Journal ArticleDOI
Decidability of Termination of Grid String Rewriting Rules
TLDR
Grid rules cover all rules which terminate by a total division order and total division orders are shown to be irrelevant for the termination problem of one-rule string rewriting.Abstract:
Termination of string rewriting is known undecidable. Termination of string rewriting with only one rule is neither known decidable nor known undecidable. This paper presents a decision procedure for rules $u\rightarrow v$ such that some letter b from u occurs as often or less often in v. We call such rules "grid" rules. By far most rules are grid rules. Grid rules cover all rules which terminate by a total division order. Thus total division orders are shown to be irrelevant for the termination problem of one-rule string rewriting.read more
Citations
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Journal ArticleDOI
Decision problems for semi-Thue systems with a few rules
TL;DR: It is shown that the accessibilityproblem, the common descendant problem, the termination problem and the uniform termination problem are undecidable for 3-rules semi-Thue systems.
Book ChapterDOI
Matchbox: A Tool for Match-Bounded String Rewriting
TL;DR: Matchbox is the first program that delivers automated proofs of termination for some difficult string rewriting systems and can search for proof or disproof of a Boolean combination of match-height properties of a given rewrite system, and some of its transformed variants.
Book ChapterDOI
Open. Closed. Open.
TL;DR: The history (and geography) of two mature, challenging, partially open, partially closed problems in the theory of rewriting, the two paradigmatic properties of interest for rewrite systems of any flavor are recounted.
Journal Article
Termination of string rewriting rules that have one pair of overlaps
TL;DR: A partial solution to the long standing open problem whether termination of one-rule string rewriting is decidable by characterize termination of all one- rule string rewriting systems that have one such overlap at either end.
Journal ArticleDOI
On One-Rule Grid Semi-Thue Systems
Michel Latteux,Yves Roos +1 more
TL;DR: It is proved that for any one-rule grid semi-Thue system S, the set S(w) of all words obtainable from w using repeatedly the rewriting rule of S is a constructible context-free language.
References
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Book ChapterDOI
Simple Word Problems in Universal Algebras
Donald E. Knuth,Peter B. Bendix +1 more
TL;DR: In this article, an algorithm is described which is capable of solving certain word problems: i.e., deciding whether or not two words composed of variables and operators can be proved equal as a consequence of a given set of identities satisfied by the operators.
Proceedings ArticleDOI
Decision problems for semi-Thue systems with a few rules
TL;DR: It is shown that the the Termination Problem, the U-Termination problem, the Accessibility Problem and the Common-Descendant Problem are undecidable for 3 rules semi-Thue systems.
Journal ArticleDOI
Simulation of Turing machines by a regular rewrite rule
TL;DR: It is proved that for any Turing machine, there exists a regular (i.e. left-linear and nonoverlapping, also called orthogonal) and variable-preserving rule that simulates its behaviour.