Temporal Logic Specifications Research Articles

Formal Requirement Debugging for Testing and Verification of Cyber-Physical Systems

A framework for the elicitation and debugging of formal specifications for Cyber-Physical Systems is presented. The elicitation of specifications is handled through a graphical interface. Two debugging algorithms are presented. The first checks for erroneous or incomplete temporal logic specifications without considering the system. The second can be utilized for the analysis of reactive requirements with respect to system test traces. The specification debugging framework is applied on a number of formal specifications collected through a user study. The user study establishes that requirement errors are common and that the debugging framework can resolve many insidious specification errors.

Application of formal verification and falsification to large-scale chemical plant automation systems

In this paper, we apply formal verification and falsification of temporal logic specifications to analyze chemical plant automation systems. We present new results, obtained by applying a recently-developed approach to handle combined invariance and reachability requirements. In addition, we develop a set of tests that can be generated automatically for a given control system, some of which have the same form as those in the existing literature, and some of which combine invariance and reachability, to which we apply the new approach mentioned previously. In both cases, we work with abstractions of the automation systems in order to apply symbolic model checking to industrial-scale problems. We demonstrate the results using a series of small illustrative examples, and also report results from an industrial case study. The methods that we apply are implemented in a pair of open-source software tools, which we describe briefly.

Cost-Aware Path Planning Under Co-Safe Temporal Logic Specifications

This letter presents a path planning algorithm for generating a cost-efficient path that satisfies mission requirements specified in linear temporal logic (LTL). We assume that a cost function is defined over the configuration space. Examples of a cost function include hazard levels, wireless connectivity, and energy consumption, to name a few. The proposed method consists of two parts: sampling-based cost-aware path planning considering the vehicle dynamics based on rapidly-exploring random trees (RRT*), and a high-level logic which determines how to extend the RRT tree based on spatiotemporal specifications of an LTL formula. In order to find a low-cost trajectory with computational efficiency, the proposed method expands the RRT tree with long extensions using cross entropy, while the rewiring step of RRT* is used to preserve the asymptotic optimality. In simulation and experiments, we show that the proposed method performs favorably compared to existing methods.

Policy learning in continuous-time Markov decision processes using Gaussian Processes

Continuous-time Markov decision processes provide a very powerful mathematical framework to solve policy-making problems in a wide range of applications, ranging from the control of populations to cyber–physical systems. The key problem to solve for these models is to efficiently compute an optimal policy to control the system in order to maximise the probability of satisfying a set of temporal logic specifications. Here we introduce a novel method based on statistical model checking and an unbiased estimation of a functional gradient in the space of possible policies. Our approach presents several advantages over the classical methods based on discretisation techniques, as it does not assume the a-priori knowledge of a model that can be replaced by a black-box, and does not suffer from state-space explosion. The use of a stochastic moment-based gradient ascent algorithm to guide our search considerably improves the efficiency of learning policies and accelerates the convergence using the momentum term. We demonstrate the strong performance of our approach on two examples of non-linear population models: an epidemiology model with no permanent recovery and a queuing system with non-deterministic choice.

An Approximate Dynamic Programming Approach to Multiagent Persistent Monitoring in Stochastic Environments With Temporal Logic Constraints

We consider the problem of generating control policies for a team of robots moving in a stochastic environment. The team is required to achieve an optimal surveillance mission, in which a certain “optimizing proposition” needs to be satisfied infinitely often. In addition, a correctness requirement expressed as a temporal logic formula is imposed. By modeling the robots as game transition systems and the environmental elements as Markov chains, the problem reduces to finding an optimal control policy for a Markov decision process, which also satisfies a temporal logic specification. The existing approaches based on dynamic programming are computationally intensive, thus not feasible for large environments and/or large numbers of robots. We propose an approximate dynamic programming (ADP) framework to obtain suboptimal policies with reduced computational complexity. Specifically, we choose a set of basis functions to approximate the optimal costs and find the best approximation through the least-squares method. We also propose a simulation-based ADP approach to further reduce the computational complexity by employing low-dimensional calculations and simulation samples.

Relaxing Exclusive Control in Boolean Games

In the typical framework for boolean games (BG) each player can change the truth value of some propositional atoms, while attempting to make her goal true. In standard BG goals are propositional formulas, whereas in iterated BG goals are formulas of Linear Temporal Logic. Both notions of BG are characterised by the fact that agents have exclusive control over their set of atoms, meaning that no two agents can control the same atom. In the present contribution we drop the exclusivity assumption and explore structures where an atom can be controlled by multiple agents. We introduce Concurrent Game Structures with Shared Propositional Control (CGS-SPC) and show that they ac- count for several classes of repeated games, including iterated boolean games, influence games, and aggregation games. Our main result shows that, as far as verification is concerned, CGS-SPC can be reduced to concurrent game structures with exclusive control. This result provides a polynomial reduction for the model checking problem of specifications in Alternating-time Temporal Logic on CGS-SPC.

