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International Conference on Machines, Computations, and Universality

MCU 2018: Machines, Computations, and Universality pp 69–87Cite as

The Language (and Series) of Hammersley-Type Processes

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10881)

Abstract

We study languages and formal power series associated to (variants of) the Hammersley process. We show that the ordinary Hammersley process yields a regular language and the Hammersley tree process yields deterministic context-free (but non-regular) languages. For the Hammersley interval process we show that there are two relevant variants of formal languages. One of them leads to the same language as the ordinary Hammersley tree process. The other one yields non-context-free languages.

The results are motivated by the problem of studying the analog of the famous Ulam-Hammersley problem for heapable sequences. Towards this goal we also give an algorithm for computing formal power series associated to the Hammersley process. We employ this algorithm to settle the nature of the scaling constant, conjectured in previous work to be the golden ratio. Our results provide experimental support to this conjecture.

This work was supported by a grant of Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0842, within PNCDI III.

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Notes

  1. 1.

    Nonrigorous computations predict that \(c_{0}=c_{2}=\frac{\sqrt{5}-1}{2}, c_{1}=\frac{3+\sqrt{5}}{2}.\).

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Authors and Affiliations

  1. Department of Computer Science, West University of Timişoara, Bd. V. Pârvan 4, Timişoara, Romania

    Cosmin Bonchiş, Gabriel Istrate & Vlad Rochian

  2. e-Austria Research Institute, Bd. V. Pârvan 4, cam. 045 B, Timişoara, Romania

    Cosmin Bonchiş & Gabriel Istrate

Authors
  1. Cosmin Bonchiş
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  2. Gabriel Istrate
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  3. Vlad Rochian
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Corresponding author

Correspondence to Gabriel Istrate .

Editor information

Editors and Affiliations

  1. Université d'Orléans, Orleans, France

    Jérôme Durand-Lose

  2. Université Paris Est, Creteil, France

    Sergey Verlan

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Bonchiş, C., Istrate, G., Rochian, V. (2018). The Language (and Series) of Hammersley-Type Processes. In: Durand-Lose, J., Verlan, S. (eds) Machines, Computations, and Universality. MCU 2018. Lecture Notes in Computer Science(), vol 10881. Springer, Cham. https://doi.org/10.1007/978-3-319-92402-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-92402-1_4

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