Design of testable sequential circuits by repositioning flip-flops

This paper presents a technique to enhance the testability of sequential circuits by repositioning flip-flops. A novel retiming for testability technique is proposed that reduces cycle lengths in the dependency graph, converts sequential redundancies into combinational redundancies, and yields retimed circuits that usually require fewer scan flip-flops to break all cycles (except self-loops) as compared to the original circuit. Our technique is based on a new minimum cost flow formulation that simultaneously considers the interactions among all strongly connected components (SCCs) of the circuit graph to minimize the number of flip-flops in the SCCs. A circuit graph has a vertex for every gate, primary input and primary output. If gatea has a fanout to gateb, then the circuit graph has an arc from vertexa to vertexb. Experimental results on several large sequential circuits demonstrate the effectiveness of the proposed retiming for testability technique in reducing the number of partial scan flip-flops.