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Model-checking games for fixpoint logics with partial order models

2011
*
Information and Computation
*

While in the interleaving case they coincide

doi:10.1016/j.ic.2010.12.002
fatcat:6ohjhbv23jds7m6jeuulgl2qre
*with*the local*model*-*checking**games**for*the μ-calculus, in a*partial**order*setting they verify properties of a number of*fixpoint*modal*logics*that can specify ... In this paper, we introduce*model*-*checking**games*that allow local second-*order*power on sets of independent transitions in the underlying*partial**order**models*where the*games*are played. ... Acknowledgments The author thank the reviewers of the Information and Computation journal and of CONCUR 2009*for*their comments, respectively, on this article and on a preliminary conference version [ ...##
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Model-Checking Games for Fixpoint Logics with Partial Order Models
[chapter]

2009
*
Lecture Notes in Computer Science
*

While in the interleaving case they coincide

doi:10.1007/978-3-642-04081-8_24
fatcat:ks3nzubf3jbxla34m55tglxjgy
*with*the local*model*-*checking**games**for*the µ-calculus, Lµ, in a noninterleaving setting they verify properties of Separation*Fixpoint**Logic*(SFL), a*logic*... We introduce*model*-*checking**games*that allow local secondorder power on sets of independent transitions in the underlying*partial**order**models*where the*games*are played. ... We, therefore, abandon the traditional approach to defining*model*-*checking**games**for**logics**with**partial**order**models*and introduce a new class of*games*called 'trace local monadic second-*order*(LMSO) ...##
###
Logics and Games for True Concurrency
[article]

2010
*
arXiv
*
pre-print

Such dualities are used to define new mu-calculi and

arXiv:1011.1172v1
fatcat:jmahyvyacffzheloesvuwy25xq
*logic**games**for*the analysis of concurrent systems*with**partial**order*semantics. ... ; and the definition of (infinite) higher-*order**logic**games**for*bisimulation and*model*-*checking*, where the players of the*games*are given (local) monadic second-*order*power on the sets of elements they ... In particular, using a*game*-theoretic approach, we study*fixpoint*modal*logics**with**partial**order**models*as well as their associated bisimulation and*model*-*checking*problems. ...##
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Three notes on the complexity of model checking fixpoint logic with chop

2007
*
RAIRO - Theoretical Informatics and Applications
*

This paper analyses the complexity of

doi:10.1051/ita:2007011
fatcat:qj7kuj4r6rcslbp6yoewgk5huq
*model**checking**Fixpoint**Logic**with*Chop -an extension of the modal µ-calculus*with*a sequential composition operator. ... It uses two known*game*-based characterisations to derive the following results: the combined*model**checking*complexity as well as the data complexity of FLC are EXPTIMEcomplete. ... We are also very grateful to Marcin Jurdziński*for*discussing FLC's*model**checking*problem -in particular asking*for*the data and expression complexity. ...##
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Quasipolynomial Computation of Nested Fixpoints
[chapter]

2021
*
Lecture Notes in Computer Science
*

that

doi:10.1007/978-3-030-72016-2_3
fatcat:up2kucajgbdj5nkkrrkxwq5sqa
*model**checking**for*these $$\mu $$ μ -calculi is in $$\textsc {QP}$$ QP . ...*For*instance, the*model**checking*problems*for*the energy $$\mu $$ μ -calculus, finite latticed $$\mu $$ μ -calculi, and the graded and the (two-valued) probabilistic $$\mu $$ μ -calculus –*with*numbers ...*games*and*model**checking**for*the energy μ-calculus [2, 10] , and*model**checking*and satisfiability*checking**for*the coalgebraic μ-calculus [12] . ...##
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The Complexity of Independence-Friendly Fixpoint Logic
[chapter]

2005
*
Lecture Notes in Computer Science
*

We study the complexity of

doi:10.1007/11538363_25
fatcat:n7ezlxjlknhbznyeqytnhlkw6m
*model*-*checking**for*the*fixpoint*extension of Hintikka and Sandu's independence-friendly*logic*. ... We show that this*logic*captures ExpTime; and by embedding PFP, we show that its combined complexity is ExpSpace-hard, and moreover the*logic*includes second*order**logic*(on finite structures). ... Acknowledgements Part of this work was done while the second author was a postdoctoral fellow in Edinburgh supported by the EU Research and Training Network*GAMES*(*Games*and Automata*for*Synthesis and ...##
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A Measured Collapse of the Modal μ-Calculus Alternation Hierarchy
[chapter]

2004
*
Lecture Notes in Computer Science
*

The -calculus can be viewed as a fragment of first-

doi:10.1007/978-3-540-24749-4_46
fatcat:rowfrzniqrfozgqwcqbnmtuu4u
*order**fixpoint**logic*. ... The complexity of a naive algorithm*for**model**checking*a -calculus formula is exponential in the alternation depth of . ...*logic*", which is the extension of first-*order**logic**with*least and greatest*fixpoint*operators. ...##
###
Quasipolynomial Computation of Nested Fixpoints
[article]

