ADVANCED LOGIC DESIGN.

Marek Perkowski, Professor of ECE.

This class is entirely based on new papers and ideas. Grades are based on projects. No exams, no homeworks.

  • Overview of Design Automation Systems.
  • Basic Combinatorial Problems: set covering, Petrick Function, Satisfiability, Tautology, Complementation, Graph Coloring, Solving Boolean Equations.
  • Representations of Boolean and Multiple-Valued Logic Functions and Relations. Maps, Cube Calculus, Binary Decision Diagrams, Zero Supressed BDDs, Functional Decision Diagrams, Kronecker Functional Decision Diagrams, *BMDs, *KFDDs, etc. Multiple-Valued Cube Diagram Bundles.
  • Operations of Cube Calculus: Intersection, Supercube, Sharp, Crosslink. Introduction to Cube Calculus Machine.
  • Methods to solve logic equations.
  • Tree Search Methods.
  • Sum of Product and Product of Sums minimization. Espresso, Espresso-Exact, Espresso-Signature. New approaches. Applications in Machine Learning.
  • Reed-Muller Logic: Positive Polarity RM, Fixed Polarity RM, Kronecker RM, Generalized RM, Fixed Polarity RM, Generalized Kronecker RM.
  • Fundamental Theorem of Linearly Independent Logic. Applications, families of LI forms and diagrams.
  • Galois Fields and algebraic properties. Galois Field Logic as generalization of Reed-Muller Logic. Galois Generalized RM Forms. Linearly Independent Galois Logic.
  • Fundamental multi-level Logic Synthesis.
  • Program MIS.
  • Design technologies. ASICs versus PLDs.
  • Basic logic minimization methods for PLAs, PALs, and EPLDs.
  • Modern topics in Programmable Logic. TANT networks, use of EXOR gates, EXOR PLAs, applications of LI logic,
  • Negative Gates, Complex CMOS gates. Layout generators for Complex CMOS gates and logic synthesis for them.
  • Electronically Programmable Logic Devices and Field Programmable Gate Arrays.
  • Applications of multiple-valued logic. Partitioning and folding.
  • Synthesis methods for Xilinx and Actel families of devices.
  • Recent devices from several leading companies will be presented as examples: Lookup-Table, Multiplexer-based, specialized, routing-plane based, and cellular.
  • Applications of Shannon and Davio expansions to cellular logic. Tree and levellized circuits. Applications to cellular logic.
  • Symmetry, pseudo-symmetry, partial symmetry, symmetrization. Applications to design of new FPGAs and layout for deep sub-micron technology.
  • New method of synthesis of circuits with high EXOR component.
  • Ashenhurst Decomposition of Boolean functions.
  • Curtis Decomposition of Boolean functions.
  • AC Decomposition of Multiple-Valued functions and relations. Applications to FPGA design, applications to VLSI design,
  • Applications of AC decomposition to Machine Learning. Constructive Induction Approach to ML. Noise problem in Machine Learning. Discretization problem in ML.
  • Logic synthesis using Complex Gates for layout generator.
  • Genetic Algorithms and Genetic Programming for Logic synthesis.
  • Hierarchy of Linearly Independent Galois logic.
  • Logic Synthesis using Symmetry Concepts.
  • Multi-valued Cube Calculus and Simplified Cube Calculus Machine.
  • Xilinx FPGAs, and DEC PERLE-1 reconfigurable supercomputer.