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Sbornik: Mathematics, 2015, Volume 206, Issue 9, Pages 1173–1190
DOI: https://doi.org/10.1070/SM2015v206n09ABEH004493 (Mi sm8519) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On some slowly terminating term rewriting systems

L. D. Beklemisheva, A. A. Onoprienkob

a Steklov Mathematical Institute of Russian Academy of Sciences
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (515 kB) Citations (4)
References:
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DOI: https://doi.org/10.1070/SM2015v206n09ABEH004493
Abstract: We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic $\mathsf{PA}$. Thus, the termination of such systems is unprovable in $\mathsf{PA}$. These systems are derived from an independent combinatorial result known as the Worm principle; they can also be viewed as versions of the well-known Hercules-Hydra game introduced by Paris and Kirby.
Bibliography: 16 titles.
Keywords: term rewriting systems, Peano arithmetic, Worm principle.
Funding agency Grant number
Russian Science Foundation 14-50-00005
L. D. Beklemishev's research was financed by a grant of the Russian Science Foundation (project no. 14-50-00005) at the Steklov Mathematical Institute of the Russian Academy of Sciences. Sections 1–5 were written by L. D. Beklemishev, and § 6 was written by L. D. Beklemishev together with A. A. Onoprienko.
Received: 25.03.2015 and 21.06.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 9, Pages 3–20
DOI: https://doi.org/10.4213/sm8519
Bibliographic databases:
Document Type: Article
UDC: 510.23+510.58
MSC: 68Q42, 03D03, 03F45, 03F30
Language: English
Original paper language: Russian
Citation: L. D. Beklemishev, A. A. Onoprienko, “On some slowly terminating term rewriting systems”, Mat. Sb., 206:9 (2015), 3–20; Sb. Math., 206:9 (2015), 1173–1190
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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