E. Allen Emerson was the first graduate student of Edmund M. Clarke at Harvard University. After discussing several ideas for Allen's dissertation, they identified a promising candidate: verifying a finite-state system against a formal specification. According to Martha Clarke, Edmund's widow, it was during a walk across Harvard Yard that they decided to call it "model checking." Emerson received his Ph.D. in applied mathematics for this work in 1981. Twenty-five years later, he and Clarke (along with Joseph Sifakis) shared the ACM A.M. Turing Award in 2007 for this and related work.

With artificial intelligence (AI) being well established within the daily lives of research communities, we turn our gaze toward an application area that appears intuitively unsuited for probabilistic decision-making: the area of formal methods (FM). FM aim to provide sound and understandable reasoning about problems in computer science, which seemingly collides with the black-box nature that inhibits many AI approaches. However, many researchers have crossed this gap and applied AI techniques to enhance FM approaches. As this dichotomy of FM and AI sparked our interest, we conducted a systematic mapping study to map the current landscape of research publications. In this study, we investigate the previous five years of applied AI to FM (2019-2023), as these correspond to periods of high activity. This investigation results in 189 entries, which we explore in more detail to find current trends, highlight research gaps, and give suggestions for future research.

This paper describes use of model checking to verify synchronisation properties of an industrial welding system consisting of a cobot arm and an external turntable. The robots must move synchronously, but sometimes get out of synchronisation, giving rise to unsatisfactory weld qualities in problem areas, such as around corners. These mistakes are costly, since time is lost both in the robotic welding and in manual repairs needed to improve the weld. Verification of the synchronisation properties has shown that they are fulfilled as long as assumptions of correctness made about parts outside the scope of the model hold, indicating limitations in the hardware. These results have indicated the source of the problem, and motivated a re-calibration of the real-life system. This has drastically improved the welding results, and is a demonstration of how formal methods can be useful in an industrial setting.

Formal verification of robotic applications presents challenges due to their hybrid nature and distributed architecture. This paper introduces ROSMonitoring 2.0, an extension of ROSMonitoring designed to facilitate the monitoring of both topics and services while considering the order in which messages are published and received. The framework has been enhanced to support these novel features for ROS1 -- and partially ROS2 environments -- offering improved real-time support, security, scalability, and interoperability. We discuss the modifications made to accommodate these advancements and present results obtained from a case study involving the runtime monitoring of specific components of a fire-fighting Uncrewed Aerial Vehicle (UAV).

Behavior Trees (BTs) are high-level controllers that are useful in a variety of planning tasks and are gaining traction in robotic mission planning. As they gain popularity in safety-critical domains, it is important to formalize their syntax and semantics, as well as verify properties for them. In this paper, we formalize a class of BTs we call Stateful Behavior Trees (SBTs) that have auxiliary variables and operate in an environment that can change over time. SBTs have access to persistent shared memory (often known as a blackboard) that keeps track of these auxiliary variables. We demonstrate that SBTs are equivalent in computational power to Turing Machines when the blackboard can store mathematical (i.e., unbounded) integers. We further identify syntactic assumptions where SBTs have computational power equivalent to finite state automata, specifically where the auxiliary variables are of finitary types. We present a domain specific language (DSL) for writing SBTs and adapt the tool BehaVerify for use with this DSL. This new DSL in BehaVerify supports interfacing with popular BT libraries in Python, and also provides generation of Haskell code and nuXmv models, the latter of which is used for model checking temporal logic specifications for the SBTs. We include examples and scalability results where BehaVerify outperforms another verification tool by a factor of 100.

This EPTCS volume contains the papers from the Sixth International Workshop on Formal Methods for Autonomous Systems (FMAS 2024), which was held between the 11th and 13th of November 2024. FMAS 2024 was co-located with 19th International Conference on integrated Formal Methods (iFM'24), hosted by the University of Manchester in the United Kingdom, in the University of Manchester's Core Technology Facility.

Quantitative automata are useful representations for numerous applications, including modeling probability distributions over sequences to Markov chains and reward machines. Actively learning such automata typically occurs using explicitly gathered input-output examples under adaptations of the L-star algorithm. However, obtaining explicit input-output pairs can be expensive, and there exist scenarios, including preference-based learning or learning from rankings, where providing constraints is a less exerting and a more natural way to concisely describe desired properties. Consequently, we propose the problem of learning deterministic quantitative automata from sets of constraints over the valuations of input sequences. We present QUINTIC, an active learning algorithm, wherein the learner infers a valid automaton through deductive reasoning, by applying a theory to a set of currently available constraints and an assumed preference model and quantitative automaton class. QUINTIC performs a complete search over the space of automata, and is guaranteed to be minimal and correctly terminate. Our evaluations utilize theory of rationals in order to learn summation, discounted summation, product, and classification quantitative automata, and indicate QUINTIC is effective at learning these types of automata.

We introduce LTLf+ and PPLTL+, two logics to express properties of infinite traces, that are based on the linear-time temporal logics LTLf and PPLTL on finite traces. LTLf+/PPLTL+ use levels of Manna and Pnueli's LTL safety-progress hierarchy, and thus have the same expressive power as LTL. However, they also retain a crucial characteristic of the reactive synthesis problem for the base logics: the game arena for strategy extraction can be derived from deterministic finite automata (DFA). Consequently, these logics circumvent the notorious difficulties associated with determinizing infinite trace automata, typical of LTL reactive synthesis. We present DFA-based synthesis techniques for LTLf+/PPLTL+, and show that synthesis is 2EXPTIME-complete for LTLf+ (matching LTLf) and EXPTIME-complete for PPLTL+ (matching PPLTL). Notably, while PPLTL+ retains the full expressive power of LTL, reactive synthesis is EXPTIME-complete instead of 2EXPTIME-complete. The techniques are also adapted to optimally solve satisfiability, validity, and model-checking, to get EXPSPACE-complete for LTLf+ (extending a recent result for the guarantee level using LTLf), and PSPACE-complete for PPLTL+.

Economists model knowledge use and acquisition as a cause-and-effect calculus associating observations made by a decision-maker about their world with possible underlying causes. Knowledge models are well-established for static contexts, but not for contexts of innovative and unbounded change. We develop a representation of knowledge use and acquisition in open-ended evolutionary systems and demonstrate its primary results, including that observers embedded in open-ended evolutionary systems can agree to disagree and that their ability to theorize about their systems is fundamentally local and constrained to their frame of reference what we call frame relativity. The results of our framework formalize local knowledge use, the many-selves interpretation of reasoning through time, and motivate the emergence of nonlogical modes of reasoning like institutional and aesthetic codes.

Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution proof (or a more expressive proof), which is commonly used for verification purposes. Empirically, modern SAT solvers produce relatively short proofs, however, there are no inherent guarantees that these proofs cannot be significantly reduced. This paper proposes a novel branch-and-bound algorithm for finding the shortest resolution proofs; to this end, we introduce a layer list representation of proofs that groups clauses by their level of indirection. As we show, this representation breaks all permutational symmetries, thereby improving upon the state-of-the-art symmetry-breaking and informing the design of a novel workflow for proof minimization. In addition to that, we design pruning procedures that reason on proof length lower bound, clause subsumption, and dominance. Our experiments suggest that the proofs from state-of-the-art solvers could be shortened by 30-60% on the instances from SAT Competition 2002 and by 25-50% on small synthetic formulas. When treated as an algorithm for finding the shortest proof, our approach solves twice as many instances as the previous work based on SAT solving and reduces the time to optimality by orders of magnitude for the instances solved by both approaches.