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The Complexity of Counting Models of Linear-time Temporal Logic [article]

Hazem Torfah, Martin Zimmermann
2014 arXiv   pre-print
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic.  ...  Counting tree models is as hard as counting accepting runs of nondeterministic exponential time Turing machines, if the bound is given in unary.  ...  We would like to thank Markus Lohrey and an anonymous reviewer for bringing Ladner's work on polynomial space counting [11] to our attention.  ... 
arXiv:1408.5752v2 fatcat:b5huug37hjae7d3we45p6ee37q

Counting Models of Linear-Time Temporal Logic [chapter]

Bernd Finkbeiner, Hazem Torfah
2014 Lecture Notes in Computer Science  
We investigate the model counting problem for safety specifications expressed in linear-time temporal logic (LTL).  ...  Model counting has previously been studied for propositional logic; in planning, for example, propositional model counting is used to compute the plan's robustness in an incomplete domain.  ...  In this paper, we study the model counting problem for safety specifications expressed in linear-time temporal logic (LTL).  ... 
doi:10.1007/978-3-319-04921-2_29 fatcat:wjqxen6i5rh2bhxofc3ng6nxri

The complexity of counting models of linear-time temporal logic

Hazem Torfah, Martin Zimmermann
2016 Acta Informatica  
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic.  ...  Counting tree-models is as hard as counting accepting runs of nondeterministic exponential time Turing machines, if the bound is given in unary.  ...  We would like to thank Markus Lohrey and an anonymous reviewer for bringing Ladner's work on polynomial space counting [11] to our attention.  ... 
doi:10.1007/s00236-016-0284-z fatcat:app6yn2erng4dptiyvqsv7oneu

Specifying Event-Based Systems with a Counting Fluent Temporal Logic

German Regis, Renzo Degiovanni, Nicolas D'Ippolito, Nazareno Aguirre
2015 2015 IEEE/ACM 37th IEEE International Conference on Software Engineering  
Although by extending fluent linear temporal logic with counting fluents we obtain an undecidable, strictly more expressive formalism, we develop a sound (but incomplete) model checking approach for the  ...  Fluent linear temporal logic is a formalism for specifying properties of event-based systems, based on propositions called fluents, defined in terms of activating and deactivating events.  ...  CONCLUSIONS We have introduced Counting Fluent Linear Temporal Logic, an extension of FLTL with the concept of counting fluent.  ... 
doi:10.1109/icse.2015.86 dblp:conf/icse/RegisDDA15 fatcat:odjkjsdwengr5n3giicipb4byy

Automatic verification of multi-agent systems security properties specified with LTL

Kholud Alghamdi, Marius Silaghi
2022 Proceedings of the ... International Florida Artificial Intelligence Research Society Conference  
We propose a way to verify security requirements of critical multi-agent system processes by using logic representationsand automatic reasoning.  ...  We show a model of such security requirements by using system liveness properties, and exemplify their verification on a real system that we implement for this purpose.  ...  B üchi Automata Büchi Automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic.  ... 
doi:10.32473/flairs.v35i.130551 fatcat:vphuii6oxvhktkmj7nnv6yehsu

Probabilistic verification and approximation

Richard Lassaigne, Sylvain Peyronnet
2008 Annals of Pure and Applied Logic  
Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas.  ...  We show how some simple randomized approximation algorithms can improve the efficiency of verification of such probabilistic specifications and can be implemented in a probabilistic model checker.  ...  Acknowledgements We would like to thank Thomas Hérault for his important participation to the development of APMC, and an anonymous referee for his pertinent remarks and suggestions.  ... 
doi:10.1016/j.apal.2007.11.006 fatcat:kjhhgvh6prglxehlpepy42afju

Probabilistic Verification and Approximation

Richard Lassaigne, Sylvain Peyronnet
2006 Electronical Notes in Theoretical Computer Science  
Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas.  ...  We show how some simple randomized approximation algorithms can improve the efficiency of verification of such probabilistic specifications and can be implemented in a probabilistic model checker.  ...  Acknowledgements We would like to thank Thomas Hérault for his important participation to the development of APMC, and an anonymous referee for his pertinent remarks and suggestions.  ... 
doi:10.1016/j.entcs.2005.05.031 fatcat:usjmmp4kjzdrnoztoxpskrguka

A Survey on Temporal Logics [article]

Savas Konur
2011 arXiv   pre-print
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability  ...  In a temporal logic the structure of time is linear if any two points can be compared.  ...  Although model checking is expensive in linear time logics (for example, it is exponential for LTL), model checking complexity of CTL is very efficient, which is linear in the size of model and formula  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

