Abstract
The deterministic shrinking two-pushdown automata characterize the deterministic growing context-sensitive languages, known to be the Church-Rosser languages. Here, we initiate the investigation of reversible two-pushdown automata, RTPDAs, in particular the shrinking variant. We show that as with the deterministic version, shrinking and length-reducing RTPDAs are equivalent. We then give a separation of the deterministic and reversible shrinking two-pushdown automata, and prove that these are incomparable with the (deterministic) context-free languages. We further show that the properties of emptiness, (in)finiteness, universality, inclusion, equivalence, regularity, and context-freeness are not even semi-decidable for shrinking RTPDAs.
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At least when considered as language acceptors—for functions the picture is somewhat more complex [1].
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The extension to \((Q\cup \varGamma \cup \{\bot \})^*\) is defined by \(\varphi (xy)=\varphi (x)+\varphi (y)\) and \(\varphi (\lambda )=0\).
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Acknowledgments
The authors acknowledge partial support from COST Action IC1405 Reversible Computation. H. B. Axelsen was supported by the Danish Council for Independent Research \(\mid \) Natural Sciences under the Foundations of Reversible Computing project, and by an IC1405 STSM (short-term scientific mission) grant.
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© 2016 Springer International Publishing Switzerland
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Axelsen, H.B., Holzer, M., Kutrib, M., Malcher, A. (2016). Reversible Shrinking Two-Pushdown Automata. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_44
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DOI: https://doi.org/10.1007/978-3-319-30000-9_44
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