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

Sebastian Enqvist, Fatemeh Seifan, Yde Venema
2015 arXiv   pre-print
We characterize 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  ... 
arXiv:1502.07889v1 fatcat:gafhmhfk4fef3hr73rvrzqgpv4

A Modal Fixpoint Logic with Chop [chapter]

Markus Müller-Olm
1999 Lecture Notes in Computer Science  
Moreover, we establish 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.  ... 
doi:10.1007/3-540-49116-3_48 fatcat:xpvoo6g7ynhdxg3ylrzixwmyo4

The mu-calculus and Model Checking [chapter]

Julian Bradfield, Igor Walukiewicz
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.  ... 
doi:10.1007/978-3-319-10575-8_26 fatcat:7adhegoggvcjthaa5x5uhfpt24

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

C. R. Ramakrishnan
2001 Lecture Notes in Computer Science  
In particular, we present valuepassing 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).  ... 
doi:10.1007/3-540-45241-9_1 fatcat:2oelfds5o5agvcch5oeozwmzru

Selective mu-calculus: New Modal Operators for Proving Properties on Reduced Transition Systems [chapter]

Roberto Barbuti, Nicoletta Francesco, Antonella Santone, Gigliola Vaglini
1997 Formal Description Techniques and Protocol Specification, Testing and Verification  
We prove that 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.  ... 
doi:10.1007/978-0-387-35271-8_32 fatcat:g6qntnrszfdrtlpq4546ihh2l4

The modal mu-calculus alternation hierarchy is strict

J.C. Bradfield
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.  ... 
doi:10.1016/s0304-3975(97)00217-x fatcat:5s5cbfkq3ncdngny4qtoyqcl3e

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

J. C. Bradfield
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.  ... 
doi:10.1007/3-540-61604-7_58 fatcat:rqvgzyzj3neo7f7rpt465s5iga

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

J. C. Bradfield
1999 RAIRO - Theoretical Informatics and Applications  
Examples 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.  ... 
doi:10.1051/ita:1999122 fatcat:ylhvnxu4fnea3kdz6yutg5xwje

Quotient-based Control Synthesis for Non-Deterministic Plants with Mu-Calculus Specifications

Samik Basu, Ratnesh Kumar
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
We study 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.  ... 
doi:10.1109/cdc.2006.376737 dblp:conf/cdc/0001006a fatcat:q3b6r65kmfewtelbyjcmhkzp2y

Compositional analysis for verification of parameterized systems

Samik Basu, C.R. Ramakrishnan
2006 Theoretical Computer Science  
We present a widening operation to find such a limit for properties 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.  ... 
doi:10.1016/j.tcs.2005.11.016 fatcat:mxueqair5jebxgim5eriulq7cq

Data flow analysis is model checking of abstract interpretations

David A. Schmidt
1998 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '98  
Kozen's 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.  ... 
doi:10.1145/268946.268950 dblp:conf/popl/Schmidt98 fatcat:2muvgfeo6bhvva6gnqkukobs7e

Compositional Analysis for Verification of Parameterized Systems [chapter]

Samik Basu, C. R. Ramakrishnan
2003 Lecture Notes in Computer Science  
We present a widening operation to find such a limit for properties 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.  ... 
doi:10.1007/3-540-36577-x_23 fatcat:t2tacyzrmnb3jm67sv4jmxhq4q

Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree

Julian C. Bradfield
1998 BRICS Report Series  
We provide an elementary proof 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.  ... 
doi:10.7146/brics.v5i53.19499 fatcat:t3btzhwmgvcsreaectbnk36a2q

Objects, Types and Modal Logics

Dan S. Andersen, Lars H. Pedersen, Hans Hüttel, Josva Kleist
1996 BRICS Report Series  
We<br />investigate 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).  ... 
doi:10.7146/brics.v3i49.20051 fatcat:ysnjewqzenfmbj764v7qrepppi

Recursive Checkonly QVT-R Transformations with General when and where Clauses via the Modal Mu Calculus [chapter]

Julian Bradfield, Perdita Stevens
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 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'.  ... 
doi:10.1007/978-3-642-28872-2_14 fatcat:xt7ud4mzd5bnfcgdvn6kih5lra
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