Handbook of theoretical computer science (vol. B)
Canonical Equational Proofs
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Equality and Disequality Constraints on Direct Subterms in Tree Automata
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Rewrite Closure for Ground and Cancellative AC Theories
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Decidable Approximations of Term Rewriting Systems
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
A new decidability technique for ground term rewriting systems with applications
ACM Transactions on Computational Logic (TOCL)
Termination of rewrite systems with shallow right-linear, collapsing, and right-ground rules
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Confluence of shallow right-linear rewrite systems
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Regular Tree Languages And Rewrite Systems
Fundamenta Informaticae
Unique Normalization for Shallow TRS
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
New Undecidability Results for Properties of Term Rewrite Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Non-Linear Rewrite Closure and Weak Normalization
Journal of Automated Reasoning
| Hi-index | 0.00 |
Computation with a term rewrite system (TRS) consists of the application of rules from a given starting term until a normal form is reached. Two natural questions arise from this the definition: whether all terms can reach at least one normal form (normalization property), and whether all terms can reach at most one normal form (unique normalization property).We study the decidability of these properties for two syntactically restricted classes of TRS: for (i) shallow right-linear TRS, and for (ii) linear right-shallow TRS.We show that the normalization property is decidable for both cases (i) and (ii), and that the unique normalization property is undecidable for case (ii), whereas for case (i) remains unknown. Nevertheless, for case (i), if the normalization property is satisfied, then the unique normalization property becomes decidable. Hence, whether all terms reach exactly one normal form for TRS of kind (i) is decidable.These results are based on known constructions of tree automata with constraints and rewrite closure, and on reducing the normalization property to normalization from a concrete finite set of terms.