Equivalence of the Frame and Halting Problems

Abstract

The open-domain Frame Problem is the problem of determining what features of an open task environment need to be updated following an action. Here we prove that the open-domain Frame Problem is equivalent to the Halting Problem and is therefore undecidable. We discuss two other open-domain problems closely related to the Frame Problem, the system identification problem and the symbol-grounding problem, and show that they are similarly undecidable. We then reformulate the Frame Problem as a quantum decision problem, and show that it is undecidable by any finite quantum computer.

Keywords

• artificial intelligence
• entanglement
• heuristic search
• Multiprover Interactive Proof*(MIP)
• robotics
• separability