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Lattice-theoretic progress measures and coalgebraic model checking

Lattice-theoretic progress measures and coalgebraic model checking
Lattice-theoretic progress measures and coalgebraic model checking
In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this paper we identify the essence of this workflow to be the notion of progress measure, and formalize it in general, possibly infinitary, lattice-theoretic terms. Our view on progress measures is that they are to nested/alternating fixed points what invariants are to safety/greatest fixed points, and what ranking functions are to liveness/least fixed points. That is, progress measures are combination of the latter two notions (invariant and ranking function) that have been extensively studied in the context of (program) verification. We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. Although the framework can be used to derive some decision procedures for finite settings, we also expect the proposed framework to form a basis for sound proof methods for some undecidable/infinitary problems.
718-732
Hasuo, Ichiro
61863486-f50a-48d5-9d68-57880cb18b31
Shimizu, Shunsuke
bbb36199-4d5d-4675-94ee-857d4dd0100b
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Hasuo, Ichiro
61863486-f50a-48d5-9d68-57880cb18b31
Shimizu, Shunsuke
bbb36199-4d5d-4675-94ee-857d4dd0100b
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea

Hasuo, Ichiro, Shimizu, Shunsuke and Cirstea, Corina (2016) Lattice-theoretic progress measures and coalgebraic model checking At 43rd Symposium on Principles of Programming Languages, United States. 20 - 23 Jan 2016. 15 pp, pp. 718-732.

Record type: Conference or Workshop Item (Paper)

Abstract

In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this paper we identify the essence of this workflow to be the notion of progress measure, and formalize it in general, possibly infinitary, lattice-theoretic terms. Our view on progress measures is that they are to nested/alternating fixed points what invariants are to safety/greatest fixed points, and what ranking functions are to liveness/least fixed points. That is, progress measures are combination of the latter two notions (invariant and ranking function) that have been extensively studied in the context of (program) verification. We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. Although the framework can be used to derive some decision procedures for finite settings, we also expect the proposed framework to form a basis for sound proof methods for some undecidable/infinitary problems.

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Accepted/In Press date: 3 November 2015
Published date: January 2016
Venue - Dates: 43rd Symposium on Principles of Programming Languages, United States, 2016-01-20 - 2016-01-23
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 386126
URI: http://eprints.soton.ac.uk/id/eprint/386126
PURE UUID: 00fbacad-795b-455c-ae38-d4a5808df8d3

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Date deposited: 29 Jan 2016 14:45
Last modified: 24 Jul 2017 16:38

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Contributors

Author: Ichiro Hasuo
Author: Shunsuke Shimizu
Author: Corina Cirstea

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