Circuit Synthesis from Fibonacci Decision Diagrams

In decision diagrams (DDs) methods for circuit synthesis, it is possible to directly transfer a DD for a given function f into a network realizing f by the replacement of non-terminal nodes in the DD with the corresponding circuit modules. The chief bottleneck of mapping a DD into a network is the inherent feature that the depth of the network produced, is equal to the number of variables in f. For this reason, it is proposed a method for small depth circuit synthesis through reachability matrices describing connections among the nodes in the DD for f. In this paper, we first generalized DD methods for circuit design to Fibonacci interconnection topologies through the Fibonacci decision diagrams (FibDDs). Then, we extended the small depth circuit synthesis method to FibDDs. In this way, design methods through DDs are completely transferred from Boolean to Fibonacci topologies.