Mu calculus

Mu calculus

The μ-calculus (also modal μ calculus) is a class of temporal logics with a least fixpoint operator μ. It is used to describe properties of labelled transition systems and for verifying these properties.

The (propositional) μ-calculus was invented by Scott and De Bakker [Kozen p.333] , and further developed by Kozen into the version most people use nowadays.

Many temporal logics can be encoded in the μ-calculus, such as LTL, CTL and CTL*. [Clarke p.108, Theorem 6; Emerson p.196]

Notes

References

*cite book
last = Clarke, Jr.
first = Edmund M.
coauthors = Orna Grumberg, Doron A. Peled
title = Model Checking
year = 1999
publisher = MIT press
location = Cambridge, Massachusetts, USA
id = ISBN 0-262-03270-8

*cite book
last = Stirling
first = Colin.
title = Modal and Temporal Properties of Processes
year = 2001
publisher = Springer Verlag
location = New York, Berlin, Heidelberg
id = ISBN 0-387-98717-7

*cite conference
first = E. Allen
last = Emerson
title = Model Checking and the Mu-calculus
booktitle = Descriptive Complexity and Finite Models
year = 1996
pages = 185-214
publisher = American Mathematical Society
id = ISBN 0-8218-0517-7

*cite journal
author = Kozen, Dexter
year = 1983
title = Results on the Propositional μ-Calculus
journal = Theoretical Computer Science
volume = 27
issue = 3
pages = 333–354
doi = 10.1016/0304-3975(82)90125-6


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