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## On Relaxing Metric Information in Linear Temporal Logic (2009)

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1310 | Temopral and Modal Logic,
- Emerson
- 1990
(Show Context)
Citation Context ...ete presentation for reference. Related work: The expressiveness and complexity of LTL and of its qualitative subset have been thoroughly investigated in the classic framework of temporal logic [12], =-=[13]-=-, [14]. With respect to expressiveness, Lamport introduced the notion of stuttering to characterize qualitative LTL [1]; the characterization was completed by Peled and Wilke [2], perfected by Etessam... |

405 |
The complexity of propositional linear temporal logics,
- Sistla, Clarke
- 1985
(Show Context)
Citation Context ...LTL with respect to its qualitative subset are well known from classic work: quantitative (metric) LTL is strictly more expressive [1], [2], [3], [4], but reasoning has the same worst-case complexity =-=[5]-=-, [6]. The present paper investigates when the metric information, encoded by nested occurrences of X , is redundant and can be relaxed. The relaxation transforms a quantitative formula into an equi-s... |

221 | Logics and models of real time: A survey.
- Alur, Henzinger
- 1992
(Show Context)
Citation Context ..., 7]. Hirshfeld and Rabinovich studied the expressiveness and decidability of Pnueli operators over dense time [20]; the operators themselves were first mentioned in a conjecture attributed to Pnueli =-=[1, 33]-=-. Section 5 introduces discrete-time qualitative variants of such operators. Counting operators [25] are somehow similar to discrete-time Pnueli operators in that they both facilitate the expression o... |

199 |
What good is temporal logic? In
- Lamport
- 1983
(Show Context)
Citation Context ...ecutive repetitions of the same state. The fundamental properties of LTL with respect to its qualitative subset are well known from classic work: quantitative (metric) LTL is strictly more expressive =-=[1]-=-, [2], [3], [4], but reasoning has the same worst-case complexity [5], [6]. The present paper investigates when the metric information, encoded by nested occurrences of X , is redundant and can be rel... |

58 | The complexity of propositional linear temporal logics in simple cases (extended abstract
- Schnoebelen
- 1998
(Show Context)
Citation Context ...ith respect to its qualitative subset are well known from classic work: quantitative (metric) LTL is strictly more expressive [1], [2], [3], [4], but reasoning has the same worst-case complexity [5], =-=[6]-=-. The present paper investigates when the metric information, encoded by nested occurrences of X , is redundant and can be relaxed. The relaxation transforms a quantitative formula into an equi-satisf... |

51 |
Stutter-invariant temporal properties are expressible without the next-time operator.
- Peled, Wilke
- 1997
(Show Context)
Citation Context ...ve repetitions of the same state. The fundamental properties of LTL with respect to its qualitative subset are well known from classic work: quantitative (metric) LTL is strictly more expressive [1], =-=[2]-=-, [3], [4], but reasoning has the same worst-case complexity [5], [6]. The present paper investigates when the metric information, encoded by nested occurrences of X , is redundant and can be relaxed.... |

49 | LTL satisfiability checking. In:
- Rozier, Vardi
- 2007
(Show Context)
Citation Context ... paper. To this end, we plan to: • implement a translator from LTL to formulas equi-satisfiable over words with bounded variability and combine it with off-the-shelf LTL satisfiability checking tools =-=[34, 3, 29, 31]-=-; • formalize systems characterized by time granularity heterogeneity, in order to determine how often the assumption of “sparse” events is compatible with accurate models thereof. 19 Acknowledgements... |

38 |
On the verification problem of nonregular properties for nonregular processes
- Bouajjani, Echahed, et al.
- 1995
(Show Context)
Citation Context ... Pnueli operators in that they both facilitate the expression of concise counting requirements; both extensions do not increase the expressive power of LTL, nor its complexity under a unary encoding. =-=[4]-=- introduce a much more expressive counting extension of LTL, which is decidable only in special cases. The proofs of Lemmas 11 and 20 use a technique that removes and adds stuttering steps in words to... |

