On MITL and Alternating Timed Automata

Brihaye, Thomas; Estiévenart, Morgane; Geeraerts, Gilles

doi:10.1007/978-3-642-40229-6_4

Cited by 12 publications

(35 citation statements)

References 17 publications

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“…To see the difficulty of transforming Type 4 and Type 5 formulas into timed automata, consider (3,4) (p → ♦ (1,2) q). Intuitively, the formula says, during the 4 th unit of time, every p should be followed by a q within 1 to 2 units of time.…”

Section: Definition 20 (Normalmentioning

confidence: 99%

Revisiting MITL to Fix Decision Procedures

Roohi

Viswanathan

2017

Lecture Notes in Computer Science

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Metric Interval Temporal Logic (MITL) is a well studied realtime, temporal logic that has decidable satisfiability and model checking problems. The decision procedures for MITL rely on the automata theoretic approach, where logic formulas are translated into equivalent timed automata. Since timed automata are not closed under complementation, decision procedures for MITL first convert a formula into negated normal form before translating to a timed automaton. We show that, unfortunately, these 20-year-old procedures are incorrect, because they rely on an incorrect semantics of the R operator. We present the right semantics of R and give new, correct decision procedures for MITL. We show that both satisfiability and model checking for MITL are EXPSPACE-complete, as was previously claimed. We also identify a fragment of MITL that we call MITL WI that is richer than MITL0,∞, for which we show that both satisfiability and model checking are PSPACE-complete.

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Section: Definition 20 (Normalmentioning

confidence: 99%

Revisiting MITL to Fix Decision Procedures

Roohi

Viswanathan

2017

Lecture Notes in Computer Science

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“…As stated in Section 2 any MITL formula can be represented by a TBA [Alur et al 1996]. Approaches for the translation were suggested in [Maler et al 2006], [Brihaye et al 2013] and [Ničković and Piterman 2010]. Note that the time-intervals considered by the MITL formulas must be on the form ≤ a due to the overapproximation of time in the abstraction.…”

Section: Constructing a Local Bwtsmentioning

confidence: 99%

Control Synthesis for Multi-Agent Systems under Metric Interval Temporal Logic Specifications * *This work was supported by the H2020 ERC Starting Grand BUCOPHSYS, the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF) and the Knut och Alice Wallenberg Foundation.

2017

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This paper presents a framework for automatic synthesis of a control sequence for multi-agent systems governed by continuous linear dynamics under timed constraints. First, the motion of the agents in the workspace is abstracted into individual Transition Systems (TS). Second, each agent is assigned with an individual formula given in Metric Interval Temporal Logic (MITL) and in parallel, the team of agents is assigned with a collaborative team formula. The proposed method is based on a correct-by-construction control synthesis method, and hence guarantees that the resulting closed-loop system will satisfy the specifications. The specifications considers boolean-valued properties under real-time. Extended simulations has been performed in order to demonstrate the efficiency of the proposed controllers.Keywords: Reachability analysis, verification and abstraction of hybrid systems, Multi-agent systems, Control design for hybrid systems, Modelling and control of hybrid and discrete event systems, Temporal Logic

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“…For this reason, research e orts have been focused on fragments of MTL with decidable satis ability, most notably Metric Interval Temporal Logic (MITL), the fragment of MTL in which 'punctual' constraining intervals are not allowed [3]. In particular, MITL formulae can be e ectively translated into timed automata (TAs) [2], giving practical EXPSPACE decision procedures for its satis ability and model-checking problems [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Revisiting timed logics with automata modalities

2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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It is well known that (timed) ω-regular properties such as 'p holds at every even position' and 'p occurs at least three times within the next 10 time units' cannot be expressed in Metric Interval Temporal Logic (MITL) and Event Clock Logic (ECL). A standard remedy to this de ciency is to extend these with modalities de ned in terms of automata. In this paper, we show that the logics EMITL 0,∞ (adding non-deterministic nite automata modalities into the fragment of MITL with only lower-and upper-bound constraints) and EECL (adding automata modalities into ECL) are already as expressive as EMITL (full MITL with automata modalities). In particular, the satis ability and model-checking problems for EMITL 0,∞ and EECL are PSPACE-complete, whereas the same problems for EMITL are EXPSPACE-complete. We also provide a simple translation from EMITL 0,∞ to diagonal-free timed automata, which enables practical satis ability and model checking based on o -the-shelf tools. CCS CONCEPTS• eory of computation → Timed and hybrid models; Logic and veri cation; Veri cation by model checking; KEYWORDS metric interval temporal logic, timed automata, model checking

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On MITL and Alternating Timed Automata

Cited by 12 publications

References 17 publications

Revisiting MITL to Fix Decision Procedures

Revisiting MITL to Fix Decision Procedures

Control Synthesis for Multi-Agent Systems under Metric Interval Temporal Logic Specifications * *This work was supported by the H2020 ERC Starting Grand BUCOPHSYS, the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF) and the Knut och Alice Wallenberg Foundation.

Revisiting timed logics with automata modalities

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