Abstract
We study the problem of testing whether a context-free language is included in a fixed set L 0, where L 0 is the language of words reducing to the empty word in the monoid defined by a complete string rewrite system. We prove that, if the monoid is cancellative, then our inclusion problem is polynomially reducible to the problem of testing equivalence of straight-line programs in the same monoid. As an application, we obtain a polynomial time algorithm for testing if a context-free language is included in a Dyck language (the best previous algorithm for this problem was doubly exponential).
Partially supported by Project M.I.U.R. PRIN 2007–2009: Mathematical aspects and forthcoming applications of automata and formal languages.
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Bertoni, A., Choffrut, C., Radicioni, R. (2009). The Inclusion Problem of Context-Free Languages: Some Tractable Cases. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_8
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DOI: https://doi.org/10.1007/978-3-642-02737-6_8
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