Physics-based Motion Planning with Temporal Logic Specifications

One of the main foci of robotics is nowadays centered in providing a great degree of autonomy to robots. A fundamental step in this direction is to give them the ability to plan in discrete and continuous spaces to find the required motions to complete a complex task. In this line, some recent approaches describe tasks with Linear Temporal Logic (LTL) and reason on discrete actions to guide sampling-based motion planning, with the aim of finding dynamically-feasible motions that satisfy the temporal-logic task specifications. The present paper proposes an LTL planning approach enhanced with the use of ontologies to describe and reason about the task, on the one hand, and that includes physics-based motion planning to allow the purposeful manipulation of objects, on the other hand. The proposal has been implemented and is illustrated with didactic examples with a mobile robot in simple scenarios where some of the goals are occupied with objects that must be removed in order to fulfill the task.

Abstraction refinement and plan revision for control synthesis under high level specifications

This paper presents a novel framework combining abstraction refinement and plan revision for control synthesis problems under temporal logic specifications. The control problem is first solved on a simpler nominal model in order to obtain a satisfying plan to be followed by the real system. A controller synthesis is then attempted for an abstraction of the real system to follow this plan. Upon failure of this synthesis, cost functions are defined to guide towards either refining the initially coarse partition to obtain a finer abstraction, or looking for an alternative plan using the nominal model as above. This tentative synthesis is then repeated until a plan and an abstraction of the real system able to follow this plan are found. The obtained controller also ensures that the real system satisfies the initial specification.

Using progress sets on non-deterministic transition systems for multiple UAV motion planning

This paper presents a new approach for control synthesis of non-deterministic transition systems under Linear Temporal Logic specifications with applications to multiple Unmanned Aerial Vehicles (UAV) motion planning problems. The consideration of such systems is motivated by the non-determinism possibly introduced while abstracting dynamical systems into finite transition systems. More precisely, we consider transition systems enhanced with a progress set describing the fact that the system cannot stay indefinitely in some subset of states. The control synthesis problem is firstly translated into a terminating planning problem. Then, a backward reachability strategy searches for a path from the initial set to the goal set. At each iteration, subsets of states contained in the progress set are added to the path, thus ensuring the reachability to the goal set in finite time. If a solution to the terminating problem is found, the obtained controller is translated back to the initial problem formulation. This approach is validated through an experiment involving two UAVs with a surveillance specification.

Control Synthesis for Multi-Agent Systems under Metric Interval Temporal Logic Specifications

This paper presents a framework for automatic synthesis of a control sequence for multi-agent systems governed by continuous linear dynamics under timed constraints. First, the motion of the agents in the workspace is abstracted into individual Transition Systems (TS). Second, each agent is assigned with an individual formula given in Metric Interval Temporal Logic (MITL) and in parallel, the team of agents is assigned with a collaborative team formula. The proposed method is based on a correct-by-construction control synthesis method, and hence guarantees that the resulting closed-loop system will satisfy the desired specifications. The specifications considers boolean-valued properties under real-time bounds. Extended simulations has been performed in order to demonstrate the efficiency of the proposed methodology.

Multi-Objective Policy Generation for Mobile Robots under Probabilistic Time-Bounded Guarantees

We present a methodology for the generation of mobile robot controllers which offer probabilistic time-bounded guarantees on successful task completion, whilst also trying to satisfy soft goals. The approach is based on a stochastic model of the robot’s environment and action execution times, a set of soft goals, and a formal task specification in co-safe linear temporal logic, which are analysed using multi-objective model checking techniques for Markov decision processes. For efficiency, we propose a novel two-step approach. First, we explore policies on the Pareto front for minimising expected task execution time whilst optimising the achievement of soft goals. Then, we use this to prune a model with more detailed timing information, yielding a time-dependent policy for which more fine-grained probabilistic guarantees can be provided. We illustrate and evaluate the generation of policies on a delivery task in a care home scenario, where the robot also tries to engage in entertainment activities with the patients.

Mining parametric temporal logic properties in model-based design for cyber-physical systems

One of the advantages of adopting a Model Based Development (MBD) process is that it enables testing and verification at early stages of development. However, it is often desirable to not only verify/falsify certain formal system specifications, but also to automatically explore the properties that the system satisfies. In this work, we present a framework that enables property exploration for Cyber-Physical Systems. Namely, given a parametric specification with multiple parameters, our solution can automatically infer the ranges of parameters for which the property does not hold on the system. In this paper, we consider parametric specifications in Metric or Signal Temporal Logic (MTL or STL). Using robust semantics for MTL, the parameter mining problem can be converted into a Pareto optimization problem for which we can provide an approximate solution by utilizing stochastic optimization methods. We include algorithms for the exploration and visualization of multi-parametric specifications. The framework is demonstrated on an industrial size, high-fidelity engine model as well as examples from related literature.

MCXplore: Automating the Validation Process of DRAM Memory Controller Designs

We present an automated framework for the validation of memory controllers (MCs) called MCXplore. In developing this framework, we construct formal models for memory requests and command interactions. MCXplore enables validation engineers to define their test plans precisely using temporal logic specifications. We use the NuSMV model-checker to generate counterexamples that serve as test templates. MCXplore uses these test templates to generate memory tests to validate the correctness properties of the MC. We show the effectiveness of MCXplore by validating various state-of-the-art MC features as well as hard-to-detect timing violations. We also provide a set of predefined test plans, and regression test suites that validate essential properties of modern MCs. MCXplore is an open-source framework to allow validation engineers and researchers to extend and use.