36 | Logics for real time: Decidability and complexity
- Hirshfeld, Rabinovich
(Show Context)
Citation Context ...lity. On the technical level, the construction that eliminates metric information relies on a normal form for LTL formulas and on discrete-time generalized versions of the dense-time Pnueli operators =-=[7]-=-. The correctness proof follows the idea of adding and removing stuttering steps to re-introduce the metric information dropped in models satisfying only qualitative constraints; it is reminiscent of ... |

24 | Temporal verification and simulation and refinement
- Kesten, Manna, et al.
- 1993
(Show Context)
Citation Context ...esentation for reference. Related work: The expressiveness and complexity of LTL and of its qualitative subset have been thoroughly investigated in the classic framework of temporal logic [12], [13], =-=[14]-=-. With respect to expressiveness, Lamport introduced the notion of stuttering to characterize qualitative LTL [1]; the characterization was completed by Peled and Wilke [2], perfected by Etessami and ... |

20 | The Complexity of Generalized Satisfiability for Linear Temporal Logic
- Bauland, Schnoor, et al.
(Show Context)
Citation Context ...t to complexity, the seminal work of Sistla and Clarke established the PSPACE-completeness of both LTL and qualitative LTL [5], and other authors have generalized or specialized the result [6], [18], =-=[19]-=-. To our knowledge, the present paper is the first investigating satisfiability-preserving relaxations of metric information in temporal logic formulas. More generally, the problem of formalizing syst... |

20 | Representing and reasoning about temporal granularities
- Combi, Franceschet, et al.
- 2004
(Show Context)
Citation Context ...etric information in temporal logic formulas. More generally, the problem of formalizing systems with heterogeneous time granularities using temporal logic [17] has been studied by only a few authors =-=[9, 10, 8, 6]-=-; [8], in particular, presents an encoding of temporal granularities in LTL, but it does not discuss efficiency of the encoding. Some of the techniques used in the the paper borrow from existing appro... |

18 | Past is for free: On the complexity of verifying linear temporal properties with past
- Markey
(Show Context)
Citation Context ...respect to complexity, the seminal work of Sistla and Clarke established the PSPACE-completeness of both LTL and qualitative LTL [5], and other authors have generalized or specialized the result [6], =-=[18]-=-, [19]. To our knowledge, the present paper is the first investigating satisfiability-preserving relaxations of metric information in temporal logic formulas. More generally, the problem of formalizin... |

15 |
M.: Modeling time in computing: a taxonomy and a comparative survey
- Furia, Mandrioli, et al.
- 2010
(Show Context)
Citation Context ... heterogeneous components evolving over wildly different time scales, such as minutes, weeks, and years. Assuming incommensurable distances are not a concern, such heterogeneity of time granularities =-=[10]-=- can, in principle, be modeled in terms of the finest-grain time units; but this solution comes with a significant price to pay to accommodate the largest time units in terms of the smallest, resultin... |

15 |
Timer formulas and decidable metric temporal logic
- Hirshfeld, Rabinovich
- 2005
(Show Context)
Citation Context ...steps to re-introduce the metric information dropped in models satisfying only qualitative constraints; it is reminiscent of the notion of stretching, also originally introduced for dense-time models =-=[21, 5]-=-. Section 4 first demonstrates this technique by showing how to transform any metric LTL formula into a qualitative one which is equi-satisfiable (for generic models) and of polynomial size. The feasi... |

12 |
A timeband framework for modelling real-time systems
- Burns, Hayes
- 2010
(Show Context)
Citation Context ...etric information in temporal logic formulas. More generally, the problem of formalizing systems with heterogeneous time granularities using temporal logic [17] has been studied by only a few authors =-=[9, 10, 8, 6]-=-; [8], in particular, presents an encoding of temporal granularities in LTL, but it does not discuss efficiency of the encoding. Some of the techniques used in the the paper borrow from existing appro... |

