Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Decision problems for patterns
Journal of Computer and System Sciences
A note on parsing pattern languages
Pattern Recognition Letters
Parameterized pattern matching: algorithms and applications
Journal of Computer and System Sciences
On the equivalence problem for E-pattern languages
Theoretical Computer Science
Journal of the ACM (JACM)
Polynomial Time Inference of Extended Regular Pattern Languages
Proceedings of RIMS Symposium on Software Science and Engineering
Patterns in Words versus Patterns in Trees: A Brief Survey and New Results
PSI '99 Proceedings of the Third International Andrei Ershov Memorial Conference on Perspectives of System Informatics
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Finding patterns common to a set of strings (Extended Abstract)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A non-learnable class of E-pattern languages
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Journal of Discrete Algorithms
Discontinuities in pattern inference
Theoretical Computer Science
Developments from enquiries into the learnability of the pattern languages from positive data
Theoretical Computer Science
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Bad news on decision problems for patterns
Information and Computation
Function matching: algorithms, applications, and a lower bound
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Inclusion problems for patterns with a bounded number of variables
DLT'10 Proceedings of the 14th international conference on Developments in language theory
International Journal of Geographical Information Science
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Patterns with bounded treewidth
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
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A word matches a pattern with variables (i.e., a string that contains terminal symbols and variable symbols) if and only if it can be obtained from the pattern by substituting the variables by terminal words. To decide for a given word whether or not it matches a pattern with variables is an NP-complete problem, which has been independently discovered and investigated in different areas of theoretical computer science and which has applications in various contexts. In this work, we show that the problem of matching patterns with variables remains NP-complete even if every variable has at most two occurrences. In addition to this, we show that if patterns can be represented as special kinds of planar graphs, then they can be matched in polynomial time.