Robust Constraint Satisfaction and Local Hidden Variables in Quantum Mechanics

Motivated by considerations in quantum mechanics, we introduce the class of robust constraint satisfaction problems in which the question is whether every partial assignment of a certain length can be extended to a solution, provided the partial assignment does not violate any of the constraints of the given instance. We explore the complexity of specific robust colorability and robust satisfiability problems, and show that they are NP-complete. We then use these results to establish the computational intractability of detecting local hidden-variable models in quantum mechanics.