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## On the Expressivity and Complexity of Quantitative Branching-Time Temporal Logics (2001)

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1310 | Temopral and Modal Logic,
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(Show Context)
Citation Context ...e consider, while introducing freeze quantifiers leads to a complexity blow-up. 1 Introduction Temporal logic is widely used as a formal language for specifying the behaviour of reactive systems (see =-=[Eme90]-=-). This approach allows model checking, i.e. the automatic verification that a finite state system satisfies its expected behavourial specifications. The main limitation to model checking is the state... |

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429 |
Model-checking for real-time systems.
- Alur, Courcoubetis, et al.
- 1990
(Show Context)
Citation Context ... natural numbers, and AP = fA; B; : : :g for a finite set of atomic propositions. Temporal formulae are interpreted over states in Kripke structures. Formally, 1 See e.g. the conjecture at the end of =-=[ACD90] which bec-=-omes an unproved statement in [ACD93]. Definition 2.1. A Kripke structure (a "KS") is a tuple S = hQ S ; RS ; l S i where QS = fq 1 ; : : :g is a non-empty set of states, R S ` QS \Theta QS ... |

354 | An automata-theoretic approach to branching-time model checking. - Kupferman, Vardi, et al. - 2000 |

326 | Model-Checking in Dense Real-Time
- Alur, Courcoubetis, et al.
(Show Context)
Citation Context ...finite set of atomic propositions. Temporal formulae are interpreted over states in Kripke structures. Formally, 1 See e.g. the conjecture at the end of [ACD90] which becomes an unproved statement in =-=[ACD93]. Definiti-=-on 2.1. A Kripke structure (a "KS") is a tuple S = hQ S ; RS ; l S i where QS = fq 1 ; : : :g is a non-empty set of states, R S ` QS \Theta QS is a total transition relation, and l S : QS ! ... |

303 | T.A.: A really temporal logic.
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- 1994
(Show Context)
Citation Context ...rmula (EF=k has size in O(logk) and not k) and do not require that one step uses one unit of time. The second extension, called TCTL c , c for "clocks", uses formula clocks, a.k.a. freeze qu=-=antifiers [AH94]-=-, and is a more general way of counting events. TCTL c can still be translated directly into CTL but model checking is expensive. The results on expressive power formalize natural intuitions which (as... |

296 | Specifying Real-Time Properties with Metric Temporal Logic - Koymans - 1990 |

221 | Logics and models of real time: A survey. - Alur, Henzinger - 1992 |

199 | What good is temporal logic? In - Lamport - 1983 |

135 | Parametric quantitative temporal reasoning,
- Emerson, Trefler
- 1999
(Show Context)
Citation Context ...Kripke structure who decides to encode the flow of elapsing time by this or that event, so that the temporal logics in use are more properly called quantitative temporal logics than real-time logics. =-=[EMSS91] showed that RTCTL (-=-i.e. CTL plus bounded modalities "A Uk " and "E Uk " in the Kripke structure framework) still enjoys the bilinear model checking time complexity of CTL. Our contribution. One impor... |

58 | The complexity of propositional linear temporal logics in simple cases (extended abstract - Schnoebelen - 1998 |

49 | On programming of arithmetic operations - Ershov - 1958 |

20 | Characterizing Kripke structures in propositional temporal logic - Browne, Clarke, et al. - 1988 |

10 | Generalized quantitative temporal reasoning: An automata-theoretic approach - Emerson, Tre - 1997 |

8 | Quantitative temporal reasoning, Real-Time Systems 4 - Emerson, Mok, et al. - 1992 |

6 |
Is you model checker on time
- Aceto, Laroussinie
- 1999
(Show Context)
Citation Context ...lete. Proof. To prove this result, it is sufficient to show that TCTL c model checking is in PSPACE 5 and that the formula complexity is PSPACE-hard. The proof of this last point relies on ideas from =-=[AL99]-=-: let P be an instance of QBF (Quantified Boolean Formula, a PSPACE-complete problem). W.l.o.g. P is some Q 1 p 1 : : : Qnpn :' (with Q i 2 f9; 8g and ' a propositional formula over p 1 ; : : : ; pn )... |

4 | CTL+ is exponentially more succint than CTL - Wilke - 1999 |

3 | A logic of concrete time intervals (extended abstract - Lewis - 1990 |