# Construct a DFA for L (determinist finite automaton)

Anonymous

Question description

Suppose that you are taking a walk with your dog along a straight-line path. Your dog is on a leash that has length two, meaning that the distance between you and your dog can be at most two units. You and your dog start at the same position. Consider the alphabet Σ = {y, d}. A string in Σ* can be thought of as a series of events in which either you or your dog moves forward one unit. For example, the string “yydd” means that you take two steps forward, then your dog takes two steps forward. Let L = { w ∈ Σ* | w describes a series of steps that ensures that you and your dog are never more than two units apart }. Construct a DFA for L.

(To double check, the string "yydddd" is valid)

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