Autocorrelation and decomposition methods in combinational logic design




Tomczuk, Randal Wade

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This dissertation shows that the autocorrelation of switching functions can be effectively utilized in combinational logic optimization and synthesis. The procedures developed exploit information contained in the autocorrelation of switching functions to perform optimization of Programmable Logic Arrays (PLAs) and to aid in a multi-level logic synthesis approach called two-place decomposition. A new optimization technique is presented, based on the autocorrelation of switching functions, to find near-optimal variable pairings for decoded PLAs. The results of this approach compare favourably to those of other researchers’ techniques. The key advantages of the new approach are its simplicity and its efficiency. The basic two-place decomposition approach is augmented with various enhancements. These include an improved decomposition merge procedure, the addition of alternate mapping functions for complex disjunctive decompositions, and the incorporation of linearization using the autocorrelation to handle functions that are non-two-place decomposable. A robust implementation of the enhanced method is presented and is used to generate function realizations for comparison with other synthesis methods. The enhanced two-place decomposition method is shown to perform particularly well for functions exhibiting high degrees of symmetry. The dissertation also presents a new synthesis technique that utilizes a particular representation of a switching function called a Reduced Ordered Binary Decision Diagram (ROBDD) and is targeted to two-place decomposition. This new technique allows the two-place decomposition approach to synthesize a much broader range of functions. Although, in comparison to one other synthesis method, the new approach does not perform as well in most cases, it has considerable promise and several enhancements are proposed for improvement. This dissertation also shows that there is a strong connection among autocorrelation, two-place decomposition, and good variable orders in an ROBDD. A first attempt to formally analyze the relationship between autocorrelation and two-place decomposition is presented. Relationships are identified between certain autocorrelation coefficients when particular two-place decompositions exist in a function. These relationships are also connected to the heuristics used in the above mentioned PLA optimization technique. Variable order can have a substantial impact on the size of an ROBDD. This dissertation shows that a good variable order is related to the two-place decompositions that are exhibited in a function. Thus, variable order is also related to the autocorrelation and this relationship can lead to an autocorrelation-based technique for determining good variable orders for ROBDDs.



Combinatorial analysis, Computer programs, Autocorrelation (Statistics), Decomposition (Mathematics)