This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr’s Level Theory: the computational level and the algorithmic level. Our reasons for believing that humans indeed deal with hard cognitive functions are threefold: (1) Several computationally hard functions are suggested in the literature, e.g., in the areas of visual search, visual perception and analogical reasoning, linguistic processing, and decision making. (2) People appear to be attracted to computationally hard recreational puzzles and games. Examples of hard puzzles include Sudoku, Minesweeper, and the 15-Puzzle. (3) A number of research articles in the area of human problem solving suggest that humans are capable of solving hard computational problems, like the Euclidean Traveling Salesperson Problem, quickly and near-optimally.

This article gives a brief introduction to some theories and foundations of complexity theory and motivates the use of computationally hard problems in human problem solving with a short survey of known results of human performance, a review of some computationally hard games and puzzles, and the connection between complexity theory and models of cognitive functions. We aim to illuminate the role that computer science, in particular complexity theory, can play in the study of human problem solving. Theoretical computer science can provide a wealth of interesting problems for human study, but it can also help to provide deep insight into these problems. In particular, we discuss the role that computer science can play when choosing computational problems for study and designing experiments to investigate human performance. Finally, we enumerate issues and pitfalls that can arise when choosing computationally hard problems as the subject of study, in turn motivating some interesting potential future lines of study. The pitfalls addressed include: choice of presentation and representation of problem instances, evaluation of problem comprehension, and the role of cognitive support in experiments. Our goal is not to exhaustively list all the ways in which these choices may impact experimental studies, but rather to provide a few simple examples in order to highlight possible pitfalls.