# Heuristics, Answer Set Programming and Markov Decision Process for Solving a Set of Spatial Puzzles

## TL;DR

This paper presents an approach combining Answer Set Programming and Markov Decision Processes, enhanced with heuristics derived from relaxed puzzles, to efficiently solve complex spatial puzzles through accelerated learning.

## Contribution

It introduces a novel heuristic-enhanced oASP(MDP) algorithm that improves learning speed in solving spatial puzzles by integrating domain-specific heuristics.

## Key findings

- Heuristics significantly accelerate the learning process.
- The approach outperforms non-heuristic methods in various puzzle settings.
- Effective in deterministic, non-deterministic, and non-stationary environments.

## Abstract

Spatial puzzles composed of rigid objects, flexible strings and holes offer interesting domains for reasoning about spatial entities that are common in the human daily-life's activities. The goal of this work is to investigate the automated solution of this kind of puzzles adapting an algorithm that combines Answer Set Programming (ASP) with Markov Decision Process (MDP), algorithm oASP(MDP), to use heuristics accelerating the learning process. ASP is applied to represent the domain as an MDP, while a Reinforcement Learning algorithm (Q-Learning) is used to find the optimal policies. In this work, the heuristics were obtained from the solution of relaxed versions of the puzzles. Experiments were performed on deterministic, non-deterministic and non-stationary versions of the puzzles. Results show that the proposed approach can accelerate the learning process, presenting an advantage when compared to the non-heuristic versions of oASP(MDP) and Q-Learning.