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International Conference on Verification, Model Checking, and Abstract Interpretation

VMCAI 2021: Verification, Model Checking, and Abstract Interpretation pp 151–173Cite as

Concurrent Correctness in Vector Space

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12597)

Abstract

Correctness verification of a concurrent history is challenging and has been proven to be an NP-complete problem. The reason that verifying correctness cannot be solved in polynomial time is a consequence of the way correctness is defined. Traditional correctness conditions require a concurrent history to be equivalent to a legal sequential history. The worst case number of legal sequential histories for a concurrent history is O(n!) with respect to n methods invoked. Existing correctness verification tools improve the time complexity by either reducing the size of the possible legal sequential histories or improving the efficiency of generating the possible legal sequential histories. Further improvements to the time complexity of correctness verification can be achieved by changing the way correctness of concurrent programs is defined. In this paper, we present the first methodology to recast the correctness conditions in literature to be defined in vector space. The concurrent histories are represented as a set of method call vectors, and correctness is defined as properties over the set of vectors. The challenge with defining correctness in vector space is accounting for method call ordering and data structure semantics. We solve this challenge by incorporating a priority assignment scheme to the values of the method call vectors. Using our new definitions of concurrent correctness, we design a dynamic analysis tool that checks the vector space correctness of concurrent data structures in \(O(n^2)\) with respect to n method calls, a significant improvement over O(n!) time required to analyze legal sequential histories. We showcase our dynamic analysis tool by using it to check the vector space correctness of a variety of queues, stacks, and hashmaps.

Keywords

  • Concurrent programs
  • Correctness condition
  • Dynamic analysis

This work was funded by NSF grants 1740095 and 1717515.

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Author information

Authors and Affiliations

  1. University of Central Florida, Orlando, FL, 32816, USA

    Christina Peterson, Victor Cook & Damian Dechev

Authors
  1. Christina Peterson
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  2. Victor Cook
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  3. Damian Dechev
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Correspondence to Christina Peterson .

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Editors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Prof. Fritz Henglein

  2. Tel Aviv University, Tel Aviv, Israel

    Sharon Shoham

  3. Technion, Haifa, Israel

    Yakir Vizel

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Peterson, C., Cook, V., Dechev, D. (2021). Concurrent Correctness in Vector Space. In: Henglein, F., Shoham, S., Vizel, Y. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2021. Lecture Notes in Computer Science(), vol 12597. Springer, Cham. https://doi.org/10.1007/978-3-030-67067-2_8

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