The Confluence Problem for Flat TRSs

We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one.

[1]  Michio Oyamaguchi,et al.  The reachability and related decision problems for monadic and semi-constructor TRSs , 2006, Inf. Process. Lett..

[2]  Michio Oyamaguchi.  The reachability and joinability problems for right-ground term-rewriting systems , 1991 .

[3]  Ashish Tiwari.  Deciding confluence of certain term rewriting systems in polynomial time , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[4]  Takashi Nagaya,et al.  Decidability for Left-Linear Growing Term Rewriting Systems , 1998, Inf. Comput..

[5]  Michio Oyamaguchi,et al.  The Church-Rosser Property for Ground Term-Rewriting Systems is Decidable , 1987, Theor. Comput. Sci..

[6]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[7]  Robert Nieuwenhuis,et al.  The confluence of ground term rewrite systems is decidable in polynomial time , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[8]  Hiroyuki Seki,et al.  Right-Linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability , 2000, RTA.

[9]  Tobias Nipkow,et al.  Term rewriting and all that , 1998 .

[10]  Yoshihito Toyama,et al.  Decidability for Left-Linaer Growing Term Rewriting Systems , 1999, RTA.

[11]  Yoshikatsu Ohta,et al.  The Joinability and Related Decision Problems for Semi-constructor TRSs , 2006 .

[12]  Ashish Tiwari,et al.  Confluence of Shallow Right-Linear Rewrite Systems , 2005, CSL.

[13]  Kai Salomaa,et al.  Deterministic Tree Pushdown Automata and Monadic Tree Rewriting Systems , 1988, J. Comput. Syst. Sci..

[14]  Ashish Tiwari,et al.  On the Confluence of Linear Shallow Term Rewrite Systems , 2003, STACS.

[15]  Florent Jacquemard,et al.  Reachability and confluence are undecidable for flat term rewriting systems , 2003, Inf. Process. Lett..

[16]  Jean-Pierre Jouannaud,et al.  Syntacticness, Cycle-Syntacticness, and Shallow Theories , 1994, Inf. Comput..

[17]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[18]  Sophie Tison,et al.  Decidability of the Confluence of Finite Ground Term Rewrite Systems and of Other Related Term Rewrite Systems , 1990, Inf. Comput..

[19]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.