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Generalized Post Embedding Problems

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Abstract

The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to undecidability.

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Notes

  1. But the problem becomes easy, decidable in linear-time and logarithmic space [8], when restricted to R = Σ+ as in PCP.

  2. PEP is undecidable if we allow constraint sets R outside Reg(Σ) [8]. Other extensions, like \(\exists x\in R_{1}:\forall y\in R_{2}:u(xy)\sqsubseteq v(xy)\), for R 1, R 2 ∈ Reg(Σ), have been shown undecidable [12].

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Authors and Affiliations

  1. Chennai Mathematical Institute, Chennai, India

    Prateek Karandikar

  2. LSV, ENS Cachan, Cachan, France

    Prateek Karandikar & Philippe Schnoebelen

  3. LSV, CNRS, Cachan, France

    Philippe Schnoebelen

Authors
  1. Prateek Karandikar
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  2. Philippe Schnoebelen
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Correspondence to Philippe Schnoebelen.

Additional information

Supported by Grant ANR-11-BS02-001. The first author was partially supported by Tata Consultancy Services. An extended abstract of this article appeared in [18].

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Karandikar, P., Schnoebelen, P. Generalized Post Embedding Problems. Theory Comput Syst 56, 697–716 (2015). https://doi.org/10.1007/s00224-014-9561-9

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