mu-calculus

E824073

fixpoint logic modal logic temporal logic formalism

The mu-calculus is a powerful modal logic with fixed-point operators used to express and verify properties of recursive and infinite-state systems in computer science.

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Observed surface forms (1)

Surface form	Occurrences
μ-calculus	0

Statements (48)

Predicate	Object
instanceOf	fixpoint logic ⓘ modal logic ⓘ temporal logic formalism ⓘ
canExpress	fairness properties ⓘ liveness properties ⓘ reachability properties ⓘ safety properties ⓘ ω-regular properties ⓘ
complexityOfModelChecking	EXPTIME-complete for general formulas ⓘ
field	mathematical logic ⓘ theoretical computer science ⓘ
hasDecisionProcedure	automata-theoretic model checking ⓘ parity game solving ⓘ
hasFeature	ability to express recursive properties ⓘ alternation of least and greatest fixpoints ⓘ fixed-point quantification over predicates ⓘ modal operators for necessity and possibility ⓘ
hasOperator	greatest fixpoint operator ν ⓘ least fixpoint operator μ ⓘ
hasSyntaxBasedOn	boolean connectives ⓘ fixpoint operators ⓘ modalities ⓘ propositional variables ⓘ
hasVariant	alternation-free μ-calculus NERFINISHED ⓘ higher-order μ-calculus NERFINISHED ⓘ probabilistic μ-calculus ⓘ
introducedInField	modal logic ⓘ
moreExpressiveThan	CTL NERFINISHED ⓘ CTL* ⓘ LTL NERFINISHED ⓘ
relatedTo	automata theory ⓘ game semantics ⓘ parity automata ⓘ
semanticsGivenBy	Kripke structures NERFINISHED ⓘ transition systems ⓘ
semanticsUses	least and greatest fixed points ⓘ monotone operators on power sets ⓘ
subsumes	Computation Tree Logic NERFINISHED ⓘ Computation Tree Logic* ⓘ Linear Temporal Logic NERFINISHED ⓘ many standard temporal logics ⓘ
typicalApplicationDomain	verification of communication protocols ⓘ verification of concurrent systems ⓘ
usedFor	expressing properties of infinite-state systems ⓘ expressing properties of recursive programs ⓘ model checking ⓘ specification of properties of transition systems ⓘ verification of reactive systems ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Dexter Kozen → knownFor → mu-calculus ⓘ

Model Checking (book) → topic → mu-calculus ⓘ

subject surface form: Model Checking