# Theory of Computation with a Vending Machine

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Problem: Consider a vending machine that accepts nickels, dimes and quarters.

1. Give an implicit definition of the set of all strings whose value mod 30 = 0.

2. Give recursive definition of the set of all strings whose value = 30 cents.

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Solution:

1.

= { str | (str ε C* ) ∧ ( (value(str) mod 30 ) = 0 ) }

2. Let describe the set of all strings whose sum is 30.

Basis case: nnnnn ∈ ,

nq ∈ and qn ∈ ...

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