Why isn’t the Generalized Super Mario Bros. obviously in NP?

It is shown in the paper: “Classic Nintendo Games are (Computationally) Hard” by Greg Aloupis, Erik D. Demaine, Alan Guo, and Giovanni Viglietta that the Generalized Super Mario Bros. (SMB, for short) video game is NP-hard.

Theorem 3.1. It is NP-hard to decide whether the goal is reachable from the start of a stage in generalized Super Mario Bros.

(When generalizing the original Super Mario Bros., we assume that the screen size covers the entire level, because the game forbids Mario from going left of the screen.)


However, it does not claim that SMB is in NP.

My problem: Why isn’t SMB obviously in NP?


I came up with two reasons.

  • First, the solution/certificate to SMB may be not of polynomial size, due to e.g., timing. Is this valid? If so, how to argue this point more formally?
  • Second, the computer can be treated as a second player. Thus, SMB is a two-player game, which may be reasonably harder. However, are the actions of the computer player determined from the beginning of the game so that we can still regard SMB as a single-player game?

Related posts:

  • What is the whole picture of the NP-hardness proof of Super Mario Bros?
  • Why are Chess, Mario, and Go not NP-complete?

Added: A follow-up paper also by Erik Demaine (et al.) which shows that a generalized level of SMB is PSPACE-complete.

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