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.