On the Expressiveness of TPTL and MTL over \omega-Data Words

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent extensions of Linear Temporal Logic to specify properties about data languages. In this paper, we consider the class of data languages of non-monotonic data words over the natural numbers. We prove that, in this setting, TPTL is strictly more expressive than MTL. To this end, we introduce Ehrenfeucht-Fraisse (EF) games for MTL. Using EF games for MTL, we also prove that the MTL definability decision problem ("Given a TPTL-formula, is the language defined by this formula definable in MTL?") is undecidable. We also define EF games for TPTL, and we show the effect of various syntactic restrictions on the expressiveness of MTL and TPTL.Comment: In Proceedings AFL 2014, arXiv:1405.527

Requirement verification in simulation-based automation testing

The emergence of the Industrial Internet results in an increasing number of complicated temporal interdependencies between automation systems and the processes to be controlled. There is a need for verification methods that scale better than formal verification methods and which are more exact than testing. Simulation-based runtime verification is proposed as such a method, and an application of Metric temporal logic is presented as a contribution. The practical scalability of the proposed approach is validated against a production process designed by an industrial partner, resulting in the discovery of requirement violations.Comment: 4 pages, 2 figures. Added IEEE copyright notic

Deciding the Satisfiability of MITL Specifications

In this paper 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.Comment: In Proceedings GandALF 2013, arXiv:1307.416

An Efficient Algorithm for Monitoring Practical TPTL Specifications

We provide a dynamic programming algorithm for the monitoring of a fragment of Timed Propositional Temporal Logic (TPTL) specifications. This fragment of TPTL, which is more expressive than Metric Temporal Logic, is characterized by independent time variables which enable the elicitation of complex real-time requirements. For this fragment, we provide an efficient polynomial time algorithm for off-line monitoring of finite traces. Finally, we provide experimental results on a prototype implementation of our tool in order to demonstrate the feasibility of using our tool in practical applications

On the expressiveness of MTL variants over dense time

Abstract. The basic modal operator bounded until of Metric Temporal Logic (MTL) comes in several variants. In particular it can be strict (when it does not constrain the current instant) or not, and matching (when it requires its two arguments to eventually hold together) or not. This paper compares the relative expressiveness of the resulting MTL variants over dense time. We prove that the expressiveness is not affected by the variations when considering non-Zeno interpretations and arbitrary nesting of temporal operators. On the contrary, the expressiveness changes for flat (i.e., without nesting) formulas, or when Zeno interpretations are allowed.

Model-checking Timed Temporal Logics

AbstractIn this paper, we present several timed extensions of temporal logics, that can be used for model-checking real-time systems. We give different formalisms and the corresponding decidability/complexity results. We also give intuition to explain these results

LNCS

Imprecision in timing can sometimes be beneficial: Metric interval temporal logic (MITL), disabling the expression of punctuality constraints, was shown to translate to timed automata, yielding an elementary decision procedure. We show how this principle extends to other forms of dense-time specification using regular expressions. By providing a clean, automaton-based formal framework for non-punctual languages, we are able to recover and extend several results in timed systems. Metric interval regular expressions (MIRE) are introduced, providing regular expressions with non-singular duration constraints. We obtain that MIRE are expressively complete relative to a class of one-clock timed automata, which can be determinized using additional clocks. Metric interval dynamic logic (MIDL) is then defined using MIRE as temporal modalities. We show that MIDL generalizes known extensions of MITL, while translating to timed automata at comparable cost

Efficient Large-scale Trace Checking Using MapReduce

The problem of checking a logged event trace against a temporal logic specification arises in many practical cases. Unfortunately, known algorithms for an expressive logic like MTL (Metric Temporal Logic) do not scale with respect to two crucial dimensions: the length of the trace and the size of the time interval for which logged events must be buffered to check satisfaction of the specification. The former issue can be addressed by distributed and parallel trace checking algorithms that can take advantage of modern cloud computing and programming frameworks like MapReduce. Still, the latter issue remains open with current state-of-the-art approaches. In this paper we address this memory scalability issue by proposing a new semantics for MTL, called lazy semantics. This semantics can evaluate temporal formulae and boolean combinations of temporal-only formulae at any arbitrary time instant. We prove that lazy semantics is more expressive than standard point-based semantics and that it can be used as a basis for a correct parametric decomposition of any MTL formula into an equivalent one with smaller, bounded time intervals. We use lazy semantics to extend our previous distributed trace checking algorithm for MTL. We evaluate the proposed algorithm in terms of memory scalability and time/memory tradeoffs.Comment: 13 pages, 8 figure