The temporal logic of programs

Amir Pnueli
1977 18th Annual Symposium on Foundations of Computer Science (sfcs 1977)  
A Logic-based Calculus of Events.  ...  ,{off, power_cut}> initially False fluent DARK = <{off, power_cut},{on}> initially True LIGHT DARK Time on off TRUE FALSE FALSE LIGHT 2015 Concurrency: logical properties 5 ©Magee/Kramer 2 nd Edition Fluents  ...  temporal logic FLTL. u We verify an LTS model against a given set of fluent propositions. u LTSA evaluates the set of fluents that hold each time an action has taken place in the model. u Until, Weak  ... 
doi:10.1109/sfcs.1977.32 dblp:conf/focs/Pnueli77 fatcat:3edaknf4e5fnnphkypc2brgf2u

Graded Computation Tree Logic

Alessandro Bianco, Fabio Mogavero, Aniello Murano
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science  
In linear-time temporal logics, such as LTL [Pnu77] , time is treated as if each moment in time has a unique possible future.  ...  Depending on the view of the underlying nature of time, two types of temporal logics are mainly considered.  ...  In linear-time temporal logics, such as LTL [Pnu77] , time is treated as if each moment in time has a unique possible future.  ... 
doi:10.1109/lics.2009.28 dblp:conf/lics/BiancoMM09 fatcat:5dj7hqhrojbllmauzvaipwn2te

Graded Computation Tree Logic [chapter]

Fabio Mogavero
2013 Logics in Computer Science  
In linear-time temporal logics, such as LTL [Pnu77] , time is treated as if each moment in time has a unique possible future.  ...  Depending on the view of the underlying nature of time, two types of temporal logics are mainly considered.  ...  In linear-time temporal logics, such as LTL [Pnu77] , time is treated as if each moment in time has a unique possible future.  ... 
doi:10.2991/978-94-91216-95-4_1 fatcat:ip7uqjm5ffe2hpcxger63dw2iu

Graded computation tree logic

Alessandro Bianco, Fabio Mogavero, Aniello Murano
2012 ACM Transactions on Computational Logic  
In linear-time temporal logics, such as LTL [Pnu77] , time is treated as if each moment in time has a unique possible future.  ...  Depending on the view of the underlying nature of time, two types of temporal logics are mainly considered.  ...  In linear-time temporal logics, such as LTL [Pnu77] , time is treated as if each moment in time has a unique possible future.  ... 
doi:10.1145/2287718.2287725 fatcat:2h62k6brdje2zkxgjgdd36f7na

Deciding Continuous-Time Metric Temporal Logic with Counting Modalities [chapter]

Marcello M. Bersani, Matteo Rossi, Pierluigi San Pietro
2013 Lecture Notes in Computer Science  
the proper;es of systems e.g., high--level requirements -descrip+ve models of systems: what vs how Motivations • Since '80s aIempts to embed explicit (real) ;me in Linear Temporal Logic (LTL, defined  ...  close to each other, but not at the same ;me • Successful formalisms and tools to capture and analyze con;nuous systems e.g., Timed Automata (Uppaal) • Con;nuous--;me temporal logics are useful to capture  ...  -On unrestricted (non Zeno) signals -By using a new decidability procedure • Now extended to deal with QTLc 1 "From MITL to Timed Automata", Maler, Nickovic and Pnueli, 2006 Background on Pnueli and Counting  ... 
doi:10.1007/978-3-642-41036-9_8 fatcat:dfavcpcwcffvdergkztullbame

Representing and Reasoning about Temporal Granularities

C. Combi
2004 Journal of Logic and Computation  
model sets of granularities by means of linear time logic formulas.  ...  time logic.  ...  We adopted the linear time logic PPLTL, interpreted over labelled linear time structures, to model possibly infinite sets of time granularities.  ... 
doi:10.1093/logcom/14.1.51 fatcat:jrecrdzmxfcedgokp2xpl3prqe

Memory Event Clocks [chapter]

James Jerson Ortiz, Axel Legay, Pierre-Yves Schobbens
2010 Lecture Notes in Computer Science  
When we introduce these clocks in the linear temporal logic of the reals, we create Recursive Memory Event Clocks Temporal Logic (RMECTL).  ...  It turns out to have the same expressiveness as the Temporal Logic with Counting (TLC) of Hirshfeld and Rabinovich. We then examine automata with recursive memory event clocks (RMECA).  ...  Temporal Logic with Counting The Temporal Logic with Counting [13] is an extension of the Temporal Logic of the Reals with Past by counting modalities.  ... 
doi:10.1007/978-3-642-15297-9_16 fatcat:yum7ozvfq5aajhvlszs6bqante
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