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The Complexity of Generalized Satisfiability for Linear Temporal Logic [article]

Michael Bauland, Thomas Schneider, Henning Schnoor, Ilka Schnoor, Heribert Vollmer
2009 arXiv   pre-print
In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used.  ...  With its help, we determine the computational complexity of LTL satisfiability for all combinations of temporal operators and all but two classes of propositional functions.  ...  Acknowledgments We thank Martin Mundhenk and the anonymous referees for helpful comments and suggestions.  ... 
arXiv:0812.4848v2 fatcat:qkonskemlrgb3n6hmbyh7gtwku

The Complexity of Generalized Satisfiability for Linear Temporal Logic [chapter]

Michael Bauland, Thomas Schneider, Henning Schnoor, Ilka Schnoor, Heribert Vollmer
Foundations of Software Science and Computational Structures  
In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used.  ...  The effect of propositional restrictions on the complexity of the satisfiability problem was first considered by Lewis for the case of classical propositional logic in [Lew79] .  ...  A model in linear temporal logic is a linear structure of states, which intuitively can be seen as different points of time, with propositional assignments.  ... 
doi:10.1007/978-3-540-71389-0_5 dblp:conf/fossacs/BaulandSSSV07 fatcat:vn5udrtnnzcz7duj5fhkrlkvdq

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  ...  [50] provides an algorithm for the satisfiability problem of CTL*, which has 2-EXPTIME complexity in the length of the formula.  ...  [47] presents a tableau method for checking the satisfiability of CTL formulas. The complexity of this procedure is EXPTIME.  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

The Complexity of Dual Models Problem of Propositional Linear Temporal Logics

Zhi-Lin WU
2007 Journal of Software (Chinese)  
The complexity of dual models problem of propositional linear temporal logics. Journal of Software, 2007,18(7):1573−1581.  ...  Then for various propositional linear temporal logics, the complexity of the problem deciding whether a formula f has dual models (denoted by DM) and the problem of determination of dual models in a Kripke-structure  ...  [2] , the complexity of SAT and MC was investigated for various propositional linear temporal logics.  ... 
doi:10.1360/jos181573 fatcat:eiysyddiljbdjal4uuu6gsqzva

Implementing Temporal Logics: Tools for Execution and Proof [chapter]

Michael Fisher
2006 Lecture Notes in Computer Science  
I thank them all for their endeavours. Summary We have overviewed a selection of tools for execution and proof within temporal logic.  ...  from within the Logic and Computation group 2 .  ...  [this shows some of the power of temporal logic as a variety of different ω-automata can be characterised in this way] A Little Complexity The decision problem for a simple propositional (discrete, linear  ... 
doi:10.1007/11750734_8 fatcat:dnerita2qfcevnmo3ah62kf24m

Real-time and Probabilistic Temporal Logics: An Overview [article]

Savas Konur
2011 arXiv   pre-print
Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature.  ...  We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed.  ...  In general, temporal logics have been introduced for specific types of problems. The general trade-off is between the complexity and simplicity.  ... 
arXiv:1005.3200v3 fatcat:xhrrcy26bzeehg7wqvjfikm26e

A survey on temporal logics for specifying and verifying real-time systems

Savas Konur
2013 Frontiers of Computer Science  
Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature.  ...  We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.  ...  Some parts of this paper exists in [231] .  ... 
doi:10.1007/s11704-013-2195-2 fatcat:5lyaji5wnzbyfdmbxwzbxjosku

Temporal Modalities in Answer Set Programming (Invited Talk)

