Complexity Results for Confluence Problems
We study the complexity of the confluence problem for restricted kinds of semi-Thue systems, vector replacement systems and general trace rewriting systems. We prove that confluence for length-reducing semi-Thue systems is P-complete and that this complexity reduces to NC2 in the monadic case. For length-reducing vector replacement systems we prove that the confluence problem is PSPACE-complete and that the complexity reduces to NP and P for monadic systems and special systems, respectively. Finally we prove that for special trace rewriting systems, confluence can be decided in polynomial time and that the extended word problem for special trace rewriting systems is undecidable.
KeywordsPolynomial Time Word Problem Critical Pair Special Trace Thue System
Unable to display preview. Download preview PDF.
- [BO93]R.V. Book and F. Otto. String-Rewriting Systems. Springer, 1993.Google Scholar
- [DR95]V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.Google Scholar
- [GHR95]R. Greenlaw, H. J. Hoover, and W. L. Ruzzo. Limits to Parallel Computation: P-Completeness Theory. Oxford University Press, 1995.Google Scholar
- [Kar72]R. M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 85–103. Plenum Press, New York, 1972.Google Scholar
- [Loh98]M. Lohrey. On the confluence of trace rewriting systems. In V. Arvind and R. Ramanujam, editors, Foundations of Software Technology and Theoretical Computer Science, volume 1530 of Lecture Notes in Computer Science, pages 319–330. Springer, 1998.Google Scholar
- [Loh99]M. Lohrey. Complexity results for confluence problems. Technical Report 1999/05, University of Stuttgart, Germany, 1999. Available via ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart_fi/TR-1999-05/.Google Scholar
- [Maz77]A. Mazurkiewicz. Concurrent program schemes and their interpretations. DAIMI Rep. PB 78, Aarhus University, Aarhus, 1977.Google Scholar
- [NB72]M. Nivat and M. Benois. Congruences parfaites et quasi-parfaites. Seminaire Dubreil, 25(7-01–09), 1971–1972.Google Scholar
- [Och85]E. Ochmański. Regular behaviour of concurrent systems. Bulletin of the European Association for Theoretical Computer Science (EATCS), 27:56–67, October 1985.Google Scholar
- [Pap94]C.H. Papadimitriou. Computational Complexity. Addison Wesley, 1994.Google Scholar
- [VRL98]R. M. Verma, M. Rusinowitch, and D. Lugiez. Algorithms and reductions for rewriting problems. In Proceedings 9th Conference on Rewriting Techniques and Applications, Tsukuba (Japan), volume 1379 of Lecture Notes in Computer Science, pages 166–180. Springer, 1998.Google Scholar