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Algorithmic Algebraic Model Checking II: Decidability of Semi-algebraic Model Checking and Its Applications to Systems Biology

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Automated Technology for Verification and Analysis (ATVA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3707))

Abstract

Motivated by applications to systems biology, and the emergence of semi-algebraic hybrid systems as a natural framework for modeling biochemical networks, we continue exploring the decidability problem for model-checking with TCTL (Timed Computation Tree Logic) over this broad class of semi-algebraic hybrid systems. Previously, we had introduced these models, demonstrated the close connection to the goals of systems biology. However, we had only developed the techniques for bounded reachability, arguing for the adequacy of such an approach in a majority of the biological applications. Here, we present a semi-decidable symbolic algebraic dense-time TCTL model checking algorithm, which satisfies two desirable properties: it can be derived automatically from the symbolic description, and it extends to and generalizes other versions of temporal logics. The main mathematical device at the core of this approach is Tarski-Collins’ real quantifier elimination employed at each fixpoint iteration, whose high complexity is the crux of its unfortunate limitation. Along with these results, we prove the undecidability of this problem in the more powerful “real” Turing machine formalism of Blum, Shub and Smale. We then demonstrate a preliminary version of our model-checker Tolque on the Delta-Notch example.

The work reported in this paper was supported by grants from NSF’s ITR program, Defense Advanced Research Projects Agency (DARPA), the US Air Force (AFRL), National Institutes of Health (NIH) and New York State Office of Science, Technology & Academic Research (NYSTAR). C.P. was partially supported by the MIUR FIRB grant RBAU018RCZ and the MIUR PRIN’04 grant 2004013015.

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Authors and Affiliations

  1. Courant Institute, New York University, New York, NY, U.S.A

    V. Mysore & B. Mishra

  2. Dept. of Mathematics and Computer Science, University of Udiné, Udine, Italy

    C. Piazza

  3. NYU School of Medicine, New York University, New York, NY, U.S.A

    B. Mishra

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  1. V. Mysore
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  2. C. Piazza
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  3. B. Mishra
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Editors and Affiliations

  1. Department of Computer Science, Bar Ilan University, 52900, Ramat Gan, Israel

    Doron A. Peled

  2. Department of Information Management, National Taiwan University, Taiwan

    Yih-Kuen Tsay

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Mysore, V., Piazza, C., Mishra, B. (2005). Algorithmic Algebraic Model Checking II: Decidability of Semi-algebraic Model Checking and Its Applications to Systems Biology. In: Peled, D.A., Tsay, YK. (eds) Automated Technology for Verification and Analysis. ATVA 2005. Lecture Notes in Computer Science, vol 3707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11562948_18

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  • DOI: https://doi.org/10.1007/11562948_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29209-8

  • Online ISBN: 978-3-540-31969-6

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