Rampersad, NaradShallit, JeffreyVandomme, Élise2020-03-182020-03-182019-07-19https://doi.org/10.1016/j.tcs.2018.10.017http://hdl.handle.net/10012/15702The final publication is available at Elsevier via https://doi.org/10.1016/j.tcs.2018.10.017. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + root2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + root5)/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalinfinite wordbalanced wordSturmian wordcritical exponentArticle