The Reactive Synthesis Competition: SYNTCOMP 2016 and Beyond

We report on the design of the third reactive synthesis competition (SYNTCOMP 2016), including a major extension of the competition to specifications in full linear temporal logic. We give a brief overview of the synthesis problem as considered in SYNTCOMP, and present the rules of the competition in 2016, as well as the ideas behind our design choices. Furthermore, we evaluate the recent changes to the competition based on the experiences with SYNTCOMP 2016. Finally, we give an outlook on further changes and extensions of the competition that are planned for the future.

Automation and intelligent scheduling of distributed system functional testing

This paper presents the approach to functional test automation of services (black-box testing) and service architectures (grey-box testing) that has been developed within the MIDAS project and is accessible on the MIDAS SaaS. In particular, the algorithms and techniques adopted for addressing input and oracle generation, dynamic scheduling, and session planning issues supporting service functional test automation are illustrated. More specifically, the paper details: (i) the test input generation based on formal methods and temporal logic specifications, (ii) the test oracle generation based on service formal specifications, (iii) the dynamic scheduling of test cases based on probabilistic graphical reasoning, and (iv) the reactive, evidence-based planning of test sessions with on-the-fly generation of new test cases. Finally, the utilisation of the MIDAS prototype for the functional test of operational services and service architectures in the healthcare industry is reported and assessed. A planned evolution of the technology deals with the testing and troubleshooting of distributed systems that integrate connected objects.

Synthesis of Joint Control and Active Sensing Strategies Under Temporal Logic Constraints

This paper proposes an approach to control of discrete systems with incomplete information and sensing capabilities, with respect to temporal logic constraints. The approach introduces active sensing to alleviate computational effort in control design for systems interacting with uncontrollable environments under incomplete information. Particularly, it transforms a deterministic controller under complete information into a randomized, observation-based controller. Interleaving the latter with strategic queries to sensors, the temporal logic specification is proven to be satisfied almost surely. The effectiveness of the method is demonstrated with robotic motion planning examples.

Route Guidance for Satisfying Temporal Logic Specifications on Aircraft Motion

A new technique for aircraft route guidance subject to linear temporal logic specifications is presented. The proposed approach is based on workspace partitioning, and it relies on the idea of so-called lifted graphs. Briefly, edges in a lifted graph are successions of adjacent edges in the topological graph associated with the workspace partition. Edges of the lifted graph are associated with certain reachability properties of the aircraft model. The main result of this paper is the precise characterization of acceptable routes (namely, sequences of cells) that are guaranteed to be traversable by admissible state trajectories of the aircraft model while satisfying the given linear temporal logic specifications. The proposed approach incorporates nonholonomic kinematic constraints, does not require complete controllability in the presence of workspace constraints, and does not require linearization of the aircraft model. Numerical methods to implement the proposed route-planning algorithm are discussed. The proposed algorithm is illustrated with numerical simulation examples that reflect the practical significance of linear temporal logic specifications in aircraft guidance.

Distributed PROMPT-LTL Synthesis

We consider the synthesis of distributed implementations for specifications in Prompt Linear Temporal Logic (PROMPT-LTL), which extends LTL by temporal operators equipped with parameters that bound their scope. For single process synthesis it is well-established that such parametric extensions do not increase worst-case complexities. For synchronous systems, we show that, despite being more powerful, the distributed realizability problem for PROMPT-LTL is not harder than its LTL counterpart. For asynchronous systems we have to consider an assume-guarantee synthesis problem, as we have to express scheduling assumptions. As asynchronous distributed synthesis is already undecidable for LTL, we give a semi-decision procedure for the PROMPT-LTL assume-guarantee synthesis problem based on bounded synthesis.

Correct-by-Construction Adaptive Cruise Control: Two Approaches

Motivated by the challenge of developing control software provably meeting specifications for real-world problems, this paper applies formal methods to adaptive cruise control (ACC). Starting from a linear temporal logic specification for ACC, obtained by interpreting relevant ACC standards, we discuss in this paper two different control software synthesis methods. Each method produces a controller that is correct-by-construction, meaning that trajectories of the closed-loop systems provably meet the specification. Both methods rely on fixed-point computations of certain set-valued mappings. However, one of the methods performs these computations on the continuous state space whereas the other method operates on a finite-state abstraction. While controller synthesis is based on a low-dimensional model, each controller is tested on CarSim, an industry-standard vehicle simulator. Our results demonstrate several advantages over classical control design techniques. First, a formal approach to control design removes potential ambiguity in textual specifications by translating them into precise mathematical requirements. Second, because the resulting closed-loop system is known a priori to satisfy the specification, testing can then focus on the validity of the models used in control design and whether the specification captures the intended requirements. Finally, the set from where the specification (e.g., safety) can be enforced is explicitly computed and thus conditions for passing control to an emergency controller are clearly defined.

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.