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Post’s Correspondence Problem: From Computer Science to Algebra

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Book cover Reachability Problems (RP 2022)

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Abstract

In this short survey we describe recent advances on the Post Correspondence Problem in group theory that were inspired by results in computer science. These algebraic advances can, in return, provide a source of interesting problems in more applied, computational settings.

Post’s Correspondence Problem (PCP) is a classical decision problem in theoretical computer science that asks whether for a pair of free monoid morphisms \(g, h:\varSigma ^*\rightarrow \varDelta ^*\) there is any non-trivial \(x\in \varSigma ^*\) such that \(g(x)=h(x)\). One can similarly phrase a PCP for general groups, rather than free monoids, by asking whether pairs g, h of group homomorphisms agree on any inputs. This leads to interesting and unexpected (un)decidability results for PCP in groups.

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Authors and Affiliations

  1. Heriot-Watt University and Maxwell Institute, Edinburgh, EH14 4AS, Scotland

    Laura Ciobanu

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  1. Laura Ciobanu
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Correspondence to Laura Ciobanu .

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Editors and Affiliations

  1. Department of Computer Science, TU Kaiserslautern, Kaiserslautern, Germany

    Anthony W. Lin

  2. Max Planck Institute for Software Systems, Kaiserslautern, Germany

    Georg Zetzsche

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Ciobanu, L. (2022). Post’s Correspondence Problem: From Computer Science to Algebra. In: Lin, A.W., Zetzsche, G., Potapov, I. (eds) Reachability Problems. RP 2022. Lecture Notes in Computer Science, vol 13608. Springer, Cham. https://doi.org/10.1007/978-3-031-19135-0_2

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  • DOI: https://doi.org/10.1007/978-3-031-19135-0_2

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