Linear temporal logic

In logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc. It is a fragment of the more complex CTL*, which additionally allows branching time and quantifiers. LTL is sometimes called propositional temporal logic, abbreviated PTL. In terms of expressive power, linear temporal logic (LTL) is a fragment of first-order logic. LTL was first proposed for the formal verification of computer programs by Amir Pnueli in 1977. Syntax LTL is built up from a finite set of propositional variables AP, the logical operators ¬ and ∨, and the temporal modal operators X (some literature uses O or N) and U. Formally, the set of LTL formulas over AP is inductively defined as follows:

if p ∈ AP then p is an LTL formula;
if ψ and φ are LTL formulas then ¬ψ, φ

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Verifying real-time systems goes beyond the verification of functional properties: it also requires the checking of real-time properties. This makes traditional contract-frameworks partially inept for checking real-time programs. This is a major problem because the failure of real-time and safety critical systems can have serious consequences. This thesis presents a solution to this problem by incorporating Design by Contract (annotating programs with function pre and post conditions) to such systems. The main contribution of this thesis is the development of a contract framework for cyclic real-time control applications written in C++. The contract framework allows the users to specify both functional and temporal properties for the applications. A novel approach of empirical cumulative distribution function (cdf ) based statistical inference is used for dynamically estimating temporal constraints and incorporating them in future contracts. The thesis also illustrates the use of Real-time Logic (RTL) for formal specification of the temporal properties. For evaluating our methodology, we have integrated it to a component-based framework called FASA (Future Automation System Architecture) developed at ABB Corporate Research for writing hard real time control applications. Experiments show that this contract framework can be smoothly integrated to existing control applications thereby increasing their reliability while having a acceptable overhead (less than 10%) on the performance.

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From Uncertainty Data to Robust Policies for Temporal Logic Planning

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving.

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