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Recently, a number of watermarking-based intellectual property protection techniques have been proposed. Although they have been applied to different stages in the design process and have a great variety of technical and theoretical features, all of them share two common properties: 1) they are applied solely to optimization problems and 2) do not involve any optimization during the watermarking process. In this paper, we propose the first set of optimization-intensive watermarking techniques for decision problems. In particular, we demonstrate, by example of the Boolean satisfiability (SAT) problem, how one can select a subset of superimposed watermarking constraints so that the uniqueness of the signature and the likelihood of satisfying the satisfiability problem are simultaneously maximized. We have developed three SAT watermarking techniques: adding clauses, deleting literals, and push-out and pull-back. Each technique targets different types of signature-induced constraint superimposition on an instance of SAT problem. In addition to comprehensive experimental validation, we theoretically analyze the potentials and limitations of the proposed watermarking techniques. Furthermore, we analyze the three proposed optimization-intensive watermarking SAT techniques in terms of their suitability for copy detection.