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Counting Multiplicity over Infinite Alphabets

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Reachability Problems (RP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5797))

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Abstract

In the theory of automata over infinite alphabets, a central difficulty is that of finding a suitable compromise between expressiveness and algorithmic complexity. We propose an automaton model where we count the multiplicity of data values on an input word. This is particularly useful when such languages represent behaviour of systems with unboundedly many processes, where system states carry such counts as summaries. A typical recognizable language is: “every process does at most k actions labelled a”. We show that emptiness is elementarily decidable, by reduction to the covering problem on Petri nets.

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, Chennai, India, 600113

    Amaldev Manuel & R. Ramanujam

Authors
  1. Amaldev Manuel
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  2. R. Ramanujam
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Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Laboratoire d’ Informatique (LIX), 91128, Palaiseau Cedex, France

    Olivier Bournez

  2. Department of Computer Science, Ashton Building, University of Liverpool, L69 3BX, Liverpool, England

    Igor Potapov

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© 2009 Springer-Verlag Berlin Heidelberg

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Manuel, A., Ramanujam, R. (2009). Counting Multiplicity over Infinite Alphabets. In: Bournez, O., Potapov, I. (eds) Reachability Problems. RP 2009. Lecture Notes in Computer Science, vol 5797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04420-5_14

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  • DOI: https://doi.org/10.1007/978-3-642-04420-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04419-9

  • Online ISBN: 978-3-642-04420-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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