Specifying real-time properties with metric temporal logic
Real-Time Systems
The temporal specification and verification of real-time systems
The temporal specification and verification of real-time systems
The benefits of relaxing punctuality
Journal of the ACM (JACM)
Logics and Models of Real Time: A Survey
Proceedings of the Real-Time: Theory in Practice, REX Workshop
On the Decidability of Metric Temporal Logic
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
On synthesizing controllers from bounded-response properties
CAV'07 Proceedings of the 19th international conference on Computer aided verification
From MTL to deterministic timed automata
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
On metric temporal logic and faulty turing machines
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Real time temporal logic: past, present, future
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
On the expressiveness of MTL with past operators
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
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Construction of automata for Metric Temporal Logics has been an active but challenging area of research. We consider here the continuous time Metric temporal logic MTL[UI, SI] as well as corresponding signal automata. In previous works by Maler, Nickovic and Pnueli, the signal automaton synthesis has mainly addressed MTL under an assumption of bounded variability. In this paper, we propose a novel technique of "Temporal Projections" that allows easy synthesis of safety signal automata for continuous time MITL[UI, SI] over finite signals without assuming bounded variability. Using the same technique, we also give synthesis of safety signal automata for MITL[UI, SI] with bounded future operators over infinite signals. For finite signals, the Temporal Projections allow us to syntactically transform an MITL formula φ(Q) over a set of propositions Q to a pure past time MITL formula ψ(P,Q) with extended set of propositions (P,Q) which is language equivalent "modulo temporal projection", i.e. L(φ) = L(∃P.ċψ). A similar such transformation over infinite signals is also formulated for MITL[UI, SI] restricted to Bounded Future formlae where the Until operators use only bounded (i.e.non-infinite) intervals. It is straightforward to construct safety-signal-automaton for the transformed formula. We give complexity bounds for the resulting automaton. Our temporal projections are inspired by the use of projections by D'Souza et al for eliminating past in MTL.