# Which “assumptions” made about the state space are Russell and Norvig referring to in their book?

I am reading the cornerstone book, "Artificial Intelligence, A Modern Approach" by Stuart Russel, and Peter Norvig, and there is a passage in the book on page 98:

The complexity results depend very strongly on the assumptions made about the state space. The simplest model studied is a state space that has a single goal and is essentially a tree with reversible actions. (The 8-puzzle satisfies the first and third of these assumptions.)

What are the "assumptions" in that context?

The complexity results depend very strongly on the assumptions made about the state space. The simplest model studied is a state space that has a single goal and is essentially a tree with reversible actions.

The assumptions are the following:

1. The simplest model studied is a state space

2. that has a single goal

3. and is essentially a tree with reversible actions.