Parameterized complexity in cognitive modeling: Foundations, applications and opportunities

Computer Journal

Volumn 51, Issue 3, 2008, Pages 385-404

  van Rooij, Iris ^a   Wareham, Todd ^b  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Cognitive modeling; Parameterized complexity

Indexed keywords

COMPUTATIONAL COMPLEXITY; MATHEMATICAL MODELS; PARAMETERIZATION; REVERSE ENGINEERING;

COGNITIVE SCIENCE; COMPUTATIONAL TRACTABILITY; PARAMETERIZED COMPLEXITY;

COGNITIVE SYSTEMS;

EID: 43249114133     PISSN: 00104620     EISSN: 14602067     Source Type: Journal    
DOI: 10.1093/comjnl/bxm034     Document Type: Review

References (101)

1. Garey, M.R. and Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco.
2. Downey, R.G. and Fellows, M.R. (1999) Parameterized Complexity. Springer-Verlag, Berlin.
3. Cummins, R. (2000) How does it work? vs. What are the laws? Two conceptions of psychological explanation. In Keil, F. and Wilson, R. (eds), Explanation and Cognition. MIT Press, Cambridge, MA.
4. Marr, D. (1981) Vision: A Computational Investigation into the Human Representation and Processing Visual Information. W.H. Freeman, San Francisco.
5. Anderson, J.R. (1990) The Adaptive Character of Thought. Lawrence Erlbaum Associates, Hillsdale, NJ.
6. Frixione, M. (2001) Tractable competence. Minds Mach., 11, 379-397.
7. Dennett, D.C. (1994) Cognitive science as reverse engineering: Several meanings of top down and bottom up. Proc. 9th Int. Congress of Logic, Methodology and Philosophy of Science, pp. 679-689. North Holland.
8. Koffka, K. (1935). Principles of Gestalt Psychology. Harcourt Brace, New York.
9. van der Helm, P.A. (2000) Simplicity versus likelihood in visual perception: From surprisals to precisals. Psychol. Bull., 126 770-800.
10. van der Helm, P.A. (2007) The resurrection of simplicity in vision. In Peterson, M.A., Gillam, B. and Sedgwick, H.A. (eds), In the Mind's Eye: Julian Hochberg on the Perception of Pictures, Film, and the World pp. 518-524. Oxford University Press, New York.
11. Chater, N. and Vitányi, P. (2003) Simplicity: A unifying principle in cognitive science? Trends Cogn. Sci., 7, 19-22.
12. Leeuwenberg, E.L.J. and van der Helm, P.A. (1996) Goodness of visual regularities: A nontransformational approach. Psychol. Rev., 103, 429-456.
13. van der Helm, P.A. (2004) Transparallel processing by hyperstrings. Proc. Natl. Acad. Sci. USA, 101, 10862-10867.
14. Bergströom, L. (1984) Underdetermination and realism. Erkenntnis 21, 349-365.
15. Quine, W.V. (1975) On empirically equivalent systems of the world. Erkenntnis 9, 313-328.
16. Anderson, J.R. (1978) Arguments concerning representations for mental imagery. Psychol. Rev., 85, 249-277.
17. van Rooij, I. (2003) Tractable cognition: Complexity theory in cognitive psychology. PhD Thesis, Department of Psychology, University of Victoria.
18. Thagard, P. (2000) Coherence in Thought and Action. MIT Press, Cambridge, MA.
19. Thagard, P. and Verbeurgt, K. (1998) Coherence as constraint satisfaction. Cogni. Sci., 22, 1-24.
20. van Rooij, I. and Wright, C. (2006) The incoherence of heuristically explaining coherence. Proc. 28th Annual Conf. of the Cognitive Science Society, p. 2622. Lawrence Erlbaum Associates, Hillsdale, NJ.
21. Koskenniemi, K. and Church, K.W. (1988) Complexity, two-level morphology, and finnish. Proc. 12th Int. Conf. Computational Linguistics (COLING'88), pp. 335-340. John von Neumann Society Lor Computing Sciences, Budapest.
22. Manaster Ramer, A. (1995) Book review: Ristad, The Language Complexity Game. Comput. Linguist., 21, 124-131.
23. Rounds, W. (1987) Book review: Barton, Berwick, and Ristad, Computational complexity and natural language. Comput. Linguist., 13, 354-356.
24. Rounds, W. (1991) The relevance of computational complexity theory to natural language processing. In Sells, P., Shieber, S. and Wasow, T. (eds), Foundational Issues in Natural Language Processing. MIT Press, Cambridge, MA.
