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DOI: 10.4230/LIPIcs.FSCD.2022.26

mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity

Authors: Clément Aubert, Thomas Rubiano, Neea Rusch, and Thomas Seiller

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract

Implicit Computational Complexity (ICC) drives better understanding of complexity classes, but it also guides the development of resources-aware languages and static source code analyzers. Among the methods developed, the mwp-flow analysis [Jones and Lars Kristiansen, 2009] certifies polynomial bounds on the size of the values manipulated by an imperative program. This result is obtained by bounding the transitions between states instead of focusing on states in isolation, as most static analyzers do, and is not concerned with termination or tight bounds on values. Those differences, along with its built-in compositionality, make the mwp-flow analysis a good target for determining how ICC-inspired techniques diverge compared with more traditional static analysis methods. This paper’s contributions are three-fold: we fine-tune the internal machinery of the original analysis to make it tractable in practice; we extend the analysis to function calls and leverage its machinery to compute the result of the analysis efficiently; and we implement the resulting analysis as a lightweight tool to automatically perform data-size analysis of C programs. This documented effort prepares and enables the development of certified complexity analysis, by transforming a costly analysis into a tractable program, that furthermore decorrelates the problem of deciding if a bound exist with the problem of computing it.

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Clément Aubert, Thomas Rubiano, Neea Rusch, and Thomas Seiller. mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 26:1-26:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aubert_et_al:LIPIcs.FSCD.2022.26,
  author =	{Aubert, Cl\'{e}ment and Rubiano, Thomas and Rusch, Neea and Seiller, Thomas},
  title =	{{mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{26:1--26:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.26},
  URN =		{urn:nbn:de:0030-drops-163071},
  doi =		{10.4230/LIPIcs.FSCD.2022.26},
  annote =	{Keywords: Static Program Analysis, Implicit Computational Complexity, Automatic Complexity Analysis, Program Verification}
}

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DOI: 10.4230/LIPIcs.CALCO.2015.86

An Intensionally Fully-abstract Sheaf Model for pi

Authors: Clovis Eberhart, Tom Hirschowitz, and Thomas Seiller

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract

Following previous work on CCS, we propose a compositional model for the pi-calculus in which processes are interpreted as sheaves on certain simple sites. We define an analogue of fair testing equivalence in the model and show that our interpretation is intensionally fully abstract for it. That is, the interpretation preserves and reflects fair testing equivalence; and furthermore, any strategy is fair testing equivalent to the interpretation of some process. The central part of our work is the construction of our sites, whose heart is a combinatorial presentation of pi-calculus traces in the spirit of string diagrams. As in previous work, the sheaf condition is analogous to innocence in Hyland-Ong/Nickau games.

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Clovis Eberhart, Tom Hirschowitz, and Thomas Seiller. An Intensionally Fully-abstract Sheaf Model for pi. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 86-100, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{eberhart_et_al:LIPIcs.CALCO.2015.86,
  author =	{Eberhart, Clovis and Hirschowitz, Tom and Seiller, Thomas},
  title =	{{An Intensionally Fully-abstract Sheaf Model for pi}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{86--100},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.86},
  URN =		{urn:nbn:de:0030-drops-55284},
  doi =		{10.4230/LIPIcs.CALCO.2015.86},
  annote =	{Keywords: concurrency, sheaves, causal models, games}
}

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mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity

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An Intensionally Fully-abstract Sheaf Model for pi

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