This article addresses computational synthesis systems that attempt to find a structural description that matches a set of initial functional requirements and design constraints with a finite sequence of production rules. It has been previously shown by the author that it is computationally difficult to identify a sequence of production rules that can lead to a satisficing design solution. As a result, computational synthesis, particularly with large volumes of selection information, requires effective design search procedures. Many computational synthesis systems utilize transformational search strategies. However, such search strategies are inefficient due to the combinatorial nature of the problem. In this article, the problem is approached using a completely different paradigm. The new approach encodes a design search problem as a Boolean (propositional) satisfiability problem, such that from every satisfying Boolean-valued truth assignment to the corresponding Boolean expression we efficiently can derive a solution to the original synthesis problem (along with its finite sequence of production rules). A major advantage of the proposed approach is the possibility of utilizing recently developed powerful randomized search algorithms for solving Boolean satisfiability problems, which considerably outperform the most widely used satisfiability algorithms. The new design-as-satisfiability technique provides a flexible framework for stating a variety of design constraints, and also represents properly the theory behind modern constraint-based design systems.