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## Weak Kripke structures and LTL (2011)

Venue: | IN: PROCEEDINGS OF THE 22ND INTERNATIONAL CONFERENCE ON CONCURRENCY THEORY |

Citations: | 3 - 0 self |

### Citations

405 |
The complexity of propositional linear temporal logics,
- Sistla, Clarke
- 1985
(Show Context)
Citation Context ...roblem has been the subject of intensive investigation. The fundamental result, by Sistla and Clarke in 1985, is that the model checking problem for linear-time temporal logic (LTL) is PSPACEcomplete =-=[21]-=-. A first refinement of this result, due to Lichtenstein and Pnueli, separates the complexity in the length of the formula from the complexity in the size of the Kripke structure. It turns out that th... |

240 | The computational complexity of provability in systems of modal propositional logic
- Ladner
- 1977
(Show Context)
Citation Context ...model checking parameterized by the number of factors of the product Kripke structure [7]. In classical modal logic, systems are defined via frame conditions. Starting with Ladners seminal results in =-=[16]-=- there is a line of research about the complexity of problems for modal logics systems under certain frame conditions (cf. [11,10] for recent results and overview on past work). 2 Computation Paths an... |

172 |
The glory of the past. In:
- Lichtenstein, Pnueli, et al.
- 1985
(Show Context)
Citation Context ... to reachability. 3 Linear-Time Temporal Logic – LTL We consider linear-time temporal logic (LTL) with the usual finite-path semantics, which includes a weak and a strong version of the Next operator =-=[17]-=-. Let AP be a set of atomic propositions. The LTL formulas are defined inductively as follows: every atomic proposition p ∈ AP is a formula. If φ and ψ are formulas, then so are ¬φ, φ ∧ ψ, φ ∨ ψ, X∃ φ... |

124 | Probabilistic verification of discrete event systems using acceptance sampling
- Younes, Simmons
- 2002
(Show Context)
Citation Context ...cking occurs in testing [1] and in several static verification techniques, notably in Monte-Carlo-based probabilistic verification, where large numbers of randomly generated sample paths are analyzed =-=[22]-=-. – Trees: Model checking trees occurs in assertion checking, querying, debugging, and searching in all kinds of parse trees, class hierarchies, thread or process trees, abstract data types, file syst... |

79 | The Boolean formula value problem is in ALOGTIME
- Buss
- 1987
(Show Context)
Citation Context ..., for example, Kripke structures that consist of a single state. The model checking problem for such Kripke structures corresponds to the problem of evaluating Boolean formulas, which is NC1-complete =-=[6]-=-. The PSPACE-hardness result relies on the possibility to encode the computations of a Turing machine as paths in the Kripke structure. What happens if the frame of the Kripke structure does not allow... |

72 | The cyclic executive model and Ada.
- Baker, Shaw
- 1989
(Show Context)
Citation Context ...data types, file systems, and XML documents and XML databases (cf. [5]). – Restricted loops: Control and scheduling programs often enter, after some initialization, an infinitely executed static loop =-=[2]-=-. The frame of the Kripke structure thus is a lasso path. If the system proceeds in stages, where each stage consists of the nondeterministically many iterations of a static loop, then the Kripke fram... |

72 |
Monitoring Programs Using Rewriting,”
- Havelund, Rosu
- 2001
(Show Context)
Citation Context ...h restricted frames occur in many different domains. – Paths: The problem of checking whether a given finite path satisfies an LTL formula plays a key role in monitoring and runtime verification (cf. =-=[9]-=-), where individual paths are checked either online, during the execution of the system, or offline, for example based on an error report. Similarly, path checking occurs in testing [1] and in several... |

58 | The complexity of propositional linear temporal logics in simple cases (extended abstract
- Schnoebelen
- 1998
(Show Context)
Citation Context ...only in the size of formula and linear in the size of the Kripke structure. Much of the subsequent work has therefore focused on detailing the complexity with respect to different classes of formulas =-=[21,14,8,4,3]-=-. However, the linear complexity in the size of the Kripke structure does not mean that the impact of the Kripke structure should be neglected. Consider, for example, Kripke structures that consist of... |

28 |
Combining test case generation and runtime verification.
- Artho, Barringer, et al.
- 2005
(Show Context)
Citation Context ...ification (cf. [9]), where individual paths are checked either online, during the execution of the system, or offline, for example based on an error report. Similarly, path checking occurs in testing =-=[1]-=- and in several static verification techniques, notably in Monte-Carlo-based probabilistic verification, where large numbers of randomly generated sample paths are analyzed [22]. – Trees: Model checki... |

23 | Relating linear and branching model checking - Kupferman, Vardi - 1998 |

23 | Model checking a path (preliminary report
- Schnoebelen
- 2003
(Show Context)
Citation Context ...e possible LTL formulas and the possible labelings of the Kripke structure, and instead focus entirely on the structure of the frame. A key role in our analysis is played by the path checking problem =-=[19]-=-, i.e., the model checking problem where the frame is restricted to a single path. We recently showed that, for LTL formulas, path checking is in NC [13]. We generalize this result to Kripke structure... |

