INFORMATION AND CONTROL 63, 58-66 (1984) The Uniform Conjugacy Problem for Finite Church-Rosser Thue Systems Is NP-Complete PALIATH NARENDRAN* General Electric Corporate Research and Development Center, Schenectady, NewYork 12345, U.S.A. FRIEDRICH OTTO t Fachbereich lnformatik, Universitaet Kaiserslautern, Postfach 3049, 6750, Kaiserslautern, West Germany AND KARL WINKLMANN $ Computer Science Department, University of Colorado, Boulder, Colorado 80309, U.S.A. The uniform conjugacy problem for finite Church-Rosser Thue systems over alphabet X is NP-complete, if X contains at least two letters. If L" contains a single letter only, then this problem is tractable. © 1984AcademicPress, Inc. 1. INTRODUCTION The Church-Rosser property has been shown to be very useful when dealing with decision problems for Thue systems. So, while in general the word problem for a finite Thue system is undecidable, this problem is decidable in linear time for a finite Thue system that is Chureh-Rosser * The work of this author was supported in part by the National Science Foundation under Grant GP-MCS-8302123. It was performed while he was at the Rensselaer Polytechnic Institute at Troy. t The work of this author was supported in part by the Deutsche Forschungsgemeinschaft and by the National Science Foundation under Grants MCS 80-11979 and MCS 83-14977. It was performed while he was visiting at the Department of Mathematics of the University of California at Santa Barbara. The work of this author was supported in part by the National Science Foundation under Grant MCS-8202964. It was performed while he was at the Department of Computer Science, Washington State University, Pullman, Washington. 58 0019-9958/84 $3.00 Copyright © 1984by AcademicPress, Inc. All rights of reproduction in any form reserved.