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How can you describe a deterministic finite automaton (DFA) used to fill a checkerboard with dominos?

A) A device that randomly places dominos on the checkerboard
B) A system that systematically fills the checkerboard using dominos without overlap
C) An algorithm that skips every other square while placing dominos
D) A mechanism that fills the checkerboard with dominos diagonally

User Don Djoe
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1 Answer

4 votes

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:

  1. Start by placing a domino horizontally on the first row, covering the first two squares.
  2. Move to the next row and place a domino vertically, covering the first two squares in that row.
  3. Repeat this pattern for each row, alternating between placing dominos horizontally and vertically.
  4. 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.

User Adrian Pascu
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