Abstract Partially Observable Markov Decision Processes (POMDPs) are the standard framework for decision-making under uncertainty. While sampling-based methods scale well, they lack formal correctness guarantees, making them unsuitable for safety-critical applications. Conversely, formal synthesis techniques provide correctness-by-construction but often struggle with scalability, as general POMDP synthesis is undecidable. To bridge this gap, we propose a synthesis framework that integrates sampling, automata learning, and model-checking. Inspired by Angluin’s $$L^*$$ L ∗ algorithm, our approach utilizes sampling as a membership oracle and model-checking as an equivalence oracle. This enables the synthesis of finite-state controllers with formal guarantees, provided the sampling-induced policy is regular. We establish a relative completeness result for this framework. Experimental results from our prototypical implementation demonstrate that this method successfully solves threshold-safety problems that remain challenging for existing formal synthesis tools. We believe our algorithm serves as a valuable component in a portfolio approach to tackling the inherent difficulty of POMDP synthesis problems.

Python implementation of OCA-L* for active learning of deterministic real-time one-counter automata and Python implementation of OCA-L* and MinOCA for active learning of visibly one-counter automata.

Concurrent games with a fixed number of agents have been thoroughly studied, with various solution concepts and objectives for the agents. In this paper, we consider concurrent games with an arbitrary number of agents, and study the problem of synthesizing a coalition strategy to achieve a global safety objective. The problem is non-trivial since the agents do not know a priori how many they are when they start the game. We prove that the existence of a safe arbitrary-large coalition strategy for safety objectives is a PSPACE-hard problem that can be decided in exponential space.

Traditional concurrent games on graphs involve a fixed number of players, who take decisions simultaneously, determining the next state of the game. In this paper, we introduce a parameterized variant of concurrent games on graphs, where the parameter is precisely the number of players. Parameterized concurrent games are described by finite graphs, in which the transitions bear regular languages to describe the possible move combinations that lead from one vertex to another. We consider the problem of determining whether the first player, say Eve, has a strategy to ensure a reachability objective against any strategy profile of her opponents as a coalition. In particular Eve’s strategy should be independent of the number of opponents she actually has. Technically, this paper focuses on an a priori simpler setting where the languages labeling transitions only constrain the number of opponents (but not their precise action choices). These constraints are described as semilinear sets, finite unions of intervals, or intervals. We establish the precise complexities of the parameterized reachability game problem, ranging from PTIME-complete to PSPACE-complete, in a variety of situations depending on the contraints (semilinear predicates, unions of intervals, or intervals) and on the presence or not of non-determinism.

International audience

We introduce a measure called width, quantifying the amount of nondeterminism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input. We describe an incremental determinisation construction on NFAs, which can be more efficient than the full powerset determinisation, depending on the width of the input NFA. This construction can be generalised to infinite words, and is particularly well-suited to coBüchi automata in this context. For coBüchi automata, this procedure can be used to compute either a deterministic automaton or a GFG one, and it is algorithmically more efficient in this last case. We show this fact by proving that checking whether a coBüchi automaton is determinisable by pruning is NP-complete. On finite or infinite words, we show that computing the width of an automaton is PSPACE-hard.

Developing an automatic signature verification system is challenging and demands a large number of training samples. This is why synthetic handwriting generation is an emerging topic in document image analysis. Some handwriting synthesizers use the motor equivalence model, the well-established hypothesis from neuroscience, which analyses how a human being accomplishes movement. Specifically, a motor equivalence model divides human actions into two steps: 1) the effector independent step at cognitive level and 2) the effector dependent step at motor level. In fact, recent work reports the successful application to Western scripts of a handwriting synthesizer, based on this theory. This paper aims to adapt this scheme for the generation of synthetic signatures in two Indic scripts, Bengali (Bangla), and Devanagari (Hindi). For this purpose, we use two different online and offline databases for both Bengali and Devanagari signatures. This paper reports an effective synthesizer for static and dynamic signatures written in Devanagari or Bengali scripts. We obtain promising results with artificially generated signatures in terms of appearance and performance when we compare the results with those for real signatures.

Handwritten signature datasets are really necessary for the purpose of developing and training automatic signature verification systems. It is desired that all samples in a signature dataset should exhibit both inter-personal and intra-personal variability. A possibility to model this reality seems to be obtained through the synthesis of signatures. In this paper we propose a method based on motor equivalence model theory to generate static Bengali signatures. This theory divides the human action to write mainly into cognitive and motor levels. Due to difference between scripts, we have redesigned our previous synthesizer [1,2], which generates static Western signatures. The experiments assess whether this method can approach the intra and inter-personal variability of the Bengali-100 Static Signature DB from a performance-based validation. The similarities reported in the experimental results proof the ability of the synthesizer to generate signature images in this script.