consecutive letters