This Article 
 Bibliographic References 
 Add to: 
Automata for the Assessment of Knowledge
May/June 2001 (vol. 13 no. 3)
pp. 451-461

Abstract—The results of this paper can be applied to construct efficient algorithms for the adaptive assessment of the students' knowledge. The problem of knowledge assessment is a special case of the problem of assessing the state of a system. These results are obtained suggesting a new assessment algorithm whose formal equivalence to previously suggested assessment algorithms is proven. A simulation study illustrates the vast improvements of efficiency with the new algorithm.

[1] J.-P. Doignon and J.-C. Falmagne, “Spaces for the Assessment of Knowledge,” Int'l J. Man-Machine Studies, vol. 23, pp. 175–196, 1985.
[2] J.-P. Doignon and J.-C. Falmagne, Knowledge Spaces. Berlin: Springer-Verlag, 1999.
[3] J.-C. Falmagne and J.-P. Doignon, “A Markovian Procedure for Assessing the State of a System,” J. Math. Psychology, vol. 32, pp. 232–258, 1988.
[4] M. Schrepp, “A Generalization of Knowledge Space Theory to Problems with More than Two Answer Alternatives,” J. Math. Psychology, vol. 41, pp. 237–243, 1997.
[5] K. Baumunk and C.E. Dowling, “Validity of Spaces for Assessing Knowledge about Fractions,” J. Math. Psychology, vol. 41, pp. 99–105, 1997.
[6] J.-C. Falmagne and J.-P. Doignon, “A Class of Stochastic Procedures for the Assessment of Knowledge,” British J. Math. and Statistical Psychology, vol. 41, pp. 1–23, 1988.
[7] J. Carroll and D. Long, Theory of Finite Automata. Englewood Cliffs, N.J.: Prentice Hall, 1989.
[8] J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Apr. 1979.
[9] E. Degreef, J.-P. Doignon, A. Ducamp, and J.-C. Falmagne, “Languages for the Assessment of Knowledge,” J. Math. Psychology, vol. 30, pp. 243–256, 1986.
[10] J.-P. Doignon, “Probabilistic Assessment of Knowledge,” Knowledge Structures, D. Albert, ed., pp. 1–56, 1994.
[11] C.E. Dowling, C. Hockemeyer, and A.H. Ludwig, “Adaptive Assessment and Training Using the Neighbourhood of Knowledge States,” Intelligent Tutoring Systems, C. Frasson, G. Gauthier, and A. Lesgold, eds., pp. 578–586, 1996.
[12] O. Ore, Theory of Graphs. Providence, R.I.: AMS Colloquium Publications, Am. Math. Soc., 1962.
[13] G. Birkhoff, Lattice Theory. Am. Math. Soc. Colloquium Publication, Am. Math. Soc., third ed., 1967.

Index Terms:
Knowledge assessment, deterministic finite automaton, knowledge space, knowledge state, assessment language.
Cornelia E. Dowling, Cord Hockemeyer, "Automata for the Assessment of Knowledge," IEEE Transactions on Knowledge and Data Engineering, vol. 13, no. 3, pp. 451-461, May-June 2001, doi:10.1109/69.929902
Usage of this product signifies your acceptance of the Terms of Use.