psychoacoustics is the study of sound perception and cognition

• how does sound work
• how we perceive it
• why? and what are its applications?

Let \(L\) be a regular language; then there is a positive integer \(P\) such that, for all strings \(w \in L\) with \(|w| \geq P\) there is a way to write \(w = x y z\), where…

• \(|y| > 0\) — so \(y \neq \varepsilon\)
• \(|x y | \leq P\)
• for all \(i \geq 0, xy^{i}z \in L\) (where \(y^{i}\) is \(y\) repeated \(i\) times); note that this also means that we can also reduce \(y\) in size to \(y \in \varepsilon\), and it will still hold.

Proof: