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Algorithmically Broad Languages for Polynomial Time and Space

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Logic, Language, Information, and Computation (WoLLIC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13038))

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Abstract

Flexible programming languages with built-in bounds on time or space resources are of obvious practical interest. Since we know that no programming language can capture exactly the PTime (or PSpace) algorithms, the challenge is to design languages that guarantee PTime while accommodating a broad spectrum of algorithmic methods. We propose here such languages for PTime and PSpace, based on size-sensitive imperative programming, parameterless procedures, and a retooling of the ramification method.

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Notes

  1. 1.

    Unlike the traditional notion of structure expansion, here may have a larger universe than .

  2. 2.

    A common alternative notation is .

  3. 3.

      memorizes the atom denoted by , in case the contraction renders that atom inaccessible.

  4. 4.

    Recall that our vocabularies are lists.

  5. 5.

      d need not be disjoint, and need not be their union.

  6. 6.

    See Definition 3.

  7. 7.

    These successor and predecessor programs are in constant time, in contrast to the linear time obtained when acting on the final atom of the input.

  8. 8.

    Leaving some ids unranked is akin to assigning them 0.

  9. 9.

    I.e. ramified recurrence over strings “with parameter substitution".

  10. 10.

    I.e. defined without subtraction or negative integers.

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Author information

Authors and Affiliations

  1. Computer Science, Indiana University, Bloomington, IN, 47405, USA

    Daniel Leivant

  2. IRIF, Université de Paris, 75205, Paris, France

    Daniel Leivant

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  1. Daniel Leivant
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Correspondence to Daniel Leivant .

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Editors and Affiliations

  1. Cornell University, New York, NY, USA

    Alexandra Silva

  2. Instituto de Matematica e Estatisrica, Universidade de São Paulo, Sao Paulo, São Paulo, Brazil

    Renata Wassermann

  3. Centro de Informática, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Ruy de Queiroz

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Leivant, D. (2021). Algorithmically Broad Languages for Polynomial Time and Space. In: Silva, A., Wassermann, R., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2021. Lecture Notes in Computer Science(), vol 13038. Springer, Cham. https://doi.org/10.1007/978-3-030-88853-4_23

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  • DOI: https://doi.org/10.1007/978-3-030-88853-4_23

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  • Online ISBN: 978-3-030-88853-4

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