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Local Completeness in Abstract Interpretation

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Challenges of Software Verification

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 238))

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Abstract

Completeness of an abstract interpretation is an ideal situation where the abstract interpreter is guaranteed to be compositional and producing no false alarm when used for verifying program correctness. Completeness for all possible programs and inputs is a very rare condition, met only by straightforward abstractions. In this paper we make a journey in the different forms of completeness in abstract interpretation that emerged in recent years. In particular, we consider the case of local completeness, requiring precision only on some specific, rather than all, program inputs. By leveraging this notion of local completeness, a logical proof system parameterized by an abstraction A, called \(\textrm{LCL}_A\), for Local Completeness Logic on A, has been put forward to prove or disprove program correctness. In this program logic a provable triple \([p]~ \textsf{c}~[q]\) not only ensures that all alarms raised for the postcondition q are true ones, but also that if q does not raise alarms then the program \(\textsf{c}\) cannot go wrong with the precondition p.

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Acknowledgements

This research has been funded by the Italian MIUR, under the PRIN2017 project no. 201784YSZ5 “AnalysiS of PRogram Analyses (ASPRA)”, and by a Meta Research unrestricted gift.

Author information

Authors and Affiliations

  1. University of Pisa, Pisa, Italy

    Roberto Bruni & Roberta Gori

  2. University of Verona, Verona, Italy

    Roberto Giacobazzi

  3. University of Padova, Padova, Italy

    Francesco Ranzato

Authors
  1. Roberto Bruni
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  2. Roberto Giacobazzi
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  3. Roberta Gori
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  4. Francesco Ranzato
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Corresponding author

Correspondence to Francesco Ranzato .

Editor information

Editors and Affiliations

  1. Department of Mathematical, Physical, and Computer Sciences, University of Parma, Parma, Italy

    Vincenzo Arceri

  2. Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University of Venice, Venice, Italy

    Agostino Cortesi

  3. Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University of Venice, Venice, Italy

    Pietro Ferrara

  4. Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University of Venice, Venice, Italy

    Martina Olliaro

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Bruni, R., Giacobazzi, R., Gori, R., Ranzato, F. (2023). Local Completeness in Abstract Interpretation. In: Arceri, V., Cortesi, A., Ferrara, P., Olliaro, M. (eds) Challenges of Software Verification. Intelligent Systems Reference Library, vol 238. Springer, Singapore. https://doi.org/10.1007/978-981-19-9601-6_8

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  • DOI: https://doi.org/10.1007/978-981-19-9601-6_8

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