L(A) = L(B)? decidability results from complete formal systems
Theoretical Computer Science
Formal languages and their relation to automata
Formal languages and their relation to automata
Word Problems and Membership Problems on Compressed Words
SIAM Journal on Computing
Ambiguity in Graphs and Expressions
IEEE Transactions on Computers
Algorithms for learning regular expressions from positive data
Information and Computation
A declarative specification of tree-based symbolic arithmetic computations
PADL'12 Proceedings of the 14th international conference on Practical Aspects of Declarative Languages
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We study the decision properties of XML languages. It was known that given a context-free language included in the Dyck language with sufficiently many pairs of parentheses, it is undecidable whether or not it is an XML language. We improve on this result by showing that the problem remains undecidable when the language is written on a unique pair of parentheses. We also prove that if the given language is deterministic, then the problem is decidable; while establishing whether its surfaces are regular turns out to be undecidable whenever the deterministic language is contained in the Dyck language with two pairs of parentheses. Our results are based on a “pumping property” of what Boasson and Berstel call the surface of a context-free language.