DeepAI AI Chat
Log In Sign Up

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible

by   Zachary Abel, et al.

We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a path in a rectangular grid graph from a start vertex to a destination vertex. The different puzzle types place different constraints on the path: preventing some edges from being visited (broken edges); forcing some edges or vertices to be visited (hexagons); forcing some cells to have certain numbers of incident path edges (triangles); or forcing the regions formed by the path to be partially monochromatic (squares), have exactly two special cells (stars), or be singly covered by given shapes (polyominoes) and/or negatively counting shapes (antipolyominoes). We show that any one of these clue types (except the first) is enough to make path finding NP-complete ("witnesses exist but are hard to find"), even for rectangular boards. Furthermore, we show that a final clue type (antibody), which necessarily "cancels" the effect of another clue in the same region, makes path finding Σ_2-complete ("witnesses do not exist"), even with a single antibody (combined with many anti/polyominoes), and the problem gets no harder with many antibodies.


page 5

page 11

page 15

page 17

page 20

page 25

page 26

page 27


Rikudo is NP-complete

Rikudo is a number-placement puzzle, where the player is asked to comple...

On Kernels for d-Path Vertex Cover

In this paper we study the kernelization of d-Path Vertex Cover (d-PVC) ...

The Complexity of Finding Temporal Separators under Waiting Time Constraints

In this work, we investigate the computational complexity of Restless Te...

Parameterized complexity of Bandwidth of Caterpillars and Weighted Path Emulation

In this paper, we show that Bandwidth is hard for the complexity class W...

On the NP-Completeness of Satisfying Certain Path and Loop Puzzles

"Eye-Witless", "Haisu" and "Oriental House" are genres of logic puzzles ...

Rectangular Spiral Galaxies are Still Hard

Spiral Galaxies is a pencil-and-paper puzzle played on a grid of unit sq...

Time-inconsistent Planning: Simple Motivation Is Hard to Find

With the introduction of the graph-theoretic time-inconsistent planning ...