We provide the following appendices In A, we give additional information about the datasets (Karel and ViZDoom). In B, we describe precisely the neural component of PLANS and its training process. In C, we present the implementation of the rule-based solver. In D, we analyse the temporal complexity of PLANS. Table 3 contains high-level information about both datasets.

Our approach offers more generality for neuro-symbolic systems. In Section 2.2, we opted for an abstract definition of action and perception primitives as For instance, Vizdoom actions include "move forward", "turn left" and "attack". We will add a detailed list in the paper. Y et there is one fundamental difference with Barman 2010. We agree that there is a conceptual connection, but it is not obvious to us whether both problems are equivalent.

In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning horizon and solve the problem of trying to find a plan of a particular length. Indeed, any optimization problem can be solved as a sequence of decision problems in which the objective value is incrementally updated. Another example is constraint dominance programming (CDP), in which search is organized into a sequence of levels. The contribution of this work is to enable a native interaction between SAT solvers and the automated modelling system Savile Row to support efficient incremental modelling and solving. This allows adding new decision variables, posting new constraints and removing existing constraints (via assumptions) between incremental steps. Two additional benefits of the native coupling of modelling and solving are the ability to retain learned information between SAT solver calls and to enable SAT assumptions, further improving flexibility and efficiency. Experiments on one optimisation problem and five pattern mining tasks demonstrate that the native interaction between the modelling system and SAT solver consistently improves performance significantly.

Recent years have seen the rise of statistical program learning based on neural models as an alternative to traditional rule-based systems for programming by example. Rule-based approaches offer correctness guarantees in an unsupervised way as they inherently capture logical rules, while neural models are more realistically scalable to raw, high-dimensional input, and provide resistance to noisy I/O specifications. We introduce PLANS (Program LeArning from Neurally inferred Specifications), a hybrid model for program synthesis from visual observations that gets the best of both worlds, relying on (i) a neural architecture trained to extract abstract, high-level information from each raw individual input (ii) a rule-based system using the extracted information as I/O specifications to synthesize a program capturing the different observations. In order to address the key challenge of making PLANS resistant to noise in the network's output, we introduce a filtering heuristic for I/O specifications based on selective classification techniques. We obtain state-of-the-art performance at program synthesis from diverse demonstration videos in the Karel and ViZDoom environments, while requiring no ground-truth program for training. We make our implementation available at github.com/rdang-nhu/PLANS.

Finding interesting patterns is a challenging task in data mining. Constraint based mining is a well-known approach to this, and one for which constraint programming has been shown to be a well-suited and generic framework. Dominance programming has been proposed as an extension that can capture an even wider class of constraint-based mining problems, by allowing to compare relations between patterns. In this paper, in addition to specifying a dominance relation, we introduce the ability to specify an incomparability condition. Using these two concepts we devise a generic framework that can do a batch-wise search that avoids checking incomparable solutions. We extend the ESSENCE language and underlying modelling pipeline to support this. We use generator itemset mining problem as a test case and give a declarative specification for that. We also present preliminary experimental results on this specific problem class with a CP solver backend to show that using the incomparability condition during search can improve the efficiency of dominance programming and reduces the need for post-processing to filter dominated solutions.