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Logic Synthesis by Branch and Bound

Logic Synthesis by Branch and Bound. A C++ Program Aditya Prasad. What is the program’s goal?. The program should be able to: Synthesize arbitrary Boolean functions Use a user-defined gate library It should be: Fast Flexible Optimal. How does it work?.

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Logic Synthesis by Branch and Bound

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  1. Logic Synthesis by Branch and Bound A C++ Program Aditya Prasad

  2. What is the program’s goal? • The program should be able to: • Synthesize arbitrary Boolean functions • Use a user-defined gate library • It should be: • Fast • Flexible • Optimal

  3. How does it work? • Depth-first search branch-and-bound design • Recursive function adds a gate and recurses, for each pair of existing gates • Bounds when • A) Reaches pre-defined gate limit • B) Determines that it is on a non-optimal path • C) It sees symmetrical solutions

  4. What are its inputs? • Takes a file from a cmd-line argument: • Gate library specification (choose from NAND, AND, NOR, OR, XOR, XNOR, IMP, NOT) • Number of inputs (up to 5 currently) • Number of desired outputs • List of desired outputs, in horizontal truth-table format, including don’t-cares • e.g.: 0 1 1 1 specifies 2-bit OR • X X X 0 specifies all 2-bit functions with fn(1,1) = 0

  5. What are its outputs? • Produces text output to file showing each gate’s inputs • e.g.: 2: 0 NAND 1 • Produces output in .gvz format, to be used as input to AT&T’s GraphViz program. GraphViz can produce .ps output.

  6. Sample output: 2-bit full adder

  7. Timing results • Version 13, using NAND only, was VERY slow… function #22 took over 8 hours, and didn’t finish • Version 13 with AND, NAND, NOR took 531 sec. for #22, 8 hours overall • Version 15 using same lib, took 20 sec for #22, only 15 min overall • Version 16 now takes 1 second, and 11 seconds overall

  8. Version13 timing results

  9. Version15 timing results

  10. Implemented speed-ups • Version 14 checked the gate fan-outs • Version 15 checked directed paths to each gate • Version 16 uses the Implication gate and XOR/XNOR, all of which are VERY useful

  11. Larger inputs • 3-input now takes 13 seconds overall with the gate lib. • 4-input and 5-input take VERY long for several reasons… • Each function should take many more gates? • Increase in number of gates causes exp. time increase

  12. Potential speedups • Bounding on same collections of gates • Increasing the gate library to include more gates • Restricting the gate library to the most useful gates

  13. Questions?

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