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



: Nowotka D, Saarela A

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

: 2018

: International Journal of Foundations of Computer Science

: INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE

: INT J FOUND COMPUT S

: 29

: 05

: 935

: 950

: 16

: 0129-0541

: 1793-6373

DOI: https://doi.org/10.1142/S0129054118420121(external)

: https://research.utu.fi/converis/portal/detail/Publication/35741481(external)


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.

Last updated on 2024-26-11 at 14:13