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The BDS Circuit Synthesis System

The BDS Circuit Synthesis System. What it Does and Doesn’t Do. What it Is. BDS (BDD Based Logic Optimization System?) is a multi-level circuit optimization system that uses local BDD representations for circuit optimization

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The BDS Circuit Synthesis System

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  1. The BDS Circuit Synthesis System What it Does and Doesn’t Do

  2. What it Is • BDS (BDD Based Logic Optimization System?) is a multi-level circuit optimization system that uses local BDD representations for circuit optimization • BDS is written by Congguang Yang and Maciej Ciesielski at the University of Massachusets

  3. How it Works (very briefly) • Builds local BDDs to represent portions of a boolean network (and therefore can handle arbitrarily large circuits without memory blowup) • Looks for dominators and generalized dominators to factor and simplify the BDD representation

  4. What’s a Dominator, Anyway? • A “1-dominator” is a node in a BDD that is situated on every path from the root to the “1” terminal. Similarly, “0-dominators” are defined. It can be shown that the presence of one of these leads to a certain algebraic decomposition of the BDD. • “Generalized dominators” are nodes with similar properties with respect to other decompositions.

  5. What it Does • Takes input as a .blif (Berkeley Logic Interchange Format) file • Outputs a circuit in terms of not, and, or, xnor, & implication gates • Can output in either .blif or .dot (for GraphVis) • Beats SIS (the standard multilevel circuit minimization tool) on a handful of benchmarks

  6. .BLIF files • Might look something like this .model model_name .inputs i1 i2 i3 i4 .outputs o1 .names i1 i2 i3 i4 o1 1-1- 1 # i am a comment 10-1 1 110- 1 .end

  7. What it Doesn’t Do • Guarantee optimal circuits (even in small cases) – but it does find them for some large cases • Use an arbitrary gate library • Do any internal don’t care based optimization

  8. Circuit Optimization - starring don’t cares • One paradigm of circuit optimization is to iteratively look at relatively small subcircuits, and replace them with optimized versions. • It is almost inevitable that the subcircuits will never recieve certain input configurations, or alternatively that certain output configurations are completely equivalent. • This yields more freedom in the choice of a replacement subcircuit – which of course can lead to smaller circuits.

  9. Don’t Cares -in two flavors • Satisfiability: The set of inputs that will never occur to a given subcircuit. • Observability: The set of inputs for which the subcircuit does not affect the circuit’s value • The union of these sets form the don’t care set of a subcircuit

  10. Don’t Cares -in quantum circuits • Quantum computers have don’t care’s of their own • The “work bits” ubiquitous in quantum algorithms are the reversible equivalent of classical don’t cares (why?) • Because of the probabilistic measurement step, a new sort of don’t cares (with no classical analogue) is introduced.

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