  This thesis studies the single-use restriction for register automata and
transducers over infinite alphabets. The restriction requires that a
read-access to a register should have the side effect of destroying its
contents. This constraint results in robust classes of languages and
transductions. For automata models, we show that one-way register automata,
two-way register automata, and orbit-finite monoids have the same expressive
power. For transducer models, we show that single-use Mealy machines and
single-use two-way transducers admit versions of the Krohn-Rhodes decomposition
theorem. Moreover, single-use Mealy machines are equivalent to an algebraic
model called local algebraic semigroup transductions. Additionally, we show
that single-use two-way transducers are equivalent to single-use streaming
string transducers (SSTs) over infinite alphabets and to regular list functions
with atoms.
  Compared with the previous work arXiv:1907.10504, this thesis offers a
coherent narrative on the single-use restriction. We introduce an abstract
notion of single-use functions and use them to define all the discussed
single-use models. We also introduce and study the algebraic models of local
semigroup transduction and local rational semigroup transduction.
