While studies have shown the importance of listener feedback in dialogue, we still know little about the factors that impact its quality. Feedback can indicate either that the addressee is aligning with the speaker (i.e. ‘positive’ feedback) or that there is some communicative trouble (i.e. ‘negative’ feedback). This study provides an in-depth account of listener feedback in task-oriented dialogue (a director–matcher game), where positive and negative feedback is produced, thus expressing both alignment and misalignment. By manipulating the listener’s cognitive load through a secondary mental task, we measure the effect of divided attention on the quantity and quality of feedback. Our quantitative analysis shows that performance and feedback quantity remain stable across cognitive load conditions, but that the timing and novelty of feedback vary: turns are produced after longer pauses when attention is divided between two speech-focused tasks, and they are more economical (i.e. include more other-repetitions) when unrelated words need to be retained in memory. These findings confirm that cognitive load impacts the quality of listener feedback. Finally, we found that positive feedback is more often generic and shorter than negative feedback and that its proportion increases over time.

A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance p match. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of the fact that there exists an infinite binary word which contains finitely many squares and simultaneously avoids words of exponent larger than 7/3. Our infinite word contains 12 squares, which is the smallest possible number of squares to get the property, and 2 factors of exponent 7/3. These are the only factors of exponent larger than 2. The value 7/3 introduces what we call the finite-repetition threshold of the binary alphabet. We conjecture it is 7/4 for the ternary alphabet, like its repetitive threshold.

We survey several quantitative problems on infinite words related to repetitions, recurrence, and palindromes, for which the Fibonacci word often exhibits extremal behaviour.

We investigate the density of critical factorizations of infinite sequences of words. The density of critical factorizations of a word is the ratio between the number of positions that permit a critical factorization, and the number of all positions of a word. We give a short proof of the Critical Factorization Theorem and show that the maximal number of noncritical positions of a word between two critical ones is less than the period of that word. Therefore, we consider only words of index one, that is words where the shortest period is larger than one half of their total length, in this paper. On one hand, we consider words with the lowest possible number of critical points and show, as an example, that every Fibonacci word longer than five has exactly one critical factorization and every palindrome has at least two critical factorizations. On the other hand, sequences of words with a high density of critical points are considered. We show how to construct an infinite sequence of words in four letters where every point in every word is critical. We construct an infinite sequence of words in three letters with densities of critical points approaching one, using square-free words, and an infinite sequence of words in two letters with densities of critical points approaching one half, using Thue–Morse words. It is shown that these bounds are optimal.