Patterns with bounded treewidth [internal report]

A pattern is a string consisting of variables and terminal symbols, and its language is the set of all words that can be obtained by substi- tuting arbitrary words for the variables. The membership problem for pattern languages, i. e., deciding on whether or not a given word is in the pattern language of a given pattern is NP-complete. We show that any parameter of patterns that is an upper bound for the treewidth of appro- priate encodings of patterns as relational structures, if restricted, allows the membership problem for pattern languages to be solved in polynomial time. Furthermore, we identify new such parameters.