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Model-checking Counting Temporal Logics on Flat Structures [article]

Normann Decker, Peter Habermehl, Martin Leucker, Arnaud Sangnier, and Daniel Thoma
2017 arXiv   pre-print
For most of these extensions, the model-checking problem is undecidable, but we show that decidability can be recovered by considering flat Kripke structures where each state belongs to at most one simple  ...  We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold.  ...  By B A for sets A and B we denote the set of all functions from A to B.the initial state, C is a finite set of counter names and ∆ :4 Model-checking Counting Temporal Logics on Flat Structures  ... 
arXiv:1706.08608v1 fatcat:y6qb7w4fhjc2vibajxtrasllma

Towards a Model-Checker for Counter Systems [chapter]

S. Demri, A. Finkel, V. Goranko, G. van Drimmelen
2006 Lecture Notes in Computer Science  
This paper deals with model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means  ...  checking.  ...  On the other hand, most of the studies on CTL -model checking are restricted to (unfoldings of) finite transition systems, and few decidability results for CTLmodel checking on essentially infinite state  ... 
doi:10.1007/11901914_36 fatcat:v2iri7t2cfcv3phe6unqer6sxq

Model-checking CTL* over flat Presburger counter systems

Stéphane Demri, Alain Finkel, Valentin Goranko, Govert van Drimmelen
2010 Journal of Applied Non-Classical Logics  
This paper studies model-checking of fragments and extensions of CTL* on infinitestate counter systems, where the states are vectors of integers and the transitions are determined by means of relations  ...  checking.  ...  In Section 7 we show the decidability of model-checking problems over admissible PCS even when CQDD-based temporal operators are added to the temporal logic.  ... 
doi:10.3166/jancl.20.313-344 fatcat:57igjjmoqbcxlfdds7bebiaczu

Graded CTL* over Finite Paths

Loredana Sorrentino, Sasha Rubin, Aniello Murano
2018 Italian Conference on Theoretical Computer Science  
After defining and justifying the logic GCTL * f , we solve its model checking problem and establish that its computational complexity is PSPACE-complete.  ...  State formulas of GCTL * f are interpreted over Kripke structures with a designated set of states, which we call "check points".  ...  Depending on the view of the underlying nature of the time, we distinguish between two types of temporal logics.  ... 
dblp:conf/ictcs/SorrentinoRM18 fatcat:4zluj6nbfnffznm64mf3o6wcra

QCTL model-checking with QBF solvers [article]

A. Hossain, F. Laroussinie
2020 arXiv   pre-print
We propose a new model-checking algorithm for QCTL based on a reduction to QBF.  ...  Quantified CTL (QCTL) extends the temporal logic CTL with quantifications over atomic propositions.  ...  It is well known that CTL model-checking is PTIME-complete and LTL model-checking (based on automata techniques) is PSPACE-complete.  ... 
arXiv:2010.03185v1 fatcat:rju2mux22fcjjarlmrdk5gv4fe

On the freeze quantifier in Constraint LTL: Decidability and complexity

Stéphane Demri, Ranko Lazić, David Nowak
2007 Information and Computation  
On the positive side, we provide complexity results when the domain is finite (EXPSPACE-completeness) or when the formulae are flat in a sense introduced in the paper.  ...  The freeze quantifier can be part of the language, as in some real-time logics, but this variable-binding mechanism is quite general and ubiquitous in many logical languages (first-order temporal logics  ...  Flat fragments of plain LTL versions have been studied in [20, 10] (see also in [21, Section 5] the design of a flat logical temporal language for model-checking pushdown machines) and our definition  ... 
doi:10.1016/j.ic.2006.08.003 fatcat:6at65uubjbhk3c2gvqgxqwunam

Witness Runs for Counter Machines [chapter]

Clark Barrett, Stéphane Demri, Morgan Deters
2013 Lecture Notes in Computer Science  
We recall several known classes of counter machines for which the reachability sets are Presburger-definable as well as temporal logics with arithmetical constraints.  ...  We discuss issues related to flat counter machines, path schema enumeration, and the use of SMT solvers.  ...  Structural restrictions seem more efficient to reduce the computational complexity of temporal model-checking.  ... 
doi:10.1007/978-3-642-40885-4_9 fatcat:kaaplwebdfdufhwiqkubk44oli

Witness Runs for Counter Machines [chapter]

Clark Barrett, Stéphane Demri, Morgan Deters
2013 Lecture Notes in Computer Science  
We recall several known classes of counter machines for which the reachability sets are Presburger-definable as well as temporal logics with arithmetical constraints.  ...  We discuss issues related to flat counter machines, path schema enumeration, and the use of SMT solvers.  ...  Structural restrictions seem more efficient to reduce the computational complexity of temporal model-checking.  ... 
doi:10.1007/978-3-642-40537-2_1 fatcat:xngwgtrz65hqpiwphe4rcqabby