25. Barton, G.E., Berwick, R.C. and Ristad, E.S. (1987) Computational Complexity and Natural Language. MIT Press, Cambridge, MA.
26. Berwick, R.C. and Weinberg, A. (1983) Parsing efficiency, computational complexity, and the evaluation of grammatical theories. Linguist. Inquiry, 13, 165-191.
27. Ristad, E.S. (1990) Computational Structure of human language. PhD Thesis, Department of Electrical Engineering and Computer Science, MIT.
28. Ristad, E.S. (1993) The Language Complexity Game. MIT Press, Cambridge, MA.
29. Wareham, T. (1996) The role of parameterized computational complexity theory in cognitive modeling. In Ling, C.X. and Sun, R. (eds), Working Notes of AAAI-96 Workshop on Computational Cognitive Modelling: Source of the Power.
30. Wareham, T. (1999) Systematic parameterized complexity analysis in computational phonology. PhD Thesis, Department of Computer Science, University of Victoria.
31. Parberry, I. (1994) Circuit Complexity and Neural Networks. MIT Press, Cambridge, MA.
32. van Emde Boas, P. (1990) Machine models and simulations. In van Leeuwen, J. (ed), Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity. MIT Press, Cambridge, MA.
33. Tsotsos, J.K. (1990) Analyzing vision at the complexity level. Behav. Brain Sci., 13, 423-469.
34. Simon, H.A. (1988) Rationality as process and as product of thought. In Bell, D.E., Raiffa, H. and Tversky, A. (eds), Decision-making: Descriptive, Normative, and Prescriptive Interactions. Cambridge University Press.
35. Martignon, L. and Hoffrage, U. (2002) Fast, frugal, and fit: Simple heuristics for paired comparison. Theory Decis., 52, 29-71.
36. Martignon, L. and Schmitt, M. (1999) Simplicity and robustness of fast and frugal heuristics. Minds Machi., 9, 565-593.
37. van Rooij, I., Stege, S. and Kadlec, H. (2005) Sources of complexity in subset choice. J. Math. Psychol., 49, 160-187.
38. Ristad, E.S. (1993) Complexity of the simplified segmental phonology. Technical Report CS-TR-388-92 (revised May 1993), Department of Computer Science, Princeton University.
39. Eisner, J. (1997) Efficient generation in primitive optimality theory. Technical Report ROA-206-0797, Rutgers Optimality Archive.
40. Downey, R.G., Fellows, M.R., Kapron, B.M., Hallett, M.T. and Wareham, T. (1994) Parameterized complexity of some problems in logic and linguistics (extended abstract). Logical Foundations of Computer Science, pp. 89-101. Lecture Notes in Computer Science, Vol. 813. Springer-Verlag, Berlin.
41. Wareham, T. (2001) The parameterized complexity of intersection and composition operations on sets of finite-state automata. Proc. Fifth Int. Conf. Implementation and Application of Automata, pp. 302-310. Lecture Notes in Computer Science, Vol. 2088. Springer-Verlag, Berlin.
42. Kaplan, R.M. and Kay, M. (1994) Regular models of phonological rule systems. Comput. Linguist., 20, 331-378.
43. Hopcroft, J.E. and Ullman, J.D. (1969) Formal Languages and Their Relation to Automata. Addison-Wesley, Reading, MA.
44. Reif, J.H. (1987) Complexity of the generalized mover's problem. In Schwartz, J.T., Sharir, M. and Hopcroft, J.E. (eds), Planning, Geometry, and Complexity of Robot Motion. Ablex Publishing, Norwood, NJ.
45. Joseph, D.A. and Plantinga, W.H. (1985) On the complexity of reachability and motion planning problems. Proc. First ACM Symp. Computational Geometry, pp. 62-66. ACM Press, New York.
46. Cesati, M. and Wareham, T. (1995) Parameterized complexity analysis in robot motion planning. Proc. 25th IEEE Int. Conf. Systems, Man, and Cybernetics: Volume 1, pp. 880-885. IEEE Press, Los Alamitos, CA.
47. Hopcroft, J.E., Schwartz, J. and Sharir, M. (1984) On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the Warehouseman's Problem Int. J. Robot. Res., 3, 76-88.
