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Winning Snake: Design Choices in Multi-Shot ASP

Elisa Böhl, Stefan Ellmauthaler, Sarah Alice Gaggl

TL;DR

Answer Set Programming (ASP) is used to model an iterative, multi-shot solving process on grid graphs $G(n,m)$ to win the Snake game by ensuring a Hamiltonian cycle (HC); this HC problem is NP-hard. The authors formalize the Snake game as Hamiltonian-snake problems (HS, MHS) and present five clingo-based multi-shot implementations (One-Shot, Ad Hoc, Preground, Assume, Nogood) with heuristic initialization and image-based visualization via clingraph. They compare approaches empirically across grid sizes, showing that reusing search progress in multi-shot ASP can reduce grounding and solving time, with results depending on $n$ and $m$ and the presence of timeouts. The study provides practical design patterns for applying multi-shot ASP to iterative, combinatorial tasks and discusses trade-offs between implementation complexity and execution efficiency, suggesting directions for future work such as alternative problem formulations and broader showcase applications.

Abstract

Answer set programming is a well-understood and established problem-solving and knowledge representation paradigm. It has become more prominent amongst a wider audience due to its multiple applications in science and industry. The constant development of advanced programming and modeling techniques extends the toolset for developers and users regularly. This paper demonstrates different techniques to reuse logic program parts (multi-shot) by solving the arcade game snake. This game is particularly interesting because a victory can be assured by solving the underlying NP-hard problem of Hamiltonian Cycles. We will demonstrate five hands-on implementations in clingo and compare their performance in an empirical evaluation. In addition, our implementation utilizes clingraph to generate a simple yet informative image representation of the game's progress.

Winning Snake: Design Choices in Multi-Shot ASP

TL;DR

Answer Set Programming (ASP) is used to model an iterative, multi-shot solving process on grid graphs to win the Snake game by ensuring a Hamiltonian cycle (HC); this HC problem is NP-hard. The authors formalize the Snake game as Hamiltonian-snake problems (HS, MHS) and present five clingo-based multi-shot implementations (One-Shot, Ad Hoc, Preground, Assume, Nogood) with heuristic initialization and image-based visualization via clingraph. They compare approaches empirically across grid sizes, showing that reusing search progress in multi-shot ASP can reduce grounding and solving time, with results depending on and and the presence of timeouts. The study provides practical design patterns for applying multi-shot ASP to iterative, combinatorial tasks and discusses trade-offs between implementation complexity and execution efficiency, suggesting directions for future work such as alternative problem formulations and broader showcase applications.

Abstract

Answer set programming is a well-understood and established problem-solving and knowledge representation paradigm. It has become more prominent amongst a wider audience due to its multiple applications in science and industry. The constant development of advanced programming and modeling techniques extends the toolset for developers and users regularly. This paper demonstrates different techniques to reuse logic program parts (multi-shot) by solving the arcade game snake. This game is particularly interesting because a victory can be assured by solving the underlying NP-hard problem of Hamiltonian Cycles. We will demonstrate five hands-on implementations in clingo and compare their performance in an empirical evaluation. In addition, our implementation utilizes clingraph to generate a simple yet informative image representation of the game's progress.
Paper Structure (23 sections, 1 equation, 3 figures, 1 table, 8 algorithms)

This paper contains 23 sections, 1 equation, 3 figures, 1 table, 8 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Answer Set Programming
  4. Multi-Shot ASP in clingo
  5. Graphs, Paths, and Hamiltonian Cycles
  6. Snake Game
  7. Formalizing and Winning snake Optimally with ASP
  8. Goal Specification.
  9. Problem Description for Iterations
  10. Complexity.
  11. Snake Strategies
  12. Multi-Shot Implementation Approaches
  13. One-Shot.
  14. Ad Hoc.
  15. Preground.
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Examples for a snake on a $6\times{}6$ grid generated by our software. The snake head is marked with eyes.
  • Figure 2: Examples for a snake on a $6\times{}6$ grid. Black lines indicate HCs.
  • Figure 3: Average number of steps (solid lines) and timeout rate in percent (dashed lines) per iteration for different grid sizes for timeout 60s. Dotted gray line is the expected step count for the naive strategy (baseline).