Finite State Controllers (FSCs) are an effective way to compactly represent sequential plans. By imposing appropriate conditions on transitions, FSCs can also represent generalized plans (plans that solve a range of planning problems from a given domain). In this paper we introduce the concept of hierarchical FSCs for planning by allowing controllers to call other controllers. This call mechanism allows hierarchical FSCs to represent generalized plans more compactly than individual FSCs, to compute controllers in a modular fashion or even more, to compute recursive controllers. The paper introduces a classical planning compilation for computing hierarchical FSCs that solve challenging generalized planning tasks. The compilation takes as input a finite set of classical planning problems from a given domain. The output of the compilation is a single classical planning problem whose solution induces: (1) a hierarchical FSC and (2), the corresponding validation of that controller on the input classical planning problems.

Generalized planningstudies the representation, computation and evaluation of solutions that are valid for multiple planning instances. These are topics studied since the early days of AI. However, in recent years, we are experiencing the appearance of novel formalisms to compactly represent generalized planning tasks, the solutions to these tasks (calledgeneralized plans) and efficient algorithms to compute generalized plans. The paper reviews recent advances in generalized planning and relates them to existing planning formalisms, such asplanning with domain control knowledgeand approaches forplanning under uncertainty, that also aim at generality.

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This paper presents a novel approach for generating Context-Free Grammars (CFGs) from small sets of input strings (a single input string in some cases). Our approach is to compile this task into a classical planning problem whose solutions are sequences of actions that build and validate a CFG compliant with the input strings. In addition, we show that our compilation is suitable for implementing the two canonical tasks for CFGs, string production and string recognition.

Although heuristic search is one of the most successful approaches to classical planning, this planning paradigm does not apply straightforwardly to Generalized Planning (GP). Planning as heuristic search traditionally addresses the computation of sequential plans by searching in a grounded state-space. On the other hand, GP aims at computing algorithm-like plans that can branch and loop, and that generalize to a (possibly infinite) set of planning instances. This paper adapts the {\em planning as heuristic search} paradigm to the particularities of GP and presents the first native heuristic search approach to GP. First, the paper defines a novel GP solution space that is independent of the number of planning instances in a GP problem, and the size of these instances. Second, the paper defines several evaluation and heuristic functions, that do not require grounding, for guiding a combinatorial search in the GP solution space, making it possible to handle state variables with large numerical domains (e.g. integers). Lastly, the paper defines an algorithm for GP called Best-First Generalized Planning (BFGP), that implements a best-first search in the solution space guided by our evaluation/heuristic functions.