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Temporal Logics Beyond Regularity

Martin Lange
2007 BRICS Report Series  
In particular, it features Propositional Dynamic Logic of Context-Free Programs, Fixpoint Logic with Chop, the Modal Iteration Calculus, and Higher-Order Fixpoint Logic.  ...  This thesis surveys results about the relative expressive power and complexity of temporal logics which are capable of defining non-regular properties.  ...  Non-Regular PDL The Modal Iteration Calculus Fixpoint Logic with Chop Higher-Order Fixpoint Logic The Complexity of FLC Müller-Olm '99 SAT for FLC is undecidable Model Checking is decidable  ... 
doi:10.7146/brics.v14i13.22178 fatcat:s4wi6d5ewffnrpew3leughbmhm

Separating the Expressive Power of Propositional Dynamic and Modal Fixpoint Logics

Eric Alsmann, Florian Bruse, Martin Lange
2021 Electronic Proceedings in Theoretical Computer Science  
This is inspired by the recent discovery of a decidable program logic called Visibly Pushdown Fixpoint Logic with Chop which extends both the modal mu-calculus and PDL over visibly pushdown languages,  ...  We complete the picture by providing results separating all the PDL-based and modal fixpoint logics with regular, visibly pushdown and arbitrary context-free constructions.  ...  Non-Regular Program Logics.  ... 
doi:10.4204/eptcs.339.4 fatcat:abc7e7bc3zdjxoosdpp7idw6sm

A Modal Fixpoint Logic with Chop [chapter]

Markus Müller-Olm
1999 Lecture Notes in Computer Science  
We study a logic called FLC (Fixpoint Logic with Chop) that extends the modal mu-calculus by a chop-operator and termination formulae.  ...  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  ...  In this paper we present a logic called FLC (Fixpoint Logic with Chop) that extends the modal mu-calculus [8] , a popular point-based branching-time fixpoint logic, by a chop operator ; and termination  ... 
doi:10.1007/3-540-49116-3_48 fatcat:xpvoo6g7ynhdxg3ylrzixwmyo4

Counting in Trees for Free [chapter]

Helmut Seidl, Thomas Schwentick, Anca Muscholl, Peter Habermehl
2004 Lecture Notes in Computer Science  
We show here that a decidable logic is obtained if we use a modal fixpoint logic instead.  ...  The non-emptiness for Presburger tree automata (PTA) is PSPACEcomplete, which is moderate given that it is already PSPACE-hard to test whether the complement of a regular expression is non-empty.  ...  It remains a challenging engineering problem to obtain an implementation of the new logic which behaves well on practical examples.  ... 
doi:10.1007/978-3-540-27836-8_94 fatcat:xa5ds54akbad5h6ex2mtmqm5x4

Temporal Logic with Recursion

Florian Bruse, Martin Lange, Martin Theobald, Ana Ozaki, Emilio Muñoz-Velasco
2020 International Symposium/Workshop on Temporal Representation and Reasoning  
We advocate these logics by showing how the recursion operator can be used to express interesting non-regular properties.  ...  Unlike other proposals for modal fixpoint logics of high expressive power, we obtain logics that retain some of the appealing pragmatic advantages of CTL and LTL, yet have expressive power beyond that  ...  Higher-Order Fixpoint Logic (HFL): it allows functions of arbitrary higher-order to be built from modal and Boolean operators as well as fixpoints.  ... 
doi:10.4230/lipics.time.2020.6 dblp:conf/time/BruseL20 fatcat:3h7kiqtownhy7mjkzbaw2ri7yu

Symbolic Model Checking of Non-regular Properties [chapter]

Martin Lange
2004 Lecture Notes in Computer Science  
This paper presents a symbolic model checking algorithm for Fixpoint Logic with Chop, an extension of the modal µ-calculus capable of defining non-regular properties.  ...  Some empirical data about running times of a naive implementation of this algorithm are given as well.  ...  The standard example of a non-regular and even non-context-free property is the following, taken from [MO99] .  ... 
doi:10.1007/978-3-540-27813-9_7 fatcat:gizk33jb3jghdndfjrebkx25iu

A Tree Logic with Graded Paths and Nominals [article]

Everardo Barcenas (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), Pierre Geneves (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), Nabil Layaida (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), Alan Schmitt (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble)
2010 arXiv   pre-print
While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential  ...  The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes.  ...  Conclusion We introduced a modal logic of trees equipped with (1) converse modalities, which allow to succinctly express forward and backward navigation, (2) a least fixpoint operator for recursion, and  ... 
arXiv:1005.5623v1 fatcat:cttrbs66fjcddjnuurq257cv74

