Abstract
We present a new and simple decidability proof for the language inclusion problem between context-free languages and languages accepted by superdeterministic pushdown automata (Sdpdas). The language class of Sdpdas is one of the largest language classes \(\mathcal {C}\) for which the inclusion \(L_{\text {cfl}} \subseteq L_{\mathcal {C}}\) is decidable for an arbitrary context-free language \(L_{\text {cfl}}\) and arbitrary language \(L_{\mathcal {C}}\) in \(\mathcal {C}\). We introduce generalized pushdown automata and reformulate Sdpdas as a subclass of them. This reformulation naturally leads to a monoid that captures Sdpdas. The monoid is key to our simple decidability proof because we translate the inclusion problem on Sdpdas to the corresponding monoid inclusion problem. In addition to the decidability result, we present a new undecidability result regarding the inclusion problem on indexed languages.
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Acknowledgement
We are grateful to the anonymous reviewers for their careful reading, pointing out some mistakes, and invaluable suggestions. This work was supported by JSPS KAKENHI Grant Number 15J01843 and 15K00087.
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Uezato, Y., Minamide, Y. (2016). Monoid-Based Approach to the Inclusion Problem on Superdeterministic Pushdown Automata. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_32
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DOI: https://doi.org/10.1007/978-3-662-53132-7_32
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