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Design Pattern Detection is a part of many solutions to Software Engineering problems. It is a part of reengineering process and thus gives significant information to the designer. Design Pattern improves the program understanding and software maintenance. Therefore, a reliable design pattern discovery is required. Graph theoretic approaches have been used for design pattern detection in past. Here we are applying state space representation of graph matching algorithm for design pattern detection. State space representation easily describes the graph matching process. Using our approach variants of each design pattern as well as any occurrence of a design pattern can be detected.