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On Representations of Abstract Systems with Partial Inputs and Outputs

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Theory and Applications of Models of Computation (TAMC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8402))

Abstract

We consider a class of mathematical models called blocks which generalize some input-output models which appear in mathematical systems theory, control theory, signal processing. A block maps partial functions of time to nonempty sets of partial functions of time. A class of strongly nonanticipative blocks can be considered as an analog of the class of causal time systems studied by M. Mesarovic and Y. Takahara. The behavior of a strongly nonanticipative block can be represented using an abstract dynamical system called Nondeterministic Complete Markovian System (NCMS) which is close to the notion of a solution system by O. Hájek. We show that conversely, each initial input-output NCMS (i.e. NCMS with inputs and outputs) is a representation of a strongly nonanticipative block. This result generalizes a link between causality and the existence of state-space representations that exists in several variants of mathematical systems theory to models with partial inputs and outputs.

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Authors and Affiliations

  1. Université Paul Sabatier, 118 route de Narbonne, Toulouse, France

    Ievgen Ivanov

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  1. Ievgen Ivanov
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, College of Engineering, Anna University, Chennai, 600 025, Chennai, India

    T. V. Gopal

  2. Department of Computer Science and Engineering, Indian Institute of Technology, 208016, Kanpur, India

    Manindra Agrawal

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Zhongguancun, Haidian District, 100190, Beijing, China

    Angsheng Li

  4. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

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Ivanov, I. (2014). On Representations of Abstract Systems with Partial Inputs and Outputs. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2014. Lecture Notes in Computer Science, vol 8402. Springer, Cham. https://doi.org/10.1007/978-3-319-06089-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-06089-7_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06088-0

  • Online ISBN: 978-3-319-06089-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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