List of publications » One-Variable Word Equations and Three-Variable Constant-Free Word Equations

A1 Journal article – refereed

One-Variable Word Equations and Three-Variable Constant-Free Word Equations

List of Authors: Nowotka D, Saarela A

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

Publication year: 2018

Journal: International Journal of Foundations of Computer Science

Journal name in source: INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE

Journal acronym: INT J FOUND COMPUT S

Volume number: 29

Issue number: 05

Number of pages: 16

ISSN: 0129-0541

eISSN: 1793-6373

Abstract

We prove connections between one-variable word equations and three-variable constant-free word equations, and use them to prove that the number of equations in an independent system of three-variable constant-free equations is at most logarithmic with respect to the length of the shortest equation in the system. We also study two well-known conjectures. The first conjecture claims that there is a constant c such that every one-variable equation has either infinitely many solutions or at most c. The second conjecture claims that there is a constant c such that every independent system of three-variable constant-free equations with a nonperiodic solution is of size at most c. We prove that the first conjecture implies the second one, possibly for a different constant.

We prove connections between one-variable word equations and three-variable constant-free word equations, and use them to prove that the number of equations in an independent system of three-variable constant-free equations is at most logarithmic with respect to the length of the shortest equation in the system. We also study two well-known conjectures. The first conjecture claims that there is a constant c such that every one-variable equation has either infinitely many solutions or at most c. The second conjecture claims that there is a constant c such that every independent system of three-variable constant-free equations with a nonperiodic solution is of size at most c. We prove that the first conjecture implies the second one, possibly for a different constant.

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