Pedro Cabalar, Martin Theobald, Ana Ozaki, Emilio Muñoz-Velasco
2020 International Symposium/Workshop on Temporal Representation and Reasoning  
As a result, TEL is an expressive non-monotonic modal logic that shares the syntax of Linear-Time Temporal Logic (LTL) but interprets temporal formulas under a non-monotonic semantics that properly extends  ...  This formalism constitutes a modal, linear-time extension of Equilibrium Logic which, in its turn, is a complete logical characterisation of (standard) ASP based on the intermediate logic of Here-and-There  ...  We refer to the resulting logic as (Linear) Dynamic logic of Here-and-There (DHT for short).  ... 
doi:10.4230/lipics.time.2020.2 dblp:conf/time/Cabalar20 fatcat:mg7snegse5cv5jgn3k3lnms7re

Branching vs. Linear Time: Final Showdown [chapter]

Moshe Y. Vardi
2001 Lecture Notes in Computer Science  
One of the beliefs dominating this discussion has been that "while specifying is easier in LTL (linear-temporal logic), verification is easier for CTL (branching-temporal logic)".  ...  On the other hand, while model checking for CTL can be done in time that is linear in the size of the specification, it takes time that is exponential in the specification for LTL.  ...  The complexity of model checking for both linear and branching temporal logics is well understood: suppose we are given a transition system of size n and a temporal logic formula of size m.  ... 
doi:10.1007/3-540-45319-9_1 fatcat:2i2vgpeuzfabtj66rylhspbn5y

Automatic Abstraction Using Generalized Model Checking [chapter]

Patrice Godefroid, Radha Jagadeesan
2002 Lecture Notes in Computer Science  
In the context of automatic abstraction, generalized model checking means checking whether there exists a concretization of an abstraction that satisfies a temporal logic formula.  ...  We study the cost needed to improve precision by presenting new upper and lower bounds for the complexity of generalized model checking in the size of the abstraction.  ...  In the case of branchingtime temporal logics, generalized model checking has the same complexity in the size of the formula as satisfiability.  ... 
doi:10.1007/3-540-45657-0_11 fatcat:pq2p3k4hgjcvbef35ziwvs3kta

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 prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification.  ...  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

On complexity of propositional Linear-time Temporal Logic with finitely many variables [article]

Mikhail Rybakov, Dmitry Shkatov
2017 arXiv   pre-print
It is known [DemriSchnoebelen02] that both satisfiability and model-checking problems for propositional Linear-time Temporal Logic, LTL, with only a single propositional variable in the language are PSPACE-complete  ...  , which coincides with the complexity of these problems for LTL with an arbitrary number of propositional variables [SislaClarke85].  ...  Conclusion We have shown both model-checking and satisfiability for the single-variable fragment of the propositional Linear-time Temporal Logic LTL is PSPACE-complete, and therefore has the same complexity  ... 
arXiv:1706.04108v2 fatcat:emxnrgs7qzgunanyx6zjdtmh6q

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 prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification.  ...  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

An automata-theoretic approach to branching-time model checking (Extended abstract) [chapter]

Orna Bernholtz, Moshe Y. Vardi, Pierre Wolper
1994 Lecture Notes in Computer Science  
Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear-time model-checking, and for obtaining many extensions and improvements to this verification  ...  Recently, Bernholtz and Grumberg have shown that this exponential penalty can be avoided, though they did not match the linear complexity of non-automata-theoretic algorithms.  ...  showed that this explains the exponential decidability of satisfiability for various branching temporal logics. We show here that this also explains the efficiency of model checking for those logics.  ... 
doi:10.1007/3-540-58179-0_50 fatcat:uwvhl43uvjht3ok7epblznjduy

Graded Computation Tree Logic

Alessandro Bianco, Fabio Mogavero, Aniello Murano
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science  
Extended Abstract Temporal logic is a suitable framework for reasoning about the correctness of concurrent programs.  ...  Depending on the view of the underlying nature of time, two types of temporal logics are mainly considered.  ...  Extended Abstract Temporal logic is a suitable framework for reasoning about the correctness of concurrent programs.  ... 
doi:10.1109/lics.2009.28 dblp:conf/lics/BiancoMM09 fatcat:5dj7hqhrojbllmauzvaipwn2te
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