scholarly journals An Optimal Bound on the Solution Sets of One-Variable Word Equations and its Consequences

2022 ◽  
Vol 51 (1) ◽  
pp. 1-18
Author(s):  
Dirk Nowotka ◽  
Aleksi Saarela
Keyword(s):  
Solution Sets ◽  
Optimal Bound ◽  
Word Equations

scholarly journals On the structure of solution-sets to regular word equations

2021 ◽  
Author(s):  
Joel D. Day ◽  
Florin Manea
Keyword(s):  
Directed Graph ◽  
Regular Word ◽  
Combinatorial Proof ◽  
Solution Sets ◽  
Word Equation ◽  
All Solutions ◽  
Word Equations ◽  
Rewriting Rules

AbstractFor quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. For regular word equations – those for which each variable occurs at most once on each side of the equation – we investigate the properties of this graph, such as bounds on its diameter, size, and DAG-width, as well as providing some insights into symmetries in its structure. As a consequence, we obtain a combinatorial proof that the problem of deciding whether a regular word equation has a solution is in NP.

Studying Word Equations by a Method of Weighted Frequencies

2018 ◽  
Vol 162 (2-3) ◽  
pp. 223-235 ◽  
Author(s):  
Aleksi Saarela
Keyword(s):  
Word Equations
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