The constant depth threshold circuit complexity of iterated addition, multiplication, and iterated multiplication in rings Z Z], where is an algebraic integer, is studied. It is shown that iterated addition is 1{approximable, multiplication is 2{approximable, and iterated multiplication is 3{approximable.

Iterated hairpin completion is an operation on formal languages that is inspired by the hairpin formation in DNA biochemistry. Iterated hairpin completion of a word (or more precisely a singleton language) is always a context-sensitive language and for some words it is known to be non-context-free. However, it is unknown whether regularity of iterated hairpin completion of a given word is decid...