Abstract
We consider the pseudo-inversion operation inspired by a biological event as a result of the partial inversion. We define the pseudo-inversion of a string w = uxv to consist of all strings v R xu R, where uv ≠ λ and consider the operation from a formal language theoretic viewpoint. We show that regular languages are closed under the pseudo-inversion operation whereas context-free languages are not. Furthermore, we consider the iterated pseudo-inversion operation and establish the basic properties. Finally, we introduce the pseudo-inversion-freeness and examine closure properties and decidability problems for regular and context-free languages. We establish that pseudo-inversion-freeness is decidable in polynomial time for regular languages and undecidable for context-free languages.
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Cho, DJ., Han, YS., Kang, SD., Kim, H., Ko, SK., Salomaa, K. (2014). Pseudo-inversion on Formal Languages. In: Ibarra, O., Kari, L., Kopecki, S. (eds) Unconventional Computation and Natural Computation. UCNC 2014. Lecture Notes in Computer Science(), vol 8553. Springer, Cham. https://doi.org/10.1007/978-3-319-08123-6_8
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DOI: https://doi.org/10.1007/978-3-319-08123-6_8
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