On MITL and Alternating Timed Automata over Infinite Words

Brihaye, Thomas; Estiévenart, Morgane; Geeraerts, Gilles

doi:10.1007/978-3-319-10512-3_6

Cited by 9 publications

(25 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Formula (15) states that for θ to become true with a rising edge in t, γ must also become true (possibly in a singular manner). This is sufficient if t " 0.…”

Section: Reduction Of Mitl+past To Cltlocmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Hence, the delay between change points of Future can be measured by a finite set of clocks, whose cardinality depends on the constants a, b. Recent works by [14,15] propose an automata-based approach to MITL by a translation into alternating timed automata, which could allow for efficient implementations in the case of the less general pointwise semantics (i.e., when interpreting formulae over timed words rather than over signals).Rather than going through a translation into Timed Automata, in this paper we propose a new logic-based approach, which still exploits the previous property of the finite number of clocks for Future (and Until) formulae. Our work also assumes the continuous semantics of MITL over finitely-variable models.…”

mentioning

confidence: 99%

See 2 more Smart Citations

An SMT-based approach to satisfiability checking of MITL

Bersani¹,

Rossi²,

Pietro³

2015

Information and Computation

View full text Add to dashboard Cite

We present a satisfiability-preserving reduction from MITL interpreted over finitely-variable continuous behaviors to Constraint LTL over clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded satisfiability checker is available. The result is a new complete and effective decision procedure for MITL. Although decision procedures for MITL already exist, the automata-based techniques they employ appear to be very difficult to realize in practice, and, to the best of our knowledge, no implementation currently exists for them. A prototype tool for MITL based on the encoding presented here has, instead, been implemented and is publicly available. IntroductionComputer systems are inherently discrete-time objects, but their application to real-time control and monitoring often requires to deal with external asynchronous events that may not always happen at integer-valued times. Hence, a discrete-time assumption requires to approximate continuous time by choosing some fixed minimal interval, thus limiting the accuracy of modeling, verification and validation of such systems. To overcome this restriction, many continuoustime models have been developed, most notably Timed Automata [4], a densetime operational model based on finite-state machines, but also descriptive models such as the continuous-time temporal logics MTL (Metric Temporal Logic) [5,6] and MITL (Metric Interval Temporal Logic) [6]. In general, the role of temporal logics in verification and validation is two-fold. First, temporal logic allows abstract, concise and convenient expression of required properties of $ This research was supported by the Programme IDEAS-ERC, Project 227977-SMScom, and by PRIN Project 2010LYA9RH. $$ Parts of this work were previously published in [1], [2] and [3], of which this article is an extension.Email addresses: marcellomaria.bersani@polimi.it (Marcello M. Bersani), matteo.rossi@polimi.it (Matteo Rossi), pierluigi.sanpietro@polimi.it (Pierluigi San Pietro) Preprint submitted to ElsevierJanuary 9, 2015 a system. Linear Temporal Logic (LTL) is often used with this goal in the verification of finite-state models, e.g., in model checking [7]. Second, temporal logic allows a descriptive approach to specification and modeling (see, e.g., [8,9]). A descriptive model is based on axioms, written in some (temporal) logic, defining a system by means of its general properties, rather than by an operational model based on some kind of machine (e.g., a Timed Automaton) behaving in the desired way. In this case, verification typically consists of satisfiability checking of the conjunction of the model and of the (negation of) its desired properties. An example of the latter approach is Bounded Satisfiability Checking (BSC) [10], where MTL specifications and properties on discrete time are translated into Boolean logic, in an approach similar to Bounded Model Checking of LTL properties of finite-state machines.In general, verification of continuous-time temporal logics is not as well supported as for discre...

show abstract

“…Formula (15) states that for θ to become true with a rising edge in t, γ must also become true (possibly in a singular manner). This is sufficient if t " 0.…”

Section: Reduction Of Mitl+past To Cltlocmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

An SMT-based approach to satisfiability checking of MITL

Bersani¹,

Rossi²,

Pietro³

2015

Information and Computation

View full text Add to dashboard Cite

show abstract

“…As for pointwise semantics, in previous papers [9,8], we have provided a constructions and a tool component (Casaal) for translating the safety fragment and co-safety of MTL0,∞ into timed automata. In a recent paper [6], Thomas Brihaye et al proposed a technique to translate MITL into Timed Büchi Automata through alternating timed automata. Their approach is based on a new (interval) semantics, where clock valuations are not real values, but intervals with real endpoints.…”

Section: Introductionmentioning

confidence: 99%

Practical controller synthesis for MTL _0,∞

Jensen

Larsen

et al. 2017

Proceedings of the 24th ACM SIGSOFT International SPIN Symposium on Model Checking of Software

View full text Add to dashboard Cite

Metric Temporal Logic MTL0,∞ is a timed extension of linear temporal logic, LTL, with time intervals whose left endpoints are zero or whose right endpoints are infinity. Whereas the satisfiability and model-checking problems for MTL0,∞ are both decidable, we note that the controller synthesis problem for MTL0,∞ is unfortunately undecidable. As a remedy of this we propose an approximate method to the synthesis problem, which we demonstrate to be adequate and scalable to practical examples. We define a method for converting MTL0,∞ formulas into (nondeterministic) Timed Game Büchi Automata and furthermore show how to construct determinized over-and underapproximation of a such. For the proposed method, we present a toolchain seamlessly integrating the needed components for practical MTL0,∞ synthesis. Lastly we demonstrate on a number of case-studies the applicability and scalability of the proposed method.

show abstract

“…Therefore, their algorithm does not fix the problem in [2]. Papers [4,5] present decision procedures for an event-based semantics for MITL which associates a time with every event. State-based semantics, considered here and in [2,8], is very different.…”

Section: Introductionmentioning

confidence: 99%

Revisiting MITL to Fix Decision Procedures

Roohi

Viswanathan

2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

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.

show abstract

On MITL and Alternating Timed Automata over Infinite Words

Cited by 9 publications

References 18 publications

An SMT-based approach to satisfiability checking of MITL

An SMT-based approach to satisfiability checking of MITL

Practical controller synthesis for MTL _0,∞

Revisiting MITL to Fix Decision Procedures

Contact Info

Product

Resources

About

On MITL and Alternating Timed Automata over Infinite Words

Cited by 9 publications

References 18 publications

An SMT-based approach to satisfiability checking of MITL

An SMT-based approach to satisfiability checking of MITL

Practical controller synthesis for MTL 0,∞

Revisiting MITL to Fix Decision Procedures

Contact Info

Product

Resources

About

Practical controller synthesis for MTL _0,∞