Notation symbol $x$ for functions

Question

On the Modern Stream Ciphers slide #6, the following expression is used:

$$ \{0,1\}^s × R ⟶ \{0,1\}^n$$

What does $×$ mean? I've seen $×$ used in a few other contexts, and I suspect it means "transforms", but I'm uncertain.

Answer 1

It represents what is called a Cartesian product of two sets. This operation takes in multiple sets and simply returns a single set, often referred to as the product set. To put it logically:

$$A\times B = \{\,(a,b)\mid a\in A \ \wedge \ b\in B\,\}$$

An easy way of visualizing this is a standard deck of cards. You have the set of the 13 standard ranks: Queens, Kings and so forth. You also have the set of 4 suits. When you take the Cartesian product of these two sets, you get out the deck of cards. This is: 52 ordered pairs of suits and ranks.