12 | On expressiveness and complexity in real-time model checking
- Bouyer, Markey, et al.
- 2008
(Show Context)
Citation Context ...ain results of the present paper use a technique that removes and adds stuttering steps in words to match some metric requirements; the notion of stretching — introduced in [HR05] and further used in =-=[BMOW08]-=- — exploits a related technique but over dense time models. Hirshfeld and Rabinovich studied the expressiveness and decidability of Pnueli operators over dense time [HR04]; the operators themselves we... |

11 | Stutter-invariant languages, omega-automata, and temporal logic
- Etessami
(Show Context)
Citation Context ...respect to expressiveness, Lamport introduced the notion of stuttering to characterize qualitative LTL [1]; the characterization was completed by Peled and Wilke [2], perfected by Etessami and others =-=[15]-=-, [3], [16], [17], and generalized by Kučera and Strejček [4]. With respect to complexity, the seminal work of Sistla and Clarke established the PSPACE-completeness of both LTL and qualitative LTL [5]... |

10 | The stuttering principle revisited
- Kučera, Strejček
- 2005
(Show Context)
Citation Context ...ions of the same state. The fundamental properties of LTL with respect to its qualitative subset are well known from classic work: quantitative (metric) LTL is strictly more expressive [1], [2], [3], =-=[4]-=-, but reasoning has the same worst-case complexity [5], [6]. The present paper investigates when the metric information, encoded by nested occurrences of X , is redundant and can be relaxed. The relax... |

9 |
Temporal Logic (vol. 1): mathematical foundations and computational aspects, ser. Oxford Logic Guides
- Gabbay, Hodkinson, et al.
- 1994
(Show Context)
Citation Context ... complete presentation for reference. Related work: The expressiveness and complexity of LTL and of its qualitative subset have been thoroughly investigated in the classic framework of temporal logic =-=[12]-=-, [13], [14]. With respect to expressiveness, Lamport introduced the notion of stuttering to characterize qualitative LTL [1]; the characterization was completed by Peled and Wilke [2], perfected by E... |

9 | Trio2Promela: A model checker for temporal metric specifications
- Bianculli, Morzenti, et al.
- 2007
(Show Context)
Citation Context ... paper. To this end, we plan to: • implement a translator from LTL to formulas equi-satisfiable over words with bounded variability and combine it with off-the-shelf LTL satisfiability checking tools =-=[34, 3, 29, 31]-=-; • formalize systems characterized by time granularity heterogeneity, in order to determine how often the assumption of “sparse” events is compatible with accurate models thereof. 19 Acknowledgements... |

8 | A note on a question of Peled and Wilke regarding stutter-invariant
- Etessami
- 2000
(Show Context)
Citation Context ...petitions of the same state. The fundamental properties of LTL with respect to its qualitative subset are well known from classic work: quantitative (metric) LTL is strictly more expressive [1], [2], =-=[3]-=-, [4], but reasoning has the same worst-case complexity [5], [6]. The present paper investigates when the metric information, encoded by nested occurrences of X , is redundant and can be relaxed. The ... |

8 |
E.: Dealing with different time scales in formal specifications
- Corsetti, Crivelli, et al.
- 1991
(Show Context)
Citation Context ...etric information in temporal logic formulas. More generally, the problem of formalizing systems with heterogeneous time granularities using temporal logic [17] has been studied by only a few authors =-=[9, 10, 8, 6]-=-; [8], in particular, presents an encoding of temporal granularities in LTL, but it does not discuss efficiency of the encoding. Some of the techniques used in the the paper borrow from existing appro... |

8 | On the Merits of Temporal Testers
- Pnueli, Zaks
- 2006
(Show Context)
Citation Context ...Some of the techniques used in the the paper borrow from existing approaches in the literature. The normal forms for LTL introduced in Section 3 are related to a construction used in temporal testers =-=[28]-=-. The definition of bounded variability in Section 2 translates to discrete time a notion introduced for dense (or continuous) time models [33, 16, 18, 7]. Hirshfeld and Rabinovich studied the express... |

