Maximum Realizability for Linear Temporal Logic Specifications

Abstract

Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning, control of autonomous systems, and load distribution in power networks. A common specification pattern in such applications consists of an LTL formula describing the requirements on the behaviour of the system, together with a set of additional desirable properties. We study the synthesis problem in settings where the overall specification is unrealizable, more precisely, when some of the desirable properties have to be (temporarily) violated in order to satisfy the system's objective. We provide a quantitative semantics of sets of safety specifications, and use it to formalize the "besteffort" satisfaction of such soft specifications while satisfying the hard LTL specification. We propose an algorithm for synthesizing implementations that are optimal with respect to this quantitative semantics. Our method builds upon the idea of the bounded synthesis approach, and we develop a MaxSAT encoding which allows for maximizing the quantitative satisfaction of the safety specifications. We evaluate our algorithm on scenarios from robotics and power distribution networks.

Rule-based optimal control for autonomous driving

“…After we determine which rules (i.e., S r (t)) need to be relaxed through the receding horizon approach introduced above, we apply the control from solving (20) with k = 0 only one time step forward at the current time. This is due to the fact that the state estimation errors of the instances and the error of the predictive model (18) with respect to (1) increases as k increases.…”

MaxSAT Evaluation 2018: New Developments and Detailed Results

“…max-realizability. These are a set of instances involving the synthesis of systems satisfying a collection of linear temporal logic (LTL) formulas (specifications) [12]. If the synthesized system satisfies one of the LTL formulas f , then f is said to be realized.…”

Reactive synthesis with maximum realizability of linear temporal logic specifications

“…Thus, we conclude that T |= ψ v . Clearly, ψ v also satisfies condition (1). Now, consider a transition system T with T |= ψ v .…”

“…We implemented the proposed approach to maximum realizability 1 Each experiment was run on a machine with a 2.3 GHz Intel Xeon E5-2686 v4 processor and 16 GiB of memory. While the processor is quad-core, only a single core was used.…”

“…Lastly, Section 7 states the concluding remarks and future directions. This paper is an extension of the conference publication [1]. It contains the complete proofs and presents (Section 5.4) a generalization of the maximum realizability problem to soft specifications in the full class of LTL formulas and to prioritized specifications.…”