# Half-Positional Objectives Recognized by Deterministic B"uchi Automata

arXiv: https://arxiv.org/abs/2205.01365 · HTML: https://mlsanity.com/paper/2205.01365/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2022.

## Built on by (most cited first, 1 of 1)

- [Simplicity Lies in the Eye of the Beholder: A Strategic Perspective on Controllers in Reactive Synthesis](https://mlsanity.com/paper/2509.04129/) (2025)

## Abstract (arXiv)

In two-player games on graphs, the simplest possible strategies are those that can be implemented without any memory. These are called positional strategies. In this paper, we characterize objectives recognizable by deterministic B"uchi automata (a subclass of omega-regular objectives) that are half-positional, that is, for which the protagonist can always play optimally using positional strategies (both over finite and infinite graphs). Our characterization consists of three natural conditions linked to the language-theoretic notion of right congruence. Furthermore, this characterization yields a polynomial-time algorithm to decide half-positionality of an objective recognized by a given deterministic B"uchi automaton.