2020
*
arXiv
*
pre-print

via nested

arXiv:1907.07020v4
fatcat:k6rhwkj3pbdndp5dffscpaisdu
*fixpoints*of functions that differ substantially from the function*for*parity*games*but still can be computed in quasipolynomial time; our result hence implies that*model**checking**for*these ...*For*instance, the*model**checking*problems*for*the energy μ-calculus, finite latticed μ-calculi, and the graded and the (two-valued) probabilistic μ-calculus –*with*numbers coded in binary – can be solved ...*checking**for*the*model*µ-calculus reduces to solving*fixpoint*equation systems. ...##
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Decomposition theorems and model-checking for the modalμ-calculus

2014
*
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14
*

As far as we are aware, these are the first fpt results

doi:10.1145/2603088.2603144
dblp:conf/csl/BojanczykDK14
fatcat:vfhrvywtezbvjis7i3mglnqzfq
*for*L_μ which do not follow from embedding into monadic second-*order**logic*. ... As a consequence we show that the*model*-*checking*problem*for*L_μ is fixed-parameter tractable (fpt) on classes of structures of bounded Kelly-width or bounded DAG-width. ... of Lµ*model*-*checking*are based on parity*games*. ...##
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Game-Based Local Model Checking for the Coalgebraic mu-Calculus

2019
*
International Conference on Concurrency Theory
*

The coalgebraic µ-calculus is a generic framework

doi:10.4230/lipics.concur.2019.35
dblp:conf/concur/HausmannS19
fatcat:2b4524tktjchhkr3v2aybi6qq4
*for**fixpoint**logics**with*varying branching types that subsumes, besides the standard relational µ-calculus, such diverse*logics*as the graded µ-calculus ... In the present work, we give a local*model**checking*algorithm*for*the coalgebraic µ-calculus using a coalgebraic variant of parity*games*that runs, under mild assumptions on the complexity of the so-called ... [9] provide an automata-based*model**checking*procedure*for*quantitative linear time*logics*over systems*with*weights in a*partial*commutative semiring, using coalgebraic methods. ...##
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NP Reasoning in the Monotone $$\mu $$-Calculus
[chapter]

2020
*
Lecture Notes in Computer Science
*

Satisfiability

doi:10.1007/978-3-030-51074-9_28
fatcat:sb3lc777s5ba5onnylztv4esne
*checking**for*monotone modal*logic*is known to be (only) NP-complete. ... We show that this remains true when the*logic*is extended*with*alternation-free*fixpoint*operators as well as the universal modality; the resulting*logic*-the alternation-free monotone μ-calculus*with*...*For*many next-step modal*logics*(i.e. modal*logics*without*fixpoint*operators), satisfiability*checking*becomes harder under global assumptions. ...##
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Page 1161 of Mathematical Reviews Vol. , Issue 98B
[page]

1998
*
Mathematical Reviews
*

The transformation follows the style of the algorithm

*for*CTL*model**checking*.” ... First a system combining intersection types*with*higher-*order*subtyping is introduced. The soundness of this system is proved by constructing a semantic*model*based on*partial*equivalence relations. ...##
###
Concurrent Logic Games on Partial Orders
[chapter]

2011
*
Lecture Notes in Computer Science
*

Most

doi:10.1007/978-3-642-20920-8_17
fatcat:us3zq2unn5gazgnqdsackfl4ya
*games**for*analysing concurrent systems are played on interleaving*models*, such as graphs or infinite trees. ... systems*with**partial**order*semantics, such as Petri nets or event structures. ... The main idea is that by enriching a*logic**game**with*the explicit information about local and independent behaviour that comes*with*any*partial**order**model*, the traditional, sequential setting*for**logic*...##
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THE MODAL µ-CALCULUS: A SURVEY

2005
*
TASK Quarterly
*

The modal µ-calculus is an extension of modal

doaj:3c3858f737b04247b9bda1a46646b7c7
fatcat:gnx6n4z5srg4tb354bp6ngn2ya
*logic**with*two operators µ and ν, which give the least and greatest*fixpoints*of monotone operators on powersets. ... This powerful*logic*is widely used in computer science, in the area of verification of correctness of concurrent systems. ... Monadic*logic*Recall that monadic second*order**logic*is first*order**logic*plus quantifiers on sets. ...##
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On independence-friendly fixpoint logics

2004
*
Philosophia Scientiæ
*

Abstract: We introduce a

doi:10.4000/philosophiascientiae.568
fatcat:vuezjblzpbcadbu6ktxxiq75l4
*fixpoint*extension of Hintikka and Sandu's IF (independence-friendly)*logic*. We obtain some results on its complexity and expressive power. ... We relate it to parity*games*of imperfect information, and show its application to defining independence-friendly modal mu-calculi. ... The*model*-*checking**game**for*FOL extends to a*model*-*checking**game**for*LFP by assigning even ranks to maximal*fixpoints*and odd to minimal, such that the rank of an inner*fixpoint*is less than the rank of ...
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