7 | Expressive completeness of temporal logic of action
- Rabinovich
(Show Context)
Citation Context ...expressiveness, Lamport introduced the notion of stuttering to characterize qualitative LTL [1]; the characterization was completed by Peled and Wilke [2], perfected by Etessami and others [15], [3], =-=[16]-=-, [17], and generalized by Kučera and Strejček [4]. With respect to complexity, the seminal work of Sistla and Clarke established the PSPACE-completeness of both LTL and qualitative LTL [5], and other... |

6 | Safe runtime verification of real-time properties
- Colombo, Pace, et al.
- 2009
(Show Context)
Citation Context ...3 are related to a construction used in temporal testers [28]. The definition of bounded variability in Section 2 translates to discrete time a notion introduced for dense (or continuous) time models =-=[33, 16, 18, 7]-=-. Hirshfeld and Rabinovich studied the expressiveness and decidability of Pnueli operators over dense time [20]; the operators themselves were first mentioned in a conjecture attributed to Pnueli [1, ... |

6 | A metric encoding for bounded model checking
- Pradella, Morzenti, et al.
- 2009
(Show Context)
Citation Context ... paper. To this end, we plan to: • implement a translator from LTL to formulas equi-satisfiable over words with bounded variability and combine it with off-the-shelf LTL satisfiability checking tools =-=[34, 3, 29, 31]-=-; • formalize systems characterized by time granularity heterogeneity, in order to determine how often the assumption of “sparse” events is compatible with accurate models thereof. 19 Acknowledgements... |

5 | Decidability of duration calculi on restricted model classes
- Fränzle
- 1996
(Show Context)
Citation Context ...3 are related to a construction used in temporal testers [28]. The definition of bounded variability in Section 2 translates to discrete time a notion introduced for dense (or continuous) time models =-=[33, 16, 18, 7]-=-. Hirshfeld and Rabinovich studied the expressiveness and decidability of Pnueli operators over dense time [20]; the operators themselves were first mentioned in a conjecture attributed to Pnueli [1, ... |

4 | Specification languages for stutter-invariant regular properties
- Dax, Klaedtke, et al.
- 2009
(Show Context)
Citation Context ...siveness, Lamport introduced the notion of stuttering to characterize qualitative LTL [1]; the characterization was completed by Peled and Wilke [2], perfected by Etessami and others [15], [3], [16], =-=[17]-=-, and generalized by Kučera and Strejček [4]. With respect to complexity, the seminal work of Sistla and Clarke established the PSPACE-completeness of both LTL and qualitative LTL [5], and other autho... |

4 | MTL with bounded variability: Decidability and complexity
- Furia, Rossi
- 2008
(Show Context)
Citation Context ...3 are related to a construction used in temporal testers [28]. The definition of bounded variability in Section 2 translates to discrete time a notion introduced for dense (or continuous) time models =-=[33, 16, 18, 7]-=-. Hirshfeld and Rabinovich studied the expressiveness and decidability of Pnueli operators over dense time [20]; the operators themselves were first mentioned in a conjecture attributed to Pnueli [1, ... |

2 |
time granularities, and automata
- Calendars
(Show Context)
Citation Context |

2 |
Eudes Petonnet. Counting LTL
- Laroussinie, Meyer
- 2010
(Show Context)
Citation Context ...se time [20]; the operators themselves were first mentioned in a conjecture attributed to Pnueli [1, 33]. Section 5 introduces discrete-time qualitative variants of such operators. Counting operators =-=[25]-=- are somehow similar to discrete-time Pnueli operators in that they both facilitate the expression of concise counting requirements; both extensions do not increase the expressive power of LTL, nor it... |

1 |
formulas and decidable metric temporal logic
- “Timer
- 2005
(Show Context)
Citation Context ...steps to re-introduce the metric information dropped in models satisfying only qualitative constraints; it is reminiscent of the notion of stretching, also originally introduced for dense-time models =-=[8]-=-, [9]. Besides the theoretical interest, the results of the present paper may be practically useful to simplify the temporallogic analysis of systems characterized by heterogeneous components evolving... |