Decision problems for patterns
Journal of Computer and System Sciences
A note on parsing pattern languages
Pattern Recognition Letters
Handbook of formal languages, vol. 1
On the equivalence problem for E-pattern languages
Theoretical Computer Science
Frontier between decidability and undecidability: a survey
Theoretical Computer Science - Special issue on universal machines and computations
Polynomial Time Inference of Extended Regular Pattern Languages
Proceedings of RIMS Symposium on Software Science and Engineering
Developments from enquiries into the learnability of the pattern languages from positive data
Theoretical Computer Science
Four Small Universal Turing Machines
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Bad news on decision problems for patterns
Information and Computation
Expressive languages for path queries over graph-structured data
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Inclusion problems for patterns with a bounded number of variables
DLT'10 Proceedings of the 14th international conference on Developments in language theory
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We study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach [D.D. Freydenberger, D. Reidenbach, Bad news on decision problems for patterns, Information and Computation 208 (1) (2010) 83-96] by showing that restricting the inclusion problem to significantly more restricted classes of patterns preserves undecidability, at least for comparatively large bounds. For smaller bounds, we prove the existence of classes of patterns with complicated inclusion relations, and an open inclusion problem, that are related to the Collatz Conjecture. In addition to this, we give the first proof of the undecidability of the inclusion problem for NE-pattern languages that, in contrast to previous proofs, does not rely on the inclusion problem for E-pattern languages, and proves the undecidability of the inclusion problem for NE-pattern languages over binary and ternary alphabets.