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Regular Games -- an Automata-Based General Game Playing Language

Radosław Miernik, Marek Szykuła, Jakub Kowalski, Jakub Cieśluk, Łukasz Galas, Wojciech Pawlik

TL;DR

Regular Games (RG) introduces a General Game Playing framework featuring a minimal, automaton-based low-level language (RG) and higher-level HRG for game design; the core approach is to encode rules as a finite automaton and compile to a fast C++ forward model, with a broader ecosystem for optimization and tooling. Theoretical results show RG is universal for finite turn-based games with imperfect information and randomness, with EXPSPACE-complete decision problems and PSPACE-complete when type length is fixed. Empirically, RG-based descriptions outperform existing systems (RBG and Ludii) in forward-model efficiency, with substantial reductions in automaton size and translation times under 100 ms. The work also enables cross-language interoperability through translations from RBG and GDL to RG and provides an extensible platform for procedural content generation and new game formats.

Abstract

We propose a new General Game Playing (GGP) system called Regular Games (RG). The main goal of RG is to be both computationally efficient and convenient for game design. The system consists of several languages. The core component is a low-level language that defines the rules by a finite automaton. It is minimal with only a few mechanisms, which makes it easy for automatic processing (by agents, analysis, optimization, etc.). The language is universal for the class of all finite turn-based games with imperfect information. Higher-level languages are introduced for game design (by humans or Procedural Content Generation), which are eventually translated to a low-level language. RG generates faster forward models than the current state of the art, beating other GGP systems (Regular Boardgames, Ludii) in terms of efficiency. Additionally, RG's ecosystem includes an editor with LSP, automaton visualization, benchmarking tools, and a debugger of game description transformations.

Regular Games -- an Automata-Based General Game Playing Language

TL;DR

Regular Games (RG) introduces a General Game Playing framework featuring a minimal, automaton-based low-level language (RG) and higher-level HRG for game design; the core approach is to encode rules as a finite automaton and compile to a fast C++ forward model, with a broader ecosystem for optimization and tooling. Theoretical results show RG is universal for finite turn-based games with imperfect information and randomness, with EXPSPACE-complete decision problems and PSPACE-complete when type length is fixed. Empirically, RG-based descriptions outperform existing systems (RBG and Ludii) in forward-model efficiency, with substantial reductions in automaton size and translation times under 100 ms. The work also enables cross-language interoperability through translations from RBG and GDL to RG and provides an extensible platform for procedural content generation and new game formats.

Abstract

We propose a new General Game Playing (GGP) system called Regular Games (RG). The main goal of RG is to be both computationally efficient and convenient for game design. The system consists of several languages. The core component is a low-level language that defines the rules by a finite automaton. It is minimal with only a few mechanisms, which makes it easy for automatic processing (by agents, analysis, optimization, etc.). The language is universal for the class of all finite turn-based games with imperfect information. Higher-level languages are introduced for game design (by humans or Procedural Content Generation), which are eventually translated to a low-level language. RG generates faster forward models than the current state of the art, beating other GGP systems (Regular Boardgames, Ludii) in terms of efficiency. Additionally, RG's ecosystem includes an editor with LSP, automaton visualization, benchmarking tools, and a debugger of game description transformations.

Paper Structure

This paper contains 90 sections, 4 theorems, 1 equation, 50 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contribution: Regular Games System
  4. Low-level Language
  5. High-level Languages
  6. Regular Games Language
  7. Full Definition
  8. Types and values
  9. Type aliases, constants, and variables
  10. Expressions
  11. Rules automaton
  12. Game state
  13. Paths
  14. Actions
  15. Special definitions
  16. ...and 75 more sections

Key Result

Theorem 1

Regular Games Language is universal for the class of all finite turn-based games, including imperfect information and with randomness, where probabilities are rational numbers.

Figures (50)

  • Figure 1: Regular Games ecosystem.
  • Figure 2: The IDE is split into two parts. The left side contains the code editor, while the right side includes benchmarking tools, automaton visualization, transformation configuration, and a snapshot of the game description after every transformation. It is available online at Anonymized.
  • Figure 3: Before compact comparisons
  • Figure 4: After compact comparisons
  • Figure 5: Before inline assignment
  • ...and 45 more figures

Theorems & Definitions (9)

  • Theorem 1
  • proof : Proof idea
  • Theorem 2
  • proof : Proof idea
  • Theorem 3
  • proof
  • Definition 1
  • Theorem 4
  • proof