48. Fernau, H., Hagerup, T., Nishimura, N., Ragde, P. and Reinhardt, K. (2003) On the parameterized complexity of a generalized Rush Hour puzzle. Proc. 15th Canadian Conf. Computational Geometry (CCCG'03) pp. 6-9.
49. Bylander, T. (1994) The computational complexity of propositional STRIPS planning. Artif. Intell., 69, 165-204.
50. Fikes, R.E. and Nilsson, N.J. (1971) STRIPS: A new approach to the application of theorem proving to problem solving. Artif. Intell., 2, 189-208.
51. Downey, R.G., Fellows, M.R. and Stege, U. (1999) Parameterized complexity: A framework for systematically confronting computational intractability. The Future of Discrete Mathematics: Proc. First DIMACS-DIMATIA Workshop, pp. 49-99. AMS-DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 49. American Mathematical Society, Providence, RI.
52. Chater. N. and Vitányi, P. (2003) Generalized law of universal generalization. Journal of Mathematical Psychology, 47, 346-369.
53. Cooper, G.F. (1990) The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell., 42 393-405.
54. Fishburn, P.C. and LaValle, I.H. (1996) Binary interactions and subset choice. Eur. J. Oper. Res., 92, 182-192.
55. Levesque, H.J. (1988) Logic and the complexity of reasoning. J. Philos. Log., 17, 355-389.
56. Roth, D. (1996) On the hardness of approximate reasoning. Artif. Intell., 82, 273-302.
57. Veale. T.. O'Donoghue, D. and Keane, M.T. (1999) Computability as a limiting cognitive constraint: Complexity concerns in metaphor comprehension about which cognitive linguists should be aware. In Hiraga, E.M., Sinha, C. and Wilcox, S. (eds), Cultural, Psychological and Typological Issues in Cognitive Linguistics. John Benjamins Amsterdam.
58. Fishburn, P.C. and LaValle, I.H. (1993) Subset preferences in linear and nonlinear utility theory, J. Math. Psychol., 37, 611-623.
59. Ford, K.W. and Pylyshyn, Z. (eds) (1996) The Robot's Dilemma Revisited: The Frame Problem in Artificial Intelligence. Ablex Publishing, Norwood, N.J.
60. Haselager, W.F.G. (1997) Cognitive science and folk psychology: The right frame of mind. Sage, London.
61. Pylyshyn, Z. (ed) (1987) The Robot's Dilemma: The Frame Problem in Artificial Intelligence. Ablex Publishing, Norwood, NJ.
62. Stege, U. and van Rooij, I. (2006). Computing maximum coherence: A hard nut to crack? Paper presented at the 39th Annual Meeting of the Society for Mathematical Psychology, Vancouver, BC.
63. Li, M. and Vitányi. P. (1997) An Introduction to Kolmogorov Complexity and its Applications (2nd edn). Springer-Verlag, Berlin.
64. van der Helm, P.A. and Leeuwenberg, E.L.J. (1986) Avoiding explosive search in automatic selection of simple pattern codes. Pattern Recognit., 19, 181-191.
65. Treisman, A. (1982) Perceptual grouping and attention in visual search for features and for objects. J. Exp. Psychol.: Hum. Percept. Perform. 8, 194-214.
66. Wolfe, J. M. (2003) Moving towards solutions to some enduring controversies in visual search. Trends Cogn, Sci. 7, 70-76.
67. Tsotsos, J.K. (1988) A complexity level analysis of immediate vision. Int. J. Comput. Vis., 2, 303-320.
68. Tsotsos, J.K. (1989) The complexity of perceptual search tasks. In Sridharan, N.S. (ed), Proc. Int. Joint Conf. Artificial Intelligence pp. 1571-1577. Morgan Kaufmann Publishers, San Francisco.
69. Tsotsos, J.K. (1991) Is complexity theory appropriate for analyzing cognitive systems? Behav. Brain Sci., 14, 770-773.
70. Kube, P.R. (1990) Complexity is complicated. Behav. Brain Sci., 13, 450-151.
71. Kube, P.R. (1991) Unbounded visual search is not both biologically plausible and NP-complete. Behav. Brain Sci., 14, 768-773.
72. Reif, J.H. and Sharir. M. (1994) Motion planning in the presence of moving obstacles. J. ACM, 41, 764-790.
73. Baral, C., Kreinovich, V. and Trejo, R. (2000) Computational complexity of planning and approximate planning in presence of incompleteness. Artif. Intell., 122, 241-267.
