On word problems in equational theories
14th International Colloquium on Automata, languages and programming
Critical pair criteria for completion
Journal of Symbolic Computation
Only prime superpositions need be considered in the Knuth-Bendix completion procedure
Journal of Symbolic Computation
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Handbook of theoretical computer science (vol. B)
String-rewriting systems
Simulation of Turing machines by a regular rewrite rule
Theoretical Computer Science
On the conjecture of Yves Me´tivier
Theoretical Computer Science - Special issue on number theory, combinatorics and applications to computer science
Confluence by decreasing diagrams
Theoretical Computer Science
On termination of one rule rewrite systems
Theoretical Computer Science
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Parallel reductions in &lgr;-calculus
Information and Computation
Total termination of term rewriting is undecidable
Journal of Symbolic Computation
Proof lengths for equational completion
Information and Computation - special issue: symposium on theoretical aspects of computer software TACS '94
On termination of confluent one-rule string-rewriting systems
Information Processing Letters
Contributions of Ronald V. Book to the theory of string-rewriting systems
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
On normalizing non-terminating one-rule string rewriting systems
Theoretical Computer Science
Termination and derivational complexity of confluent one-rule string-rewriting systems
Theoretical Computer Science
Decidability of Termination of Grid String Rewriting Rules
SIAM Journal on Computing
Semi-Thue Systems with an Inhibitor
Journal of Automated Reasoning
Relative undecidability in term rewriting: I. the termination Hierarchy
Information and Computation
Termination of Linear Rewriting Systems (Preliminary Version)
Proceedings of the 8th Colloquium on Automata, Languages and Programming
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
Relative Undecidability in the Termination Hierarchy of Single Rewrite Rules
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
A Confluence Criterion Based on the Generalised Neman Lemma
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Confluence of One-Rule Thue Systems
IWWERT '90 Proceedings of the First International Workshop on Word Equations and Related Topics
Simultaneous Critical Pairs and Church-Rosser Property
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Simulation of Turning Machines by a Left-Linear Rewrite Rule
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
On the Termination Problem for One-Rule Semi-Thue System
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Development Closed Critical Pairs
HOA '95 Selected Papers from the Second International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Confluence without Termination via Parallel Critical Pairs
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
A New Parallel Closed Condition for Church-Rossser of Left-Linear Term Rewriting Systems
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Decision Problems for Semi-Thue Systems with a Few Rules
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Deleting string rewriting systems preserve regularity
Theoretical Computer Science - Developments in language theory
Termination Proofs for String Rewriting Systems via Inverse Match-Bounds
Journal of Automated Reasoning
Abstract canonical presentations
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
ACM Transactions on Computational Logic (TOCL)
Handling the growth by definition of mechanical languages
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
Termination of string rewriting rules that have one pair of overlaps
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Termination of single-threaded one-rule semi-thue systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Decreasing Diagrams and Relative Termination
Journal of Automated Reasoning
Decreasing diagrams and relative termination
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
| Hi-index | 0.00 |
As a window into the subject, we recount some of the history (and geography) of two mature, challenging, partially open, partially closed problems in the theory of rewriting (numbers 13 and 21 from the original RTA List of Open Problems). One problem deals with (criteria for left-linear) confluence and the other with termination (of one linear or string rule), the two paradigmatic properties of interest for rewrite systems of any flavor. Both problems were formulated a relatively long time ago, have seen considerable progress, but remain open. We also venture to contemplate the future evolution and impact of these investigations.