Cohen, L. orcid.org/0000-0002-6608-3000, Jabarin, A. orcid.org/0009-0006-1519-7661, Popescu, A. orcid.org/0000-0001-8747-0619 et al. (1 more author) (2024) The complex(ity) landscape of checking infinite descent. In: Hicks, M., (ed.) Proceedings of the ACM on Programming Languages. 50th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2023), 15-21 Jan 2023, Boston, Massachusetts, United States. Association for Computing Machinery (ACM) , pp. 1352-1384.
Abstract
Cyclic proof systems, in which induction is managed implicitly, are a promising approach to automatic verification. The soundness of cyclic proof graphs is ensured by checking them against a trace-based Infinite Descent property. Although the problem of checking Infinite Descent is known to be PSPACE-complete, this leaves much room for variation in practice. Indeed, a number of different approaches are employed across the various cyclic proof systems described in the literature. In this paper, we study criteria for Infinite Descent in an abstract, logic-independent setting. We look at criteria based on Büchi automata encodings and relational abstractions, and determine their parameterized time complexities in terms of natural dimensions of cyclic proofs: the numbers of vertices of the proof-tree graphs, and the vertex width—an upper bound on the number of components (e.g., formulas) of a sequent that can be simultaneously tracked for descent. We identify novel algorithms that improve upon the parameterised complexity of the existing algorithms. We implement the studied criteria and compare their performance on various benchmarks.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2024 Owner/Author. This work is licensed under a Creative Commons Attribution 4.0 International License. https://creativecommons.org/licenses/by/4.0/ |
Keywords: | Theory Of Computation; Applied Mathematics; Information and Computing Sciences; Pure Mathematics; Mathematical Sciences |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 22 Feb 2024 12:59 |
Last Modified: | 22 Feb 2024 12:59 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Refereed: | Yes |
Identification Number: | 10.1145/3632888 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:209459 |