Reactive synthesis with maximum realizability of linear temporal logic specifications

Abstract

A challenging problem for autonomous systems is to synthesize a reactive controller that conforms to a set of given correctness properties. Linear temporal logic (LTL) provides a formal language to specify the desired behavioral properties of systems. In applications in which the specifications originate from various aspects of the system design, or consist of a large set of formulas, the overall system specification may be unrealizable. Driven by this fact, we develop an optimization variant of synthesis from LTL formulas, where the goal is to design a controller that satisfies a set of hard specifications and minimally violates a set of soft specifications. To that end, we introduce a value function that, by exploiting the LTL semantics, quantifies the level of violation of properties. Inspired by the idea of bounded synthesis, we fix a bound on the implementation size and search for an implementation that is optimal with respect to the said value function. We propose a novel maximum satisfiability encoding of the search for an optimal implementation (within the given bound on the implementation size). We iteratively increase the bound on the implementation size until a termination criterion, such as a threshold over the value function, is met.

Finite-Horizon Shield for Path Planning Ensuring Safety/Co-Safety Specifications and Security Policies

“…where H p is the length of ρ p and V p (π ) = L p (ρ p ). We assume that path specification ϕ p is partitioned into a mandatory and an optional specification, that is, ϕ p := ϕ s ∧ϕ o , where ϕ s and ϕ o represent the mandatory and the optional specification, respectively: a similar partition of the specification was proposed in [58] and [19]. The mandatory specification is related to safety or co-safety properties and it should be satisfied even after modification.…”

“…Specifications have become complex owing to recent advances in automated systems, and temporal logics are useful tools for their detailed descriptions [10], [11]. Linear temporal logic (LTL) formulas are typically used for logical specifications in synthesis problems [12], and numerous reactive synthesis problems for LTL specifications have been studied [13], [14], [15], [16], [17], [18], [19]. Signal temporal logic (STL) formulas can describe the dynamic properties of real-valued continuous signals [20], [21], and they have been applied to controller synthesis problems [22], [23], [24].…”

Synthesis of Cost-Optimal Multi-Agent Systems for Resource Allocation

“…To the best of our knowledge, our technique is the first Max-SAT-based approach to the synthesis of cost-optimal strategies for multi-agent systems. In related fields, Max-SAT has been employed to find optimal coalitions of agents for solving network security problems [15], to synthesise reactive controllers of autonomous systems [9], and to model check quantitative hyper-properties [10].…”