Coalgebraic CTL: fixpoint characterization and polynomial-time model checking
Coalgebraic CTL: fixpoint characterization and polynomial-time model checking
We introduce a path-based coalgebraic temporal logic, Coalgebraic
CTL (CCTL), as a categorical abstraction of standard Computation
Tree Logic (CTL). Our logic can be used to formalize properties
of systems modeled as coalgebras with branching. We present the syntax
and path-based semantics of CCTL, and show how to encode this logic
into a coalgebraic fixpoint logic with a step-wise semantics. Our main
result shows that this encoding is semantics-preserving. We also present
a polynomial-time model-checking algorithm for CCTL, inspired by the
standard model-checking algorithm for CTL but described in categorical
terms. A key contribution of our paper is to identify the categorical
essence of the standard encoding of CTL into the modal mu-calculus.
This categorical perspective also explains the absence of a similar encoding
of PCTL (Probabilistic CTL) into the probabilistic mu-calculus.
Kojima, Ryota
d01773fa-38d6-4233-8ad2-bba48100e4dc
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Muroya, Koko
24a22926-ece4-4492-a0ad-22d144d85dde
Hasuo, Ichiro
4a4c712f-1d59-4caf-9dbd-aff060defd90
Kojima, Ryota
d01773fa-38d6-4233-8ad2-bba48100e4dc
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Muroya, Koko
24a22926-ece4-4492-a0ad-22d144d85dde
Hasuo, Ichiro
4a4c712f-1d59-4caf-9dbd-aff060defd90
Kojima, Ryota, Cirstea, Corina, Muroya, Koko and Hasuo, Ichiro
(2024)
Coalgebraic CTL: fixpoint characterization and polynomial-time model checking.
Urbat, Henning and Konig, Barbara
(eds.)
In Coalgebraic Methods in Computer Science -- 17th IFIP WG 1.3 International Workshop, CMCS 2024.
Springer.
23 pp
.
(In Press)
Record type:
Conference or Workshop Item
(Paper)
Abstract
We introduce a path-based coalgebraic temporal logic, Coalgebraic
CTL (CCTL), as a categorical abstraction of standard Computation
Tree Logic (CTL). Our logic can be used to formalize properties
of systems modeled as coalgebras with branching. We present the syntax
and path-based semantics of CCTL, and show how to encode this logic
into a coalgebraic fixpoint logic with a step-wise semantics. Our main
result shows that this encoding is semantics-preserving. We also present
a polynomial-time model-checking algorithm for CCTL, inspired by the
standard model-checking algorithm for CTL but described in categorical
terms. A key contribution of our paper is to identify the categorical
essence of the standard encoding of CTL into the modal mu-calculus.
This categorical perspective also explains the absence of a similar encoding
of PCTL (Probabilistic CTL) into the probabilistic mu-calculus.
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Accepted/In Press date: 1 May 2024
Identifiers
Local EPrints ID: 490674
URI: http://eprints.soton.ac.uk/id/eprint/490674
PURE UUID: c8342f32-a7e5-4423-81b4-def7c3f876a0
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Date deposited: 03 Jun 2024 17:04
Last modified: 04 Jun 2024 01:38
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Contributors
Author:
Ryota Kojima
Author:
Corina Cirstea
Author:
Koko Muroya
Author:
Ichiro Hasuo
Editor:
Henning Urbat
Editor:
Barbara Konig
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