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Model-checking games for fixpoint logics with partial order models

Julian Gutierrez, Julian Bradfield
2011 Information and Computation  
While in the interleaving case they coincide 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 [  ... 
doi:10.1016/j.ic.2010.12.002 fatcat:6ohjhbv23jds7m6jeuulgl2qre

Model-Checking Games for Fixpoint Logics with Partial Order Models [chapter]

Julian Gutierrez, Julian Bradfield
2009 Lecture Notes in Computer Science  
While in the interleaving case they coincide 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)  ... 
doi:10.1007/978-3-642-04081-8_24 fatcat:ks3nzubf3jbxla34m55tglxjgy

Logics and Games for True Concurrency [article]

Julian Gutierrez
2010 arXiv   pre-print
Such dualities are used to define new mu-calculi and 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.  ... 
arXiv:1011.1172v1 fatcat:jmahyvyacffzheloesvuwy25xq

Three notes on the complexity of model checking fixpoint logic with chop

Martin Lange
2007 RAIRO - Theoretical Informatics and Applications  
This paper analyses the complexity of 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.  ... 
doi:10.1051/ita:2007011 fatcat:qj7kuj4r6rcslbp6yoewgk5huq

Quasipolynomial Computation of Nested Fixpoints [chapter]

Daniel Hausmann, Lutz Schröder
2021 Lecture Notes in Computer Science  
that 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] .  ... 
doi:10.1007/978-3-030-72016-2_3 fatcat:up2kucajgbdj5nkkrrkxwq5sqa

The Complexity of Independence-Friendly Fixpoint Logic [chapter]

Julian Bradfield, Stephan Kreutzer
2005 Lecture Notes in Computer Science  
We study the complexity of 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  ... 
doi:10.1007/11538363_25 fatcat:n7ezlxjlknhbznyeqytnhlkw6m

A Measured Collapse of the Modal μ-Calculus Alternation Hierarchy [chapter]

Doron Bustan, Orna Kupferman, Moshe Y. Vardi
2004 Lecture Notes in Computer Science  
The -calculus can be viewed as a fragment of first-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.  ... 
doi:10.1007/978-3-540-24749-4_46 fatcat:rowfrzniqrfozgqwcqbnmtuu4u

Quasipolynomial Computation of Nested Fixpoints [article]

Daniel Hausmann, Lutz Schröder
2020 arXiv   pre-print
via nested 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.  ... 
arXiv:1907.07020v4 fatcat:k6rhwkj3pbdndp5dffscpaisdu

Decomposition theorems and model-checking for the modalμ-calculus

Mikolaj Bojanczyk, Christoph Dittmann, Stephan Kreutzer
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 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.  ... 
doi:10.1145/2603088.2603144 dblp:conf/csl/BojanczykDK14 fatcat:vfhrvywtezbvjis7i3mglnqzfq

Game-Based Local Model Checking for the Coalgebraic mu-Calculus

Daniel Hausmann, Lutz Schröder, Michael Wagner
2019 International Conference on Concurrency Theory  
The coalgebraic µ-calculus is a generic framework 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.  ... 
doi:10.4230/lipics.concur.2019.35 dblp:conf/concur/HausmannS19 fatcat:2b4524tktjchhkr3v2aybi6qq4

NP Reasoning in the Monotone $$\mu $$-Calculus [chapter]

Daniel Hausmann, Lutz Schröder
2020 Lecture Notes in Computer Science  
Satisfiability 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.  ... 
doi:10.1007/978-3-030-51074-9_28 fatcat:sb3lc777s5ba5onnylztv4esne

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]

Julian Gutierrez
2011 Lecture Notes in Computer Science  
Most 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  ... 
doi:10.1007/978-3-642-20920-8_17 fatcat:us3zq2unn5gazgnqdsackfl4ya

THE MODAL µ-CALCULUS: A SURVEY

GIACOMO LENZI
2005 TASK Quarterly  
The modal µ-calculus is an extension of modal 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.  ... 
doaj:3c3858f737b04247b9bda1a46646b7c7 fatcat:gnx6n4z5srg4tb354bp6ngn2ya

On independence-friendly fixpoint logics

J. C. Bradfield
2004 Philosophia Scientiæ  
Abstract: We introduce a 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  ... 
doi:10.4000/philosophiascientiae.568 fatcat:vuezjblzpbcadbu6ktxxiq75l4
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