Reactive Synthesis Beyond Realizability (Invited Tutorial)

The automatic synthesis of reactive systems from high-level specifications is a highly attractive and increasingly viable alternative to manual system design, with applications in a number of domains such as robotic motion planning, control of autonomous systems, and development of communication protocols. The idea of asking the system designer to describe what the system should do instead of how exactly it does it holds a great promise. However, providing the right formal specification of the desired behavior of a system is a challenging task in itself. In practice it often happens that the system designer provides a specification that is unrealizable, that is, there is no implementation that satisfies it. Such situations typically arise because the desired behavior represents a trade-off between multiple conflicting requirements, or because crucial assumptions about the environment in which the system will execute are missing. Addressing such scenarios necessitates a shift towards synthesis algorithms that utilize quantitative measures of system correctness. In this tutorial, I will discuss two recent advances in this research direction. First, I will talk about the maximum realizability problem, where the input to the synthesis algorithm consists of a hard specification that must be satisfied by the synthesized system, and soft specifications which describe other desired, possibly prioritized properties, whose violation is acceptable. I will present a synthesis algorithm that maximizes a quantitative value associated with the soft specifications while guaranteeing the satisfaction of the hard specification. In the second half of the tutorial, I will present algorithms for synthesis in bounded environments, where a bound is associated with the sequences of input values produced by the environment. More concretely, these sequences consist of an initial prefix followed by a finite sequence repeated infinitely often, and satisfy the constraint that the sum of the lengths of the initial prefix and the loop does not exceed a given bound. I will also discuss the synthesis of approximate implementations from unrealizable specifications, which are guaranteed to satisfy the specification on at least a specified portion of the bounded-size input sequences. I will conclude by outlining some of the open avenues and challenges in quantitative synthesis from temporal logic specifications

Max-SAT-based synthesis of optimal and Nash equilibrium strategies for multi-agent systems

We present techniques for verifying strategic abilities of multi-agent systems via SAT-based and Max-SAT-based bounded model checking. In our approach we focus on systems of agents that pursue goals with regard to the allocation of shared resources. One of the problems to be solved is to determine whether a coalition of agents has a joint strategy that guarantees the achievement of all resource goals, irrespective of how the opposing agents in the system act. Our approach does not only decide whether such a winning strategy exists, but also synthesises the strategy. Winning strategies are particularly useful in the presence of an opposition because they guarantee that each agent of the coalition will achieve its individual goal, no matter how the opposition behaves. However, for the grand coalition consisting of all agents in the system, following a winning strategy may involve an inefficient use of resources. A winning strategy will only ensure that each agent will reach its goal at some time. But in practical resource allocation problems it may be of additional importance that once-off resource goals will be achieved as early as possible or that repetitive goals will be achieved as frequent as possible. We present an extended technique that synthesises strategies that are collectively optimal with regard to such quantitative performance criteria. A collectively optimal strategy allows to optimise the overall system performance but it may favour certain agents over others. In competitive scenarios a Nash equilibrium strategy may be a more adequate solution. It guarantees that no agent can improve its individual performance by unilaterally deviating from the strategy. We developed an algorithm that initially generates a collectively optimal strategy and then iteratively alternates this strategy until the strategy becomes a Nash equilibrium or a cycle of non-equilibrium strategies is detected. Our approach is based on a propositional logic encoding of strategy synthesis problems. We reduce the synthesis of winning strategies to the Boolean satisfiability problem and the synthesis of optimal and Nash equilibrium strategies to the maximum satisfiability problem. Hence, efficient SAT- and Max-SAT solvers can be employed to solve the encoded strategy synthesis problemshttp://www.elsevier.com/locate/scicoam2024Computer ScienceSDG-09: Industry, innovation and infrastructur

Reactive synthesis with maximum realizability of linear temporal logic specifications

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

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing