Metric Temporal Logic Specifications Research Articles

Distributed runtime verification of metric temporal properties

Distributed Systems are often composed of geographically separated components, where the clocks may not be perfectly synchronized. As such verifying the correctness of such system properties are a major challenge and are of utmost importance. In this paper, we describe a centralized runtime monitoring technique for distributed system. First, we propose a generalized runtime verification technique for verifying partially synchronous distributed computations for the metric temporal logic (MTL) by exploiting bounded-skew clock synchronization. Second, we introduce a progression-based formula rewriting scheme for monitoring MTL specifications which employs SMT solving techniques and report experimental results. Third, we also quantify each event according to the possible time of occurrence and calculate the probabilistic guarantee for generating the verification verdict. Lastly, we have implemented the entire procedure and report on extensive synthetic experimental results using UPPAAL, a set of cross-chain transactions implemented on Ethereum and an Industrial Control System of a water treatment plant.

Controlling timed automata against MTL specifications with TACoS

TACoS is a tool for synthesizing controllers against specifications of undesired behavior with timing constraints. Given a timed automaton and an MTL specification, the tool synthesizes a controller that guarantees that every possible execution of the system satisfies the given specification. TACoS comes with a C++ library with a simple-to-use API and can read from and write to human-readable text input and output. In this paper, we outline the approach of the tool and present two examples in further detail. • TACoS is a tool for controller synthesis against specifications with timing constraints. • The tool supports full Metric Temporal Logic (MTL) as specification language. • It provides a C++ library with a simple-to-use API. • It also supports human-readable text input and output. • It uses several techniques such as heuristic search to improve performance.

A More Scalable Mixed-Integer Encoding for Metric Temporal Logic

The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is sound and complete, but struggles to scale to long and complex specifications. Drawing on recent advances in trajectory optimization for piecewise-affine systems, we propose a new MICP encoding for finite transition systems that significantly improves scalability to long and complex MTL specifications. Rather than seeking to reduce the number of variables in the MICP, we focus instead on designing an encoding with a tight convex relaxation. This leads to a larger optimization problem, but significantly improves branch-and-bound solver performance. In simulation experiments involving a mobile robot in a grid-world, the proposed encoding can reduce computation times by several orders of magnitude.

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.

Fast, Composable Rescue Mission Planning for UAVs using Metric Temporal Logic

We present a hybrid compositional approach for real-time mission planning for multi-rotor unmanned aerial vehicles (UAVs) in a time critical search and rescue scenario. Starting with a known environment, we specify the mission using Metric Temporal Logic (MTL) and use a hybrid dynamical model to capture the various modes of UAV operation. We then divide the mission into several sub-tasks by exploiting the invariant nature of safety and timing constraints along the way, and the different modes (i.e., dynamics) of the UAV. For each sub-task, we translate the MTL specifications into linear constraints and solve the associated optimal control problem for desired path, using a Mixed Integer Linear Program (MILP) solver. The complete path for the mission is constructed recursively by composing the individual optimal sub-paths. We show by simulations that the resulting suboptimal trajectories satisfy the mission specifications, and the proposed approach leads to significant reduction in computational complexity of the problem, making it possible to implement in real-time. Our proposed method ensures the safety of UAVs at all times and guarantees finite time mission completion. It is also shown that our approach scales up nicely for a large number of UAVs.

Energy Storage Controller Synthesis for Power Systems With Temporal Logic Specifications

We present an energy storage controller synthesis method for power systems with respect to metric temporal logic (MTL) specifications. The power systems with both constant impedance loads and constant power loads are modeled as a set of differential–algebraic equations. After a fault is cleared, with uncertainties in the fault clearing time, the generator machine angles and rotor speed deviations will enter a set of postfault initial states. We use the robust neighborhood approach to cover this set using the initial robust neighborhoods of finitely many simulated postfault trajectories. These simulated postfault trajectories meet the frequency regulation requirements specified in MTL as they are driven by the optimal control input signals obtained through a functional gradient descent approach. In this way, all the possible postfault trajectories with the given uncertainties in the fault clearing time are guaranteed to satisfy the MTL specification. Furthermore, we learn a piecewise linear control law from the data of the simulated trajectories to generate a feedback controller.

Robustness of temporal logic specifications for continuous-time signals

In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with non-trivial metrics, for example continuous or hybrid, robustness is not only natural, but also a critical measure of system performance. Thus, we propose multi-valued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε , from unsatisfiability. We prove that any other signal that remains ε -close to the initial one also satisfies the same MTL specification under the usual Boolean semantics. Finally, our framework is applied to the problem of testing formulas of two fragments of MTL, namely Metric Interval Temporal Logic (MITL) and closed Metric Temporal Logic (clMTL), over continuous-time signals using only discrete-time analysis. The motivating idea behind our approach is that if the continuous-time signal fulfills certain conditions and the discrete-time signal robustly satisfies the temporal logic specification, then the corresponding continuous-time signal should also satisfy the same temporal logic specification.