Generalized Planning: Non-Deterministic Abstractions and Trajectory Constraints

TL;DR

This paper explores how to extend generalized planning by incorporating global structure through trajectory constraints, enabling the use of LTL synthesis and simplifying problems with integer variables.

Contribution

It introduces a method to capture global problem structure with trajectory constraints, removing the termination condition and connecting generalized planning to LTL synthesis and non-deterministic planning.

Findings

Trajectory constraints can be expressed as LTL formulas.

Global structure can be captured beyond local Markovian assumptions.

Problems with integer variables can be simplified by compiling away trajectory constraints.

Abstract

We study the characterization and computation of general policies for families of problems that share a structure characterized by a common reduction into a single abstract problem. Policies $\mu$ that solve the abstract problem P have been shown to solve all problems Q that reduce to P provided that $\mu$ terminates in Q. In this work, we shed light on why this termination condition is needed and how it can be removed. The key observation is that the abstract problem P captures the common structure among the concrete problems Q that is local (Markovian) but misses common structure that is global. We show how such global structure can be captured by means of trajectory constraints that in many cases can be expressed as LTL formulas, thus reducing generalized planning to LTL synthesis. Moreover, for a broad class of problems that involve integer variables that can be increased or decreased, trajectory constraints can be compiled away, reducing generalized planning to fully observable non-deterministic planning.