Critical exponents of infinite balanced words.

Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + 2 / 2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + 5) / 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. [ABSTRACT FROM AUTHOR]