Cognition and Intractability
A Guide to Classical and Parameterized Complexity Analysis

Provides an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science.

Iris van Rooij (Author), Mark Blokpoel (Author), Johan Kwisthout (Author), Todd Wareham (Author)

9781107043992, Cambridge University Press

Hardback, published 25 April 2019

374 pages, 67 b/w illus. 19 tables
23.4 x 15.7 x 2.4 cm, 0.65 kg

'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

Intractability is a growing concern across the cognitive sciences: while many models of cognition can describe and predict human behavior in the lab, it remains unclear how these models can scale to situations of real-world complexity. Cognition and Intractability is the first book to provide an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science. Covering both classical and parameterized complexity analysis, it introduces the mathematical concepts and proof techniques that can be used to test one's intuition of (in)tractability. It also describes how these tools can be applied to cognitive modeling to deal with intractability, and its ramifications, in a systematic way. Aimed at students and researchers in philosophy, cognitive neuroscience, psychology, artificial intelligence, and linguistics who want to build a firm understanding of intractability and its implications in their modeling work, it is an ideal resource for teaching or self-study.

Part I. Introduction: 1. Introduction
Part II. Concepts and Techniques: 2. Polynomial versus exponential time
3. Polynomial-time reductions
4. Classical complexity classes
5. Fixed-parameter tractable time
6. Parameterized reductions
7. Parameterized complexity classes
Part III. Reflections and Elaborations: 8. Dealing with intractability
9. Replies to common objections
Part IV. Applications: 10. Coherence as constraint satisfaction
11. Analogy as structure mapping
12. Communication as Bayesian inference.

Subject Areas: Neurosciences [PSAN], Maths for scientists [PDE], Mathematics & science [P], Cognition & cognitive psychology [JMR], Cognitivism, cognitive theory [JMAQ], Psychology [JM]