Cognition and Intractability

'Computational complexity has long been the elephant in the room in cognitive science. Researchers, including myself, blithely propose models that, if taken literally, would imply the brain can solve computational problems that are known to be intractable. This excellent introduction to both the technical results and their cognitive relevance should alert students and researchers to these pressing questions.' Nick Chater, University of Warwick 'Cognitive science and algorithms and complexity research are converging: mathematically speaking, there is a revolution in the cognitive models and tools available, while multivariate (parameterized) algorithmics are essential to understanding them. As our growing awareness of how natural systems algorithmically process information leads to intellectual flows in both directions, the insights in this book are highly useful to students and researchers in both fields.' Michael Fellows, University of Bergen, Norway 'Current theories in cognitive science think of mental processes as computational, but they rarely provide rigorous analysis of the relevant computations. Cognition and Intractability applies computational complexity theory to the kinds of inference that are important for human thinking. The results are mathematically elegant, pedagogically helpful, and very useful for understanding the kinds of computational processes that minds use.' Paul Thagard, University of Waterloo, Canada 'Computational complexity has long been the elephant in the room in cognitive science. Researchers, including myself, blithely propose models that, if taken literally, would imply the brain can solve computational problems that are known to be intractable. This excellent introduction to both the technical results and their cognitive relevance should alert students and researchers to these pressing questions.' Nick Chater, University of Warwick 'Cognitive science and algorithms and complexity research are converging: mathematically speaking, there is a revolution in the cognitive models and tools available, while multivariate (parameterized) algorithmics are essential to understanding them. As our growing awareness of how natural systems algorithmically process information leads to intellectual flows in both directions, the insights in this book are highly useful to students and researchers in both fields.' Michael Fellows, University of Bergen, Norway 'Current theories in cognitive science think of mental processes as computational, but they rarely provide rigorous analysis of the relevant computations. Cognition and Intractability applies computational complexity theory to the kinds of inference that are important for human thinking. The results are mathematically elegant, pedagogically helpful, and very useful for understanding the kinds of computational processes that minds use.' Paul Thagard, University of Waterloo, Canada