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Specification, Algebra, and Software pp 296–314Cite as

Behavioral Rewrite Systems and Behavioral Productivity

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8373))

Abstract

This paper introduces behavioral rewrite systems, where rewriting is used to evaluate experiments, and behavioral productivity, which says that each experiment can be fully evaluated, and investigates some of their properties. First, it is shown that, in the case of (infinite) streams, behavioral productivity generalizes and may bring to a more basic rewriting setting the existing notion of stream productivity defined in the context of infinite rewriting and lazy strategies; some arguments are given that in some cases one may prefer the behavioral approach. Second, a behavioral productivity criterion is given, which reduces the problem to conventional term rewrite system termination, so that one can use off-the-shelf termination tools and techniques for checking behavioral productivity in general, not only for streams. Finally, behavioral productivity is shown to be equivalent to a proof-theoretic (rather than model-theoretic) notion of behavioral well-specifiedness, and its difficulty in the arithmetic hierarchy is shown to be \(\Pi_2^0\)-complete. All new concepts are exemplified over streams, infinite binary trees, and processes.

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Author information

Authors and Affiliations

  1. University of Illinois at Urbana-Champaign, USA

    Grigore Roşu

  2. Alexandru Ioan Cuza University, Iaşi, Romania

    Grigore Roşu & Dorel Lucanu

Authors
  1. Grigore Roşu
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  2. Dorel Lucanu
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Editor information

Editors and Affiliations

  1. School of Network and Information, Senshu University, 2-1-1 Higashi-mita, Tama-ku, 214-8580, Kawasaki, Kanagawa, Japan

    Shusaku Iida

  2. Department of Computer Science, Thomas M. Siebel Center for Computer Science, University of Illinois at Urbana-Champaign (UIUC), 201 N. Goodwin Avenue, MC 258, 61801, Urbana, IL, USA

    José Meseguer

  3. School of Information Science, Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Kazuhiro Ogata

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Roşu, G., Lucanu, D. (2014). Behavioral Rewrite Systems and Behavioral Productivity. In: Iida, S., Meseguer, J., Ogata, K. (eds) Specification, Algebra, and Software. Lecture Notes in Computer Science, vol 8373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54624-2_15

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  • DOI: https://doi.org/10.1007/978-3-642-54624-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54623-5

  • Online ISBN: 978-3-642-54624-2

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