Computational complexity analysis for cognitive scientists

Many computationalor rational-level models of cognition postulate computations that appear to be computationally intractable (e.g., NP-hard or worse). Formally, this means that the postulated computations consume an exponential amount of time. Informally, this means that the postulated computations do not scale in any obvious way to explain how the modeled cognitive capacities can operate in the real world outside the lab. This problem of intractability is quite common in cognitive science. It is observed in practically all domains of cognition, including, for instance, perception, language, reasoning, categorization, decision-making, and motor planning. It is also not specific to any particular class of models, as it can arise for symbolic, connectionist, probabilistic (e.g. Bayesian), dynamical, logic-based, and even heuristic models of cognition. How can cognitive scientists effectively deal with the intractability of their models? Several sophisticated and well-established concepts and techniques for computational complexity analysis have been developed in theoretical computer science over the last decades that can be directly utilized by cognitive scientists. Using these techniques cognitive scientists not only can assess whether or not a particular model is intractable, but also identify parameters of the model that are responsible for that intractability. As a result, these techniques can be used to generate hypotheses about how the models can be revised so as to make them computationally tractable, thereby improving the computational plausibility and scalability of the models. With this tutorial we aim to make these techniques for computational complexity analysis available for interested cognitive scientists.