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Lattice-theoretic progress measures and coalgebraic model checking

Published:11 January 2016Publication History
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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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                • Published in

                  cover image ACM SIGPLAN Notices
                  ACM SIGPLAN Notices  Volume 51, Issue 1
                  POPL '16
                  January 2016
                  815 pages
                  ISSN:0362-1340
                  EISSN:1558-1160
                  DOI:10.1145/2914770
                  • Editor:
                  • Andy Gill
                  Issue’s Table of Contents
                  • cover image ACM Conferences
                    POPL '16: Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
                    January 2016
                    815 pages
                    ISBN:9781450335492
                    DOI:10.1145/2837614

                  Copyright © 2016 ACM

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                  • Published: 11 January 2016

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