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Application of Bipartite Graphs for Achieving Race-Free State Assignments
August 1995 (vol. 44 no. 8)
pp. 1002-1011

Abstract—Achieving race-free state assignments is an important objective in the synthesis of asynchronous sequential logic circuits (ASLCs). Traditionally, adjacency diagrams are used to help identify and resolve race conditions; however, this approach has a high degree of computational complexity. This paper presents an efficient state assignment algorithm that utilizes a pattern matching technique to predict races and to eliminate the need for enumerative searches. More specifically, the race-free state assignment problem is formulated as the embedding of a bipartite connected graph onto an n-cube and achieves a near minimum number of state variables. This algorithm has been evaluated using several representative examples. Results show that the developed algorithm provides better performance than existing algorithms. Due to the simplicity of the bipartite representation of an n-cube, the developed algorithm is suitable for ASLC synthesis that may involve a relatively large number of states.

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Index Terms:
Asynchronous sequential logic circuits, adjacency diagram, bipartite adjacency table, bipartite graph, bipartite representation of an n-cube, mapping, partitioning, race-free state assignments, state assignments algorithm.
Chin-Long Wey, Jun-Woo Kang, P. David Fisher, "Application of Bipartite Graphs for Achieving Race-Free State Assignments," IEEE Transactions on Computers, vol. 44, no. 8, pp. 1002-1011, Aug. 1995, doi:10.1109/12.403716
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