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We also stress that complexity is defined as the minimal cost of a solution, and not as a cost of a specific algorithm. This distinction is crucial since in many cases, “complexity” is used by many people as a synonym of the word “cost”. For us, complexity is a property of a problem and we are seeking an algorithm whose cost is equal to the complexity or, more likely, whose cost is as close to the complexity as possible. From a mathematical point of view, to know the complexity of a problem means that we can prove two bounds.

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