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Expressiveness of the modal mu-calculus on monotone neighborhood structures
[article]

2015
*
arXiv
*
pre-print

We characterize

arXiv:1502.07889v1
fatcat:gafhmhfk4fef3hr73rvrzqgpv4
*the**expressive*power*of**the**modal**mu*-*calculus**on*monotone neighborhood structures, in*the*style*of**the*Janin-Walukiewicz theorem for*the*standard*modal**mu*-*calculus*. ... Our main result shows that*the*monotone*modal**mu*-*calculus*corresponds exactly to*the*fragment*of*this second-order language that is invariant for neighborhood bisimulations. ... In this paper, we characterize*the**expressive*power*of**the*µ-*calculus**on*monotone neighborhood structures precisely, by exhibiting it as*the*bisimulation invariant fragment*of*a suitable monadic second-order ...##
###
A Modal Fixpoint Logic with Chop
[chapter]

1999
*
Lecture Notes in Computer Science
*

Moreover, we establish

doi:10.1007/3-540-49116-3_48
fatcat:xpvoo6g7ynhdxg3ylrzixwmyo4
*the*following results: FLC is strictly more*expressive*than*the**modal**mu*-*calculus*; it is decidable for finite-state processes but undecidable for context-free processes; satisfiability ... We study a logic called FLC (Fixpoint Logic with Chop) that extends*the**modal**mu*-*calculus*by a chop-operator and termination formulae. ... It can be found in many papers*on**the**modal**mu*-*calculus*. ...##
###
The mu-calculus and Model Checking
[chapter]

2018
*
Handbook of Model Checking
*

*The*

*mu*-

*calculus*is

*one*

*of*

*the*most important logics in model-checking. It is a logic with an exceptional balance between

*expressiveness*and algorithmic properties. ... Then it develops

*the*notion

*of*

*modal*automaton: an automaton-based model behind

*the*

*mu*-

*calculus*. ... We also present two extensions

*of*

*the*

*mu*-

*calculus*that allow us to

*express*inverse

*modalities*, some form

*of*equality, or counting. ...

##
###
A Model Checker for Value-Passing Mu-Calculus Using Logic Programming
[chapter]

2001
*
Lecture Notes in Computer Science
*

In particular, we present valuepassing

doi:10.1007/3-540-45241-9_1
fatcat:2oelfds5o5agvcch5oeozwmzru
*modal**mu*-*calculus*, its formal semantics and describe a natural implementation*of*this semantics as a logic program. ... Thus far, XMC has supported value-passing process languages, but has been limited to using*the*propositional fragment*of**modal*mucalculus as*the*property specification logic. ... Propositional*Modal**Mu*-*calculus**The**modal**mu*-*calculus*[Koz83] is an*expressive*temporal logic whose semantics is usually described over sets*of*states*of*labeled transition systems (LTSs). ...##
###
Selective mu-calculus: New Modal Operators for Proving Properties on Reduced Transition Systems
[chapter]

1997
*
Formal Description Techniques and Protocol Specification, Testing and Verification
*

We prove that

doi:10.1007/978-0-387-35271-8_32
fatcat:g6qntnrszfdrtlpq4546ihh2l4
*the*selective*mu*-*calculus*is as powerful as*the**mu*-*calculus*. ... In this approach to verification, state explosion is*one**of**the*most serious problems. ... This new*calculus*has*the*same power*of**the*original*one*:*the**mu*-*calculus*can be*expressed*by means*of**the*selective*mu*-*calculus*, and viceversa. ...##
###
The modal mu-calculus alternation hierarchy is strict

1998
*
Theoretical Computer Science
*

*One*

*of*

*the*open questions about

*the*

*modal*

*mu*-

*calculus*is whether

*the*alternation hierarchy collapses; that is, whether all

*modal*fixpoint properties can be

*expressed*with only a few alternations

*of*least ... In this paper, we resolve this question by showing that

*the*hierarchy does not collapse. @ 1998 -Elsevier Science B.V. All rights reserved ... Introduction

*The*

*modal*

*mu*-

*calculus*, or Hennessy-Milner logic with fixpoints, is a popular logic for

*expressing*temporal properties

*of*systems. ...

##
###
The modal mu-calculus alternation hierarchy is strict
[chapter]

1996
*
Lecture Notes in Computer Science
*

*One*

*of*

*the*open questions about

*the*

*modal*

*mu*-

*calculus*is whether

*the*alternation hierarchy collapses; that is, whether all

*modal*fixpoint properties can be

*expressed*with only a few alternations

*of*least ... In this paper, we resolve this question by showing that

*the*hierarchy does not collapse. @ 1998 -Elsevier Science B.V. All rights reserved ... Introduction

*The*

*modal*

*mu*-

*calculus*, or Hennessy-Milner logic with fixpoints, is a popular logic for

*expressing*temporal properties

*of*systems. ...

