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The paper analyses different techniques that might be employed in order to solve various problems of combinatorial optimization and argues that the best results can be achieved by the use of software running on a general-purpose computer together with an FPGA-based reconfigurable co-processor. It suggests an architecture for a combinatorial coprocessor that is based on hardware templates and consists of reconfigurable functional and control units. Finally the paper demonstrates how the co-processor can be applied to two practical applications formulated over discrete matrices, the Boolean satisfiability and covering problems.