Inclusion is undecidable for pattern languages
The inclusion problem for (nonerasing) pattern languages was raised by Angluin  in 1980. It has been open ever since. In this paper, we settle this open problem and show that inclusion is undecidable for (both erasing and nonerasing) pattern languages. In addition, we show that a special case of the inclusion problem, i.e., the inclusion problem for terminal-free erasing pattern languages, is decidable.
Keywordspatterns pattern languages inclusion problems equivalence problems decidability
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