This paper describes two speed-up techniques for Boolean matching of LUT-based circuits. One is one-hot encoding technique for variables representing input assignments. Though it requires more variables than existing binary encoding technique, almost all added clauses using one-hot encoding are binary clauses, which are suitable for efficient Boolean constraint propagation. The other is CEGAR (counter example guided abstraction refinement) technique which reduces the CPU time significantly. With both techniques, we can solve Boolean matching problem with 9 input function in 20 milliseconds on average, which is faster than the existing algorithms more than one order of magnitude.

Combinational logic circuits are usually implemented as multi-level networks of logic nodes. Multi-level logic simplification using the don't cares on each node is widely used. Large don't cares give good simplification results, but suffer from huge memory area and computation time. Extraction of useful don't cares and reduction of the size of the don't cares are important problems on the simplification using don't cares. In the paper, we propose a new robust heuristic method for the selection of don't cares. We consider an adaptive subnetwork for each simplified node in the network and introduce a stepwise enhancement method of the subnetwork considering the memory area and the network structure. The don't cares extracted from the adaptive subnetworks are called the local don't cares. We have implemented our method for satisfiability don't cares and observability don't cares. We have applied the method on MCNC89 benchmarks, and compared the experimental results with those of the SIS system. The results demonstrate the superiority of our method on the quality of the results and on the size of applicable circuits.