74. Eiter, T., Faber, W., Leone, N., Pfeiffer, G. and Polleres, A. (2000) Planning under Incomplete Knowledge. Proc. First Int. Conf. Computational Logic, pp. 807-821, Lecture Notes in Computer Science, vol. 1861, pp. 807-821. Springer-Verlag, Berlin.
75. Turner, H. (2002) Polynomial-lenght planning spans the polynomial hierarchy. Proc. Eight European Conf. Logics in Computer Science (JELIA 2002), pp. 111-124. Lecture Notes in Artificial Intelligence, Vol. 2424. Springer-Verlag, Berlin.
76. Holyoak, K.J. and Thagard, P. (1997) The analogical mind. Am. Psychol., 52, 35-44.
77. Rosch, E. (1973) On the internal structure of perceptual and semantic categories. In Moore, T.E. (ed), Cognitive Development and the Acquisition of Language. Academic Press, New York.
78. Rosch, E. and Mervis, C.B. (1975) Family resemblances: Studies in the internal structure of categories. Cogn. Psychol., 7, 573-605.
79. Smith, E.E. (1995) Concepts and categorization. In Osherson, D.N. and Smith, E.E. (eds), Thinking: An Invitation to Cognitive Science. MIT Press, Cambridge, MA.
80. Hahn, U., Chater, N. and Richardson, L.B. (2003) Similarity as transformation. Cognition, 87, 1-32.
81. Jones, N.C. and Pevzner, P.A. (2004) An Introduction to Bioinformatics Algorithms. MIT Press, Cambridge, MA.
82. Pevzner, P.A. (2000) Computational Molecular Biology: An Algorithmic Approach. MIT Press, Cambridge, MA.
83. Tversky, A. (1977) Features of similarity. Psychol. Rev., 84 327-352.
84. Pothos, E.M. and Chater, N. (2001) Category learning without labels - A simplicity approach. Proc. 23rd Annual Conf. Cognitive Science Society, pp. 774-779. Lawrence Erlbaum Associates, Hillsdale, NJ.
85. Pothos, E.M. and Chater, N. (2002) A simplicity principle in unsupervised human categorization. Cogn. Sci., 26, 303-343.
86. Oaksford, M.R. and Chater, N. (1998) Rationality in an Uncertain World: Essays on Cognitive Science of Human Reasoning. Psychology Press Ltd, Publishers, East Sussex, UK.
87. Oaksford, M.R. and Chater, N. (1993) Reasoning theories and bounded rationality. In Manktelow, K.I. and Over, D.E. (eds), Rationality: Psychological and philosophical perspectives. Routledge, London.
88. Reiter, R. (1980) A logic for default reasoning. Artif. Intell., 13, 81-132.
89. Chater, N., Tenebaum, J.B. and Yuillne, A. (eds) (2006) Special issue: probabilistic models in cognition. Trends Cogn. Sci., 10, 287-344.
90. Griffiths, T.L. and Tenenbaum, J.B. (2006) Optimal predictions in everyday cognition. Psychol. Sci., 17, 767-773.
91. Krynski, T.R. and Tenenbaum, J.B. (2003) The role of causal models in reasoning under uncertainty. Proc. Twenty-Fifth Annual Conf. Cognitive Science Society, pp. 692-697. Lawrence Erlbaum Associates, Hillsdale, NJ.
92. Dreyfus, H. L. (1979) What Computers Can't Do. Harper Colophon Books, New York.
93. Dreyfus, H.L. (1992) What Computers Still Can't Do. MIT Press, Cambridge, MA.
94. Abdelbar, A. and Hedetniemi, S.M. (1998) Approximation MAPs for belief networks is NP-hard and other theorems. Artif. Intell., 102, 21-38.
95. Gigerenzer, G. and Goldstein, D.G. (1996) Reasoning the fast and frugal way: Models of bounded rationality. Psychol. Rev., 103, 650-669.
96. Todd, P.M. and Gigerenzer, G. (2000) Précis of simple heuristics that make us smart. Behav. Brain Sci., 23, 727-780.
97. Valiant, L.G. (1994) Circuits of the Mind. Oxford University Press.
98. Cesati, M. and D. Ianni, M. (1997) Parallel parameterized complexity. Electron. Colloq. Comput. Complexity, 4.
99. Downey, R.G., Fellows, M.R. and Regan, K.W. (1998) Parameterized circuit complexity and the W hierarchy. Theor. Comput. Sci., 191 97-115.
100. Fellows, M.R. (2000) Parameterized complexity: New developments and research frontiers. In Downey, R.G. and Hirschfeldt, D. (eds), Aspects of Complexity, pp. 51-72. de Gruyter Series in Logic and Its Applications, Vol. 4, de Gruyler, Berlin.
101. Simon, H.A. (1990) Invariants of human behavior. Ann. Rev. Psychol. 41, 1-19.