Final answer:
A deterministic finite automaton (DFA) used to fill a checkerboard with dominos is a system that systematically fills the checkerboard using dominos without overlap. The correct option is B.
Step-by-step explanation:
A deterministic finite automaton (DFA) used to fill a checkerboard with dominos is described as a system that systematically fills the checkerboard using dominos without overlap. This means that each domino is placed in a way that it covers two adjacent squares on the checkerboard, without any two dominos overlapping. This is achieved by following a set of rules or an algorithm to determine the placement of dominos.
To explain further, let's consider a simple DFA that fills a checkerboard with dominos:
- Start by placing a domino horizontally on the first row, covering the first two squares.
- Move to the next row and place a domino vertically, covering the first two squares in that row.
- Repeat this pattern for each row, alternating between placing dominos horizontally and vertically.
- If the checkerboard has an odd number of rows, there will be one row left at the end. In that case, place a domino horizontally to cover the remaining two squares.
By following this algorithm, the DFA will systematically fill the checkerboard with dominos without any overlap, ensuring all squares are covered.