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Generalizing Parikh’s Theorem

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Games, Norms and Reasons

Part of the book series: Synthese Library ((SYLI,volume 353))

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Abstract

R. Parikh’s celebrated theorem, first proved in [37], counts the number of occurrences of letters in words of a context-free languages L over an alphabet of k letters. For a given word w, the numbers of these occurrences is denoted by a vector \(n(w) \in {\mathbb N}^k\), and the theorem states

* Partially supported by the Israel Science Foundation for the project “Model Theoretic Interpretations of Counting Functions” (2007–2010) and the Grant for Promotion of Research by the Technion–Israel Institute of Technology.

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Notes

  1. 1.

    In [32] a different definition is given, which attempts to capture the specific situation of directed graphs. But the original definition is the one which is used when dealing with hyper-graphs and general relational structures.

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Acknowledgments

Some passages are taken verbatim from [23] and from [18]. I would like to thank my co-authors A. Durand, E. Fischer, M. More and N. Jones for kindly allowing me to do so. I would like to thank B. Courcelle for valuable comments and references, and to I. Adler for making [1] available to me before it was posted.

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Authors and Affiliations

  1. Department of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel

    Johann A. Makowsky*

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  1. Johann A. Makowsky*
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Correspondence to Johann A. Makowsky* .

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  1. , Institute for Logic, Language and, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, Netherlands

    Johan van Benthem

  2. Adi Shankaracharya Marg, Powai, Mumbai, 400076, India

    Amitabha Gupta

  3. , Institute for Logic and Philosophy, Tilburg University, Warandelaan 2, Tilburg, 5037 AB, Netherlands

    Eric Pacuit

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Makowsky*, J.A. (2011). Generalizing Parikh’s Theorem. In: van Benthem, J., Gupta, A., Pacuit, E. (eds) Games, Norms and Reasons. Synthese Library, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0714-6_10

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