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A symmetric recursive algorithm for mean-payoff games

Pierre Ohlmann

Abstract

We propose a new deterministic symmetric recursive algorithm for solving mean-payoff games.

A symmetric recursive algorithm for mean-payoff games

Abstract

We propose a new deterministic symmetric recursive algorithm for solving mean-payoff games.
Paper Structure (12 sections, 8 theorems, 4 equations, 1 figure, 1 algorithm)

This paper contains 12 sections, 8 theorems, 4 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and background
  3. Presentation of the algorithm
  4. Proofs for the main lemmas
  5. Pseudocode
  6. Optimisations and variants
  7. Optimisation: better initialisation of $F$
  8. Optimisation: fixing many vertices at once
  9. Variant: choice between $\sup \! \Sigma^N$ or $\inf \! \Sigma^P$
  10. Variant: remembering the potentials
  11. Variant: lazy version
  12. Discussion

Key Result

Theorem 1

For any game, any subset $X$ of vertices, any $\mathrm{val} \in \{\mathrm{MP}, \sup \! \Sigma^X, \inf \! \Sigma^X\}$, and any vertex $v$, it holds that where $\sigma$ and $\tau$ respectively range over strategies of Min and Max, and $\pi$ ranges over paths starting from $v$.

Figures (1)

  • Figure 1: An illustration of the situation. Circles are Min-vertices and squares are Max-vertices. Red edges are escapes from $H^+$ and blue edges are escapes from $H^-$.

Theorems & Definitions (8)

  • Theorem 1: EM79BFLMS08
  • Lemma 2
  • Theorem 3: GKK88OhlmannGKK
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • Lemma 8