This work addresses the problem of finding minimal strings within a given language according to specified patterns. The authors developed a systematic approach that allows specifying patterns using regular expressions and performing operations on them, such as intersection and union of corresponding regular languages. This approach enables finding all minimal strings that satisfy multiple pattern constraints simultaneously. The problem generalizes the well-known Shortest Common Supersequence (SCS) problem, which is important in AI planning, as well as in data compression, database query optimization, and bioinformatics, where the goal is to find the shortest string that contains all given patterns as subsequences. The approach has been successfully applied to analyze DNA sequences, demonstrating its practical utility in bioinformatics applications.