Timed Trace Alignment with Metric Temporal Logic over Finite Traces

Trace Alignment is a prominent problem in Declarative Process Mining, which consists in identifying a minimal set of modifications that a log trace (produced by a system under execution) requires in order to be made compliant with a temporal specification. In its simplest form, log traces are sequences of events from a finite alphabet and specifications are written in DECLARE, a strict sublanguage of linear-time temporal logic over finite traces (LTLf ). The best approach for trace alignment has been developed in AI, using cost-optimal planning, and handles the whole LTLf . In this paper, we study the timed version of trace alignment, where events are paired with timestamps and specifications are provided in metric temporal logic over finite traces (MTLf ), essentially a superlanguage of LTLf . Due to the infiniteness of timestamps, this variant is substantially more challenging than the basic version, as the structures involved in the search are (uncountably) infinite-state, and calls for a more sophisticated machinery based on alternating (timed) automata, as opposed to the standard finite-state automata sufficient for the untimed version. The main contribution of the paper is a provably correct, effective technique for Timed Trace Alignment that takes advantage of results on MTLf decidability as well as on reachability for well-structured transition systems.

Control strategies for COVID-19 epidemic with vaccination, shield immunity and quarantine: A metric temporal logic approach

Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can specify the expected control outcomes such as “the deaths from the infection should never exceed one thousand per day within the next three months” or “the population immune from the disease should eventually exceed 200 thousand within the next 100 to 120 days”. We then develop methods for synthesizing control strategies with MTL specifications. To the best of our knowledge, this is the first paper to systematically synthesize control strategies based on the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results also show that early intervention is essential in mitigating the spread of COVID-19, and more control effort is needed for more stringent MTL specifications. For example, based on the model in Lombardy, Italy, achieving less than 100 deaths per day and 10000 total deaths within 100 days requires 441.7% more vaccination control effort than achieving less than 1000 deaths per day and 50000 total deaths within 100 days.

Algebraic Quantitative Semantics for Efficient Online Temporal Monitoring

We investigate efficient algorithms for the online monitoring of properties written in metric temporal logic (MTL). We employ an abstract algebraic semantics based on semirings. It encompasses the Boolean semantics and a quantitative semantics capturing the robustness of satisfaction, which is based on the max-min semiring over the extended real numbers. We provide a precise equational characterization of the class of semirings for which our semantics can be viewed as an approximation to an alternative semantics that quantifies the distance of a system trace from the set of all traces that satisfy the desired property.

Theorem Proving for Pointwise Metric Temporal Logic Over the Naturals via Translations

We study translations from metric temporal logic (MTL) over the natural numbers to linear temporal logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the complexity of the satisfiability problem for MTL. In each of these approaches we consider the case where the mapping between states and time points is given by (i) a strict monotonic function and by (ii) a non-strict monotonic function (which allows multiple states to be mapped to the same time point). We use this logic to model examples from robotics, traffic management, and scheduling, discussing the effects of different modelling choices. Our translations allow us to utilise LTL solvers to solve satisfiability and we empirically compare the translations, showing in which cases one performs better than the other. We also define a branching-time version of the logic and provide translations into computation tree logic.