##
###
Fixpoint alternation: arithmetic, transition systems, and the binary tree

1999
*
RAIRO - Theoretical Informatics and Applications
*

Examples

doi:10.1051/ita:1999122
fatcat:ylhvnxu4fnea3kdz6yutg5xwje
*of*properties*expressible*by*the**mu*-*calculus*are "always (*on*a-paths) P", as vZ. ... These examples are*of*just*the*form that*one*expects, if*one*is a*modal**mu*-*calculus*hacker. ...##
###
Quotient-based Control Synthesis for Non-Deterministic Plants with Mu-Calculus Specifications

2006
*
Proceedings of the 45th IEEE Conference on Decision and Control
*

We study

doi:10.1109/cdc.2006.376737
dblp:conf/cdc/0001006a
fatcat:q3b6r65kmfewtelbyjcmhkzp2y
*the*control*of*a nondeterministic discrete event system (DES) subject to a control specification*expressed*in*the*propositional*mu*-*calculus*, under complete observation*of*events. ... Thus*the*control problem is reduced to*one**of**mu*-*calculus*satisfiability. We also present a tableau-based satisfiability solving algorithm that identifies a model for*the*quotiented formula. ... An extension*of**mu*-*calculus*, called quantified*mu*-*calculus*, to*express**the*existence*of*a supervisor as part*of**the*specification logic was introduced. ...##
###
Compositional analysis for verification of parameterized systems

2006
*
Theoretical Computer Science
*

We present a widening operation to find such a limit for properties

doi:10.1016/j.tcs.2005.11.016
fatcat:mxueqair5jebxgim5eriulq7cq
*expressible*in a subset*of**modal**mu*-*calculus*. ...*The*technique views a parameterized system as an*expression*in a process algebra (CCS) and interprets this*expression*over a domain*of*formulas (*modal**mu*-*calculus*), considering a process as a property ... We also thank*the*anonymous reviewers for their valuable comments. This work is supported in part by NSF grants EIA-9705998, CCR-9876242, EIA-9805735, N000140110967, IIS-0072927, and CCF-0205376. ...##
###
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
*

Kozen's

doi:10.1145/268946.268950
dblp:conf/popl/Schmidt98
fatcat:2muvgfeo6bhvva6gnqkukobs7e
*modal**mu*-*calculus*to*express*trace properties, we*express*in simplest possible terms that a d&a. is a model check*of*a program's a.i. trace. ... In particular,*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 ... as*modal**mu*-*calculus*formulas [3, 35, 201. ...##
###
Compositional Analysis for Verification of Parameterized Systems
[chapter]

2003
*
Lecture Notes in Computer Science
*

We present a widening operation to find such a limit for properties

doi:10.1007/3-540-36577-x_23
fatcat:t2tacyzrmnb3jm67sv4jmxhq4q
*expressible*in a subset*of**modal**mu*-*calculus*. ...*The*technique views a parameterized system as an*expression*in a process algebra (CCS) and interprets this*expression*over a domain*of*formulas (*modal**mu*-*calculus*), considering a process as a property ... We also thank*the*anonymous reviewers for their valuable comments. This work is supported in part by NSF grants EIA-9705998, CCR-9876242, EIA-9805735, N000140110967, IIS-0072927, and CCF-0205376. ...##
###
Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree

1998
*
BRICS Report Series
*

We provide an elementary proof

doi:10.7146/brics.v5i53.19499
fatcat:t3btzhwmgvcsreaectbnk36a2q
*of**the*fixpoint alternation<br />hierarchy in arithmetic, which in turn allows us to simplify*the*proof*of**the**modal**mu*-*calculus*alternation hierarchy. ... We further show that*the*alternation hierarchy*on**the*binary tree is strict, resolving a problem*of*Niwinski. ... Introduction*The**modal**mu*-*calculus*, or Hennessy-Milner logic with fixpoints, is a popular logic for*expressing*temporal properties*of*systems. ...##
###
Objects, Types and Modal Logics

1996
*
BRICS Report Series
*

We<br />investigate

doi:10.7146/brics.v3i49.20051
fatcat:ysnjewqzenfmbj764v7qrepppi
*the*connection between*the*type system Ob_1<:*mu*and*the*<br />*mu*-*calculus*, providing a translation*of*types into*modal*formulae and<br />an ordering*on*formulae that is sound w.r.t. ... In this paper we present a*modal*logic for describing properties*of*<br />terms in*the*object*calculus**of*Abadi and Cardelli [AC96].*The*logic is<br />essentially*the**modal**mu*-*calculus**of*[Koz83]. ... ] can be*expressed*within*the**mu*-*calculus*). ...##
###
Recursive Checkonly QVT-R Transformations with General when and where Clauses via the Modal Mu Calculus
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we show how to interpret checkonly QVT-R -or any future model transformation language structured similarly -in

doi:10.1007/978-3-642-28872-2_14
fatcat:xt7ud4mzd5bnfcgdvn6kih5lra
*the**modal**mu**calculus*and use its well-understood model-checking game to lift ... We demonstrate and justify a corresponding extension to*the*rules*of**the*QVT-R game. ...*The*first author is partly supported by UK EPSRC grant EP/G012962/1 'Solving Parity Games and*Mu*-Calculi'. ...
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