Lifted Relational Algebra with Recursion and Connections to Modal Logic [article]

Eugenia Ternovska
2016 arXiv   pre-print
We carefully analyze several reasoning tasks and establish a precise connection between a generalized query evaluation and temporal logic model checking.  ...  The essence of our proposal is to lift Codd's relational algebra from operations on relational tables to operations on classes of structures (with recursion), and to add a direction of information propagation  ...  Temporal Logic Tasks: temp-MC, temp-SAT Here we introduce counterparts of Model Checking and Satisfiability tasks in the context of modal temporal logics. Definition 13 (Model Checking: temp-MC).  ... 
arXiv:1612.09251v1 fatcat:ulstwcfr35c3nlqinxykjptnii

The complexity of propositional linear temporal logics in simple cases [chapter]

S. Demri, Ph. Schnoebelen
1998 Lecture Notes in Computer Science  
It is well-known that model checking and satisfiability for PLTL are PSPACE-complete.  ...  In this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic  ...  , and (4) model checking for logics with X can be transformed into model checking without X. (5) Besides, when the formula ϕ has temporal height at most 1, knowing whether S |= ϕ only depends on O(|ϕ|)  ... 
doi:10.1007/bfb0028549 fatcat:tv676j3etfdkva4dxkruur3axe

The Complexity of Propositional Linear Temporal Logics in Simple Cases

Stéphane Demri, Philippe Schnoebelen
2002 Information and Computation  
It is well-known that model checking and satisfiability for PLTL are PSPACE-complete.  ...  In this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic  ...  , and (4) model checking for logics with X can be transformed into model checking without X. (5) Besides, when the formula ϕ has temporal height at most 1, knowing whether S |= ϕ only depends on O(|ϕ|)  ... 
doi:10.1006/inco.2001.3094 fatcat:22u24aacr5ax5bybc2p7bavc64

From Quantified CTL to QBF

Akash Hossain, François Laroussinie, Michael Wagner
2019 International Symposium/Workshop on Temporal Representation and Reasoning  
We propose a model-checking algorithm for QCTL based on a reduction to QBF.  ...  QCTL extends the temporal logic CTL with quantifications over atomic propositions.  ...  In this paper, we focus on the structure semantics, and we propose a model-checking algorithm based on a reduction to QBF (propositional logic augmented with quantifiers): given a Kripke structure K and  ... 
doi:10.4230/lipics.time.2019.11 dblp:conf/time/HossainL19 fatcat:qb3eklhmtbh7jhplchzuiqfrgy

A Parametric Analysis of the State Explosion Problem in Model Checking [chapter]

S. Demri, F. Laroussinie, P. Schnoebelen
2002 Lecture Notes in Computer Science  
In model checking, the state-explosion problem occurs when one checks a non-flat system, i.e., a system implicitly described as a synchronized product of elementary subsystems.  ...  Schnoebelen). 1 Contact author. 2 There are exceptions: for example, the exact complexity of model checking for the branching µ-calculus [21], or model checking over deterministic structures [15, 43] ,  ...  Parameterized complexity of non-flat temporal logic model checking In this section, we investigate the parameterized complexity of temporal logic model-checking problems when the input is a synchronized  ... 
doi:10.1007/3-540-45841-7_51 fatcat:6ovrzllbnvh7zldtqybbnbfuva

A parametric analysis of the state-explosion problem in model checking

S. Demri, F. Laroussinie, Ph. Schnoebelen
2006 Journal of computer and system sciences (Print)  
In model checking, the state-explosion problem occurs when one checks a non-flat system, i.e., a system implicitly described as a synchronized product of elementary subsystems.  ...  Schnoebelen). 1 Contact author. 2 There are exceptions: for example, the exact complexity of model checking for the branching µ-calculus [21], or model checking over deterministic structures [15, 43] ,  ...  Parameterized complexity of non-flat temporal logic model checking In this section, we investigate the parameterized complexity of temporal logic model-checking problems when the input is a synchronized  ... 
doi:10.1016/j.jcss.2005.11.003 fatcat:fjdijs52bjhubg3oaox6gxd2sy

Representing and Reasoning about Temporal Granularities

C. Combi
2004 Journal of Logic and Computation  
However, adding the concept of time granularity to a formalism does not merely mean that one can use different temporal units to represent temporal quantities in a unique flat model, but it involves semantic  ...  In the logical (or descriptive) framework for time granularity, the different granularities and their interconnections are represented by means of mathematical structures called layered structures, consisting  ...  In the proposed approach, the flat temporal structure of standard temporal logics is replaced by a layered temporal universe consisting of a possibly infinite set of related differently-grained temporal  ... 
doi:10.1093/logcom/14.1.51 fatcat:jrecrdzmxfcedgokp2xpl3prqe
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