# Unbounded Lookahead in WMSO+U Games

arXiv: https://arxiv.org/abs/1509.07495 · HTML: https://mlsanity.com/paper/1509.07495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2015.

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

- [AI Safety Considerations for Agents With Limited Time to Act](https://mlsanity.com/paper/2610.10285/) (2026)

## Abstract (arXiv)

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with the unbounding quantifier (WMSO+U), which is able to express (un)boundedness properties. It is decidable whether the delaying player is able to win such a game with bounded lookahead, i.e., if she only skips a finite number of moves. However, bounded lookahead is not always sufficient: we present a game that can be won with unbounded lookahead, but not with bounded lookahead. Then, we consider WMSO+U delay games with unbounded lookahead and show that the exact evolution of the lookahead is irrelevant: the winner is always the same, as long as the initial lookahead is large enough and the lookahead tends to infinity.