Theories of orders on the set of words
Dietrich Kuske (2010)
RAIRO - Theoretical Informatics and Applications
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It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, , 1969] and of the theory of the total lexicographic path ordering [P. Narendran and M. Rusinowitch, , 2000] and, in case of the subword and the lexicographic path order, improves...