Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet. The problem is not well understood, no polynomial time algorithm is known and its NP-hardness is also not known. The pattern-avoidability problem is equivale...

Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations π and τ , represented as sequences of integers, and the task is to determine whether τ contains a subsequence order-isomorphic to π. Bose, Buss and Lubiw proved that PPM is NP-complete on general inputs. We show that PPM is NP-complete even when π has no decreasing subsequence of length 3 and τ has...

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This paper proposes an extension to OCL that addresses a concern regarding the proliferation of navigation expressions that occur when expressing predicates over objects. Declarative patterns are introduced that can be used to match against object structures so that repeated variables reduce the need for lengthy repeated navigation expressions. Patterns provide the basis for a further contribut...