A Solver for Modal Fixpoint Logics

Oliver Friedmann, Martin Lange
2010 Electronical Notes in Theoretical Computer Science  
We present MLSolver, a tool for solving the satisfiability and validity problems for modal fixpoint logics.  ...  MLSolver is designed to allow easy extensions in the form of further modal fixpoint logics.  ...  Extending MLSolver with another modal fixpoint logic is relatively easy.  ... 
doi:10.1016/j.entcs.2010.04.008 fatcat:lkcg5djjnzc3rjf6xdp4t3tfli

Local Model Checking in a Logic for True Concurrency [chapter]

Paolo Baldan, Tommaso Padoan
2017 Lecture Notes in Computer Science  
Focusing on the alternation free fragment of the logic, along the lines of some classical work for the modal mu-calculus, we propose a local model-checking algorithm.  ...  of model-checking non-trivial.  ...  The paper [15] shows that first order logic and a restricted form of monadic second order (MSO) logic are decidable on regular trace event structures.  ... 
doi:10.1007/978-3-662-54458-7_24 fatcat:3wf3mlxqmrewxjp5wk6dpw4mjy

Modal Mu-Calculus [chapter]

Colin Stirling
2001 Texts in Computer Science  
Notation: Lµ means the modal mu-calculus, considered as a logical language (not as a theory).  ...  Modal logics in program verification The application of modal and temporal logics to programs is part of a line of program verification going back to the 1960s and program schemes and Floyd-Hoare logic  ...  It does not have the finite model property, and it can express non-regular properties.  ... 
doi:10.1007/978-1-4757-3550-5_5 fatcat:mfjlygtmd5e6lbmjdhr73oaisa

On the Count of Trees [article]

Everardo Barcenas (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), Pierre Geneves (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), Nabil Layaida (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), Alan Schmitt (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble)
2010 arXiv   pre-print
While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a decidable tree logic whose main features  ...  Our logic being closed under negation, it may be used to decide typical problems on XPath queries such as satisfiability, type checking with relation to regular types, containment, or equivalence.  ...  Counting over graphs The µ-calculus is a propositional modal logic augmented with least and greatest fixpoint operators [18] .  ... 
arXiv:1008.5073v1 fatcat:v3xydzgacnfbvgpkl5egg676sm

Propositional dynamic logic of context-free programs and fixpoint logic with chop

Martin Lange, Rafał Somla
2006 Information Processing Letters  
This paper compares Propositional Dynamic Logic of Non-Regular Programs and Fixpoint Logic with Chop. It identifies a fragment of the latter which is equiexpressive to the former.  ...  This relationship transfers several decidability and complexity results between the two logics.  ...  Hence, the equivalence result above reveals a non-trivial fragment of (alternation-free) FLC for which model checking is tractable.  ... 
doi:10.1016/j.ipl.2006.04.019 fatcat:traz7owl3vc67o37qhdmdva35e

Logics and Games for True Concurrency [article]

Julian Gutierrez
2010 arXiv   pre-print
Since these mu-calculi and logic games generalise well-known fixpoint logics and game-theoretic decision procedures for concurrent systems with interleaving semantics, the results herein give some of the  ...  groundwork for the design of a logic-based, game-theoretic framework for studying, in a uniform way, several concurrent systems regardless of whether they have an interleaving or a partial order semantics  ...  Fixpoint logics or mu-calculi [8] are logics that make use of fixpoint operators; in particular, the modal mu-calculus is a simple extension of modal logic with fixpoint operators.  ... 
arXiv:1011.1172v1 fatcat:jmahyvyacffzheloesvuwy25xq

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  ...  The games underpin a novel decision procedure for model-checking all temporal properties of a class of infinite and regular event structures, thus improving, in terms of temporal expressive power, previous  ...  The first author was financially supported by an Overseas Research Studentship (ORS) award and a School of Informatics Ph.D. studentship at The University of Edinburgh.  ... 
doi:10.1016/j.ic.2010.12.002 fatcat:6ohjhbv23jds7m6jeuulgl2qre

Coalgebraic semantics of modal logics: An overview

Clemens Kupke, Dirk Pattinson
2011 Theoretical Computer Science  
Coalgebras can be seen as a natural abstraction of Kripke frames. In the same sense, coalgebraic logics are generalised modal logics.  ...  , expressiveness and complexity in these settings, both for basic languages as well as a number of extensions, such as hybrid languages and fixpoints.  ...  for various fixpoint logics, such as fixpoint extensions of coalition logic, monotone modal logic, graded modal logic and -of course -the modal µ-calculus.  ... 
doi:10.1016/j.tcs.2011.04.023 fatcat:ffi53okdkzeqtbyqt5phjdrfaa
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