Minimal and complete word unification
Journal of the ACM (JACM)
Text algorithms
Complexity of Makanin's algorithm
Journal of the ACM (JACM)
Satisfiability of word equations with constants is in NEXPTIME
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Efficient Solving of the Word Equations in One Variable
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
Application of Lempel-Ziv Encodings to the Solution of Words Equations
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Word Equations with Two Variables
IWWERT '91 Proceedings of the Second International Workshop on Word Equations and Related Topics
The Security of Individual RSA Bits
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Satisfiability of Word Equations with Constants is in PSPACE
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Finding patterns common to a set of strings (Extended Abstract)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
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For a word equation E of length n in one variable x occurring #x times in E a resolution algorithm of O(n+#x log n) time complexity is presented here. This is the best result known and for the equations that feature #x n/log n it yields time complexity of O(n) which is optimal. Additionally, we prove that the set of solutions of one-variable word equations is either of the form F where F is a set of O(log n) words or of the form F 驴 (uv)+u where F is a set of O(log n) words and u, v are some words such that uv is a primitive word.