19 | The complexity of poor man’s logic
- Hemaspaandra
- 1999
(Show Context)
Citation Context ...e defined via frame conditions. Starting with Ladners seminal results in [16] there is a line of research about the complexity of problems for modal logics systems under certain frame conditions (cf. =-=[11,10]-=- for recent results and overview on past work). 2 Computation Paths and Kripke Structures Linear-time temporal logic reasons about linearly ordered sequences of states, which we call computation paths... |

10 | The stuttering principle revisited
- Kučera, Strejček
- 2005
(Show Context)
Citation Context ...nce. It is a well known property of the star free regular languages, which is precisely captured by LTL, that those languages can only count up to a threshold but are unable to do modulo counting. In =-=[15]-=- Kučera and Strejček introduce the notion of generalized stutter equivalence which reflects the disability to count of LTL on a syntactic level. Definition 1 (Generalized Stutter Equivalence). Given... |

9 | On the complexity of elementary modal logics
- Hemaspaandra, Schnoor
- 2008
(Show Context)
Citation Context ...e defined via frame conditions. Starting with Ladners seminal results in [16] there is a line of research about the complexity of problems for modal logics systems under certain frame conditions (cf. =-=[11,10]-=- for recent results and overview on past work). 2 Computation Paths and Kripke Structures Linear-time temporal logic reasons about linearly ordered sequences of states, which we call computation paths... |

7 | Logical definability and query languages over ranked and unranked trees
- Benedikt, Libkin, et al.
(Show Context)
Citation Context ...rtion checking, querying, debugging, and searching in all kinds of parse trees, class hierarchies, thread or process trees, abstract data types, file systems, and XML documents and XML databases (cf. =-=[5]-=-). – Restricted loops: Control and scheduling programs often enter, after some initialization, an infinitely executed static loop [2]. The frame of the Kripke structure thus is a lasso path. If the sy... |

7 | LTL Path Checking is Efficiently Parallelizable
- Kuhtz, Finkbeiner
- 2009
(Show Context)
Citation Context ...nalysis is played by the path checking problem [19], i.e., the model checking problem where the frame is restricted to a single path. We recently showed that, for LTL formulas, path checking is in NC =-=[13]-=-. We generalize this result to Kripke structures for which the model checking problem can be deterministically reduced to a polynomial number of parallel path checking problems: Kripke structures that... |

6 |
A parametric analysis of the state explosion problem in model checking
- Schnoebelen
- 2002
(Show Context)
Citation Context ...represented as some kind of product Kripke structure. Demri, Laroussinie, and Schnoebelen study the complexity of model checking parameterized by the number of factors of the product Kripke structure =-=[7]-=-. In classical modal logic, systems are defined via frame conditions. Starting with Ladners seminal results in [16] there is a line of research about the complexity of problems for modal logics system... |

6 | Model checking restricted sets of timed paths
- Markey, Raskin
- 2004
(Show Context)
Citation Context ... path checking problem for various extensions and restrictions of LTL [19] and also show that the complexity of the (finite) path checking problem for the µ-calculus is P-hard [20]. Markey and Raskin =-=[18]-=- study the complexity of the model checking problem for restricted sets of paths for extensions of LTL to continuous time. Another area of investigation that is closely related is the study of the sta... |

4 |
Model Checking Finite Paths and Trees
- Kuhtz
- 2010
(Show Context)
Citation Context ...put-face monotone planar Boolean circuits. Another area that requires more attention is the model checking problem on restricted frames for branching-time temporal logic. In the first author’s thesis =-=[12]-=-, it is shown that the model checking problem for CTL on finite trees is in NC (more precisely, in AC2(logDCFL)). The gap between NC as an upper bound and L as a lower bound for tree structures and P ... |

2 |
Mu-calculus path checking
- Schnoebelen
- 2006
(Show Context)
Citation Context ...noebelen investigate the path checking problem for various extensions and restrictions of LTL [19] and also show that the complexity of the (finite) path checking problem for the µ-calculus is P-hard =-=[20]-=-. Markey and Raskin [18] study the complexity of the model checking problem for restricted sets of paths for extensions of LTL to continuous time. Another area of investigation that is closely related... |

1 |
The tractability of model-checking for ltl: The good, the bad, and the ugly fragments
- Schneider, Schnoor, et al.
(Show Context)
Citation Context ...only in the size of formula and linear in the size of the Kripke structure. Much of the subsequent work has therefore focused on detailing the complexity with respect to different classes of formulas =-=[21,14,8,4,3]-=-. However, the linear complexity in the size of the Kripke structure does not mean that the impact of the Kripke structure should be neglected. Consider, for example, Kripke structures that consist of... |

1 |
The complexity of generalized satisfiability for linear temporal logic
- Schneider, Schnoor, et al.
(Show Context)
Citation Context ...only in the size of formula and linear in the size of the Kripke structure. Much of the subsequent work has therefore focused on detailing the complexity with respect to different classes of formulas =-=[21,14,8,4,3]-=-. However, the linear complexity in the size of the Kripke structure does not mean that the impact of the Kripke structure should be neglected. Consider, for example, Kripke structures that consist of... |