Footnotes
| 1 | By flip–flop we mean the three element monoid U2 = {1, a, b} with xy = y for y ≠ 1. |
| 2 | Historical sources do not entirely agree on the exact form. |
| 3 | The Vernam one-time pad was used on the red telephone which connected the White House to the Kremlin during the Cold War. |
| 4 | This scenario was taken from the lecture notes of a course taught by Holger Petersen at the University of Stuttgart in Summer Semester 2007. |
| 5 | The Gödel Prize is awarded annually for the best work in the field of theoretical computer science, published in the last 13 years. |
| 6 | According to Jacques Monod’s (1910–1976) book Le hasard et la nécessité. Essai sur la philosophie naturelle de la biologie moderne from 1970. |
| 7 | In the context of monoids, we use the symbol 1 for the empty word, too. Another standard notation for the empty word is λ. The symbol λ refers to the original work of Thue who published in German, where leeres Wort means empty word. |
| 8 | Given any rational set R of affine mappings the set { h(0) | h ∈ R} is a semilinear set, but we do not need this fact here. |
| 9 | Dyck was enobled “Ritter” (“Knight”) in 1901, and in 1903 he became the first rector of the Technical University of Munich. |
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