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The mu-calculus and Model Checking
[chapter]

2018
*
Handbook of Model Checking
*

*The*chapter describes in length

*the*game characterization of

*the*

*semantics*of

*the*

*mu*-

*calculus*. ... Then it develops

*the*notion of modal automaton:

*an*automaton-based model behind

*the*

*mu*-

*calculus*. ... Let us remark that

*the*Church synthesis problem [33, 117]

*for*

*the*

*mu*-

*calculus*formulas is

*an*instance of

*the*above

*for*a particular choice of M. ...

##
###
Data flow analysis is model checking of abstract interpretations

1998
*
Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '98
*

In particular,

doi:10.1145/268946.268950
dblp:conf/popl/Schmidt98
fatcat:2muvgfeo6bhvva6gnqkukobs7e
*the*classic %ow equations*for*bit-vector-based d-Jo. s reformat trivially into modal*mu*-Cal&us formulas., A surprising consequence is that two of*the*classical d&a. s are exposed as unsound ... In*the*process of making*the*above discoveries, we cIarify*the*relationship between a. i. and d-&a. in terms of*the*often-misunderstood notion of collecting*semantics*and we highlight how*the*research ... design space and*the*modal*mu*-*calculus*defines*the*design space*for*iterative static analyses. ...##
###
Page 1665 of Mathematical Reviews Vol. , Issue 91C
[page]

1991
*
Mathematical Reviews
*

{

*For**the*entire collection see MR 90i:68005.} 91c:68092 68Q60 03B25 03B70 Streett, Robert S.; Emerson, E. Allen (1-TX-C)*An*automata theoretic decision procedure*for**the**propositional**mu*-*calculus*. ... Summary: “*The**propositional**mu*-*calculus*is a*propositional*logic of programs which incorporates a least fixpoint operator and sub- sumes*the**propositional*dynamic logic of Fischer and Ladner,*the*infinite ...##
###
Efficient Patterns for Model Checking Partial State Spaces in CTL ∩ LTL

2006
*
Electronical Notes in Theoretical Computer Science
*

Hence we can compute, with linear blowup only, a

doi:10.1016/j.entcs.2006.04.004
fatcat:2nzj76v4e5canm2d5t2n3w7dfm
*semantic*minimization in*the*same temporal logic whose efficient check renders*the*precise result*for**the*original imprecise pattern. ... In this paper we determine*for*which popular specification patterns, documented at a community-led pattern repository, this under-*approximation*is precise in that*the*converse relationship holds as well ... Acknowledgments We acknowledge*the*kind support of this work by*the*UK Engineering and Physical Sciences Research Council under grant EP/D50595X/1. ...##
###
Page 7307 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
*
Mathematical Reviews
*

Kozen proposed

*an*elegant axiom system*for**the**propositional*~-*calculus*,*the*aim of*the*present paper is to show that this axiomatization is complete. ...*The**propositional*u-*calculus*is*an*extension of*the*modal system K with a least fixed point operator; it has proved to be*an*interesting logic because it subsumes most*propositional*temporal logics and ...##
###
Page 7662 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

It is well known that

*the*category of sets is not able to provide a complete standard*semantics**for*lambda-*calculus*. ... Summary: “We consider*the*minimal unsatisfiability problem*MU*(k)*for**propositional*formulas in conjunctive normal form over n variables and with n +k clauses, where k is fixed. k is called*the*difference ...##
###
Partial-order reduction in the weak modal mu-calculus
[chapter]

1997
*
Lecture Notes in Computer Science
*

We present a partial-order reduction technique

doi:10.1007/3-540-63141-0_2
fatcat:l4mwx6qrkvh2veqtvq5onuxqty
*for*local model checking of hierarchical networks of labeled transition systems in*the*weak modal*mu*-*calculus*. ... in modal*mu*-*calculus*model checking. ... We thank Xinxin Liu*for*valuable comments on this work, and Gerard Holzmann and Doron Peled*for*providing us with*the*SPIN benchmarks, and*for*making available GKPP97]. ...##
###
Symbolic model checking
[chapter]

1996
*
Lecture Notes in Computer Science
*

We describe

doi:10.1007/3-540-61474-5_93
fatcat:luz3iefbijeepg2q5cmhflefee
*the*syntax and*semantics*of a dialect of*the**Mu*-*Calculus*, and present a model checking algorithm*for**Mu*-*Calculus*formulas that uses BDDs to represent relations and formulas. ...*For**Mu*-*Calculus*formulas derived from CTL formulas, it is convenient to encode each state in*the*domain with*the*set of atomic*propositions*that are true*for*that state. ...##
###
Symbolic model checking: 1020 States and beyond

1992
*
Information and Computation
*

We describe

doi:10.1016/0890-5401(92)90017-a
fatcat:dtdxdp4uurhxrhmt3zrgbqjsbm
*the*syntax and*semantics*of a dialect of*the**Mu*-*Calculus*, and present a model checking algorithm*for**Mu*-*Calculus*formulas that uses BDDs to represent relations and formulas. ...*For**Mu*-*Calculus*formulas derived from CTL formulas, it is convenient to encode each state in*the*domain with*the*set of atomic*propositions*that are true*for*that state. ...##
###
Faster model checking for the modal Mu-Calculus
[chapter]

1993
*
Lecture Notes in Computer Science
*

Syntax and

doi:10.1007/3-540-56496-9_32
fatcat:4rrsehc4zfgyrc7zxsagv5xy34
*Semantics*of*the**Mu*-*Calculus*This section first provides a brief overview of labeled transition 8ystents, which are used as models*for**the**mu*-calcnlus. ... In thla paper, we develop*an*algorithm*for*model checking that handlu*the*full modal mucalculus including alternating fixpoints. ... Syntax and*Semantics*of Formulas*The*syntax of*the*modal*mu*-*calculus*is parameterized with respect to a (countable) set Vat of variables, a set .4 of atomic*propositions*, and a set Act of actions. ...##
###
Symmetry Reduction for the Local Mu-Calculus
[chapter]

2018
*
Lecture Notes in Computer Science
*

Considerably generalizing earlier results on invariance, it is shown that all local

doi:10.1007/978-3-319-89963-3_22
fatcat:xhuau3tcpjayxnvq273r7jngxi
*mu*-*calculus*properties, including safety and liveness properties, are preserved by neighborhood symmetries. ... This defines*an*interleaving*semantics*, with unchanged(W ) denoting that*the*values of variables in W are unchanged. A global state is a function mapping variables in V to values in their domain. ... Allen Emerson*for*inspiring discussions on*the*topic. ...##
###
Symmetry Reduction for the Local Mu-Calculus
[article]

2019
*
arXiv
*
pre-print

Considerably generalizing earlier results on invariance, it is shown that all local

arXiv:1903.10405v1
fatcat:wrwngfzwvrem3lcuiiiqgsttty
*mu*-*calculus*properties, including safety and liveness properties, are preserved by neighborhood symmetries. ... In general, local verification*approximates*verification over*the*global state space; however, if process interactions are outward-facing,*the*relationship is shown to be exact. ... Allen Emerson*for*inspiring discussions on*the*topic. ...##
###
Comparing CTL and PCTL on Labeled Markov Chains
[chapter]

1998
*
Programming Concepts and Methods PROCOMET '98
*

We interpret modal

doi:10.1007/978-0-387-35358-6_18
fatcat:acdkyetax5h2lmwtjg3wtpqcdy
*mu*-*calculus*formulas in a non-standard way as expectations over labeled Markov chains. In this*semantics*fixed-points are computed in*an*iterative incremental/ decremental fashion. ... Finally, we show soundness of our non-standard*semantics*of CTL + with respect to*the*one*for*PCTL in*the*following sense: if our*semantics*computes a positive evidence*for*¢ at state s then s satisfies ... ACKNOWLEDGMENTS We would like to thank all*the*anonymous referees*for*their constructive criticism. ...##
###
Constraint-Based Abstract Semantics for Temporal Logic: A Direct Approach to Design and Implementation
[chapter]

2010
*
Lecture Notes in Computer Science
*

Using

doi:10.1007/978-3-642-17511-4_3
fatcat:fqim7etzrnaf7gbljd2x7quobe
*the*modal µ-*calculus*to implement CTL,*the*abstract*semantics*gives*an*over-*approximation*of*the*set of states in which*an*arbitrary CTL formula holds. ... We apply*the*framework of abstract interpretation to derive*an*abstract*semantic*function*for**the*modal µ-*calculus*, which is*the*basis*for*abstract model checking. ... We gratefully acknowledge discussions with Dennis Dams, César Sánchez, Kim Guldstrand Larsen and suggestions by*the*LPAR-16 referees. ...##
###
On independence-friendly fixpoint logics

2004
*
Philosophia Scientiæ
*

We relate it to parity games of imperfect information, and show its application to defining independence-friendly modal

doi:10.4000/philosophiascientiae.568
fatcat:vuezjblzpbcadbu6ktxxiq75l4
*mu*-calculi. ... Nous la relions aux jeux de paritéà information imparfaite, et nous montrons une applicationà la définition d'un*mu*-calcul modal fait pour l'indépendance. ... [Kozen 1983 ] modal*mu*-*calculus*, a popular and interesting temporal logic -see [Bradfield & Stirling 2001]*for**an*introductory survey of modal*mu*-*calculus*. ...
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