Deterministic tree pushdown automata and monadic tree rewriting systems
Journal of Computer and System Sciences
Term rewriting and all that
Right-Linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Basic Paramodulation and Decidable Theories
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Reachability and confluence are undecidable for flat term rewriting systems
Information Processing Letters
Ground reducibility is EXPTIME-complete
Information and Computation
A new decidability technique for ground term rewriting systems with applications
ACM Transactions on Computational Logic (TOCL)
On the Normalization and Unique Normalization Properties of Term Rewrite Systems
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Termination of rewriting with right-flat rules
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Confluence of shallow right-linear rewrite systems
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Decidability of termination for semi-constructor TRSs, left-linear shallow TRSs and related systems
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
The confluence problem for flat TRSs
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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Computation with a term rewrite system (TRS) consists in the application of its rules from a given starting term until a normal form is reached, which is considered the result of the computation. The unique normalization (UN) property for a TRS $\mathcal{R}$ states that any starting term can reach at most one normal form when $\mathcal{R}$ is used, i.e. that the computation with $\mathcal{R}$ is unique. We study the decidability of this property for classes of TRS defined by syntactic restrictions such as linearity (variables can occur only once in each side of the rules), flatness (sides of the rules have height at most one) and shallowness (variables occur at depth at most one in the rules). We prove that UN is decidable in polynomial time for shallow and linear TRS, using tree automata techniques. This result is very near to the limits of decidability, since this property is known undecidable even for very restricted classes like right-ground TRS, flat TRS and also right-flat and linear TRS. We also show that UN is even undecidable for flat and right-linear TRS. The latter result is in contrast with the fact that many other natural properties like reachability, termination, confluence, weak normalization, etc. are decidable for this class of TRS.