Abstract
Computational aspects of the Post Correspondence Problem (PCP) are studied. Specifically, we describe our efforts to find difficult instances of the PCP, where a “difficult” instance is defined to mean an instance whose shortest solution is long. As a result, we attempt to quantify the difficulty of the PCP in the same way the Busy Beaver Problem does for the Turing Halting Problem. We find instances of the PCP that have quite long solutions even when the number of pairs and the length of the strings is small, e.g., four and three, respectively. We discuss algorithms for solving the PCP and for generating difficult PCP instances. This problem poses unique difficulties because the size of the search space is unbounded.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Culberson, J.: Sokoban is PSPACE-complete. In: Int. Conf. Fun with Algorithms, Elba, June 1998
Denning, P.J., Dennis, J.B., and Qualitz, J.E.: Machines, Languages and Computation. Prentice-Hall Inc, 1978
Ehrenfeucht, A, Karhumaki, J., and Rozenberg, G.: The (generalized) post correspondence problem with lists consisting of two words is decidable. Theoret. Comput. Sci., 21, 2, 119–144, 1982
Fraenkel, A.S., Garey, M. R., Johnson, D. S., Schfäer, T., and Yesha, Y.: The complexity of checkers on an N × N board-preliminary report. In: Proc. 19th IEEE Symp. On the Foundations of Computer Science, pp. 55–64, 1978
Gurari, E.: An Introduction to the Theory of Computation. Computer Science Press, 1989
Hopcroft, J.E., and Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley Publ., 1979
Junghanns, A. and Schaeffer, J: Sokoban: Improving the Search with Relevance Cuts. To appear in: Journal of Theoretical Computing Science, 1999
Lichtenstein, D., and Sipser, M.: Go is polynomial-space hard. J.ACM 23, pp. 710–719, 1976
Manna, Zohar: Mathematical Theory of Computation. McGraw Hill Inc, 1974
Marxen, H., and Buntrock, J.: Attacking the busy beaver. Bul. EATCS, 40, 247–251, 1990
Marxen, H, Buntrock, J, and Thompson, C: http://www.drb.insel.de/~heiner/BB/index.html
Murase, Y., Matsubaara, H., and Hiraga, Y.: Automatic Making of Sokoban Problems. In: Fourth Pacific Rim International Conference in Artificial Intelligence, Cairns, Australia, Aug 26-30, 1996
Post, E.L.,: A variant of a recursively unsolvable problem. Bull. of the Am. Math. Soc., 52, 264–268, 1946
Rado, T.: On non-computable functions. Bell Sys. Tech. J., 41, 3, 877–884, 1962
Reinefeld, A, and Marsland, T.A.: Enhanced Iterative-Deepening Search. In: IEEE Trans. Pattern Anal. Machine Intell., Vol. 16, No. 7, 701–710, July, 1994
Taylor, L, and Korf, R.: Pruning Duplicate Nodes in Depth-First Search. In: Proc. 11th National Conf. on AI, AAAI-93, 756–761,July 11-15,1993.
Wolf, T.: Generating tsume go problems with GoTools. In: Proceedings of the Fourth International Computer Olympidade, London, 1992
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lorentz, R.J. (2001). Creating Difficult Instances of the Post Correspondence Problem. In: Marsland, T., Frank, I. (eds) Computers and Games. CG 2000. Lecture Notes in Computer Science, vol 2063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45579-5_14
Download citation
DOI: https://doi.org/10.1007/3-540-45579-5_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43080-3
Online ISBN: 978-3-540-45579-0
eBook Packages: Springer Book Archive