Synthesis and Embedded Systems Class by Marek Perkowski

The additional (non-mandatory) meetings are on Fridays from 5 p.m. to 9 p.m. in room FAB 150. Everybody is very welcome to participate, but a grade of A is still possible without participating in these meetings. Additional meetings are devoted to solve problems, discuss homeworks, exams and projects, as well as your project ideas not directly related to the class material but where CAD algorithms may be of help.

FIRST WEEK OF CLASS.

INTRODUCTION AND REVIEW MANDATORY LECTURES

Lecture 1. Introduction, class information, grading. What are Embedded Systems. First Homework Assignment.
Lecture 2. From Combinational Circuits to State Machines to FSMD Processor. Second Homework Assignment.

SECOND AND THIRD WEEKS OF CLASS.

The software for Cellular Automata Simulation can be found here http://www.mirekw.com/ca/ and here http://cafaq.com/soft/index.php

Lecture 6. Details of some projects to be done in this class.

AUXILIARY MATERIAL FOR PROJECTS

PROJECT NUMBER 1. PROJECT "SPECTRAL"

Spectral Transforms for Object Recognition with Rotation, Scaling, and Translation.
Vamsi Srinivas Parasa - leader.
Omar Joshi - Lead HDL programmer.
Seudheer Ghoshi - FPGA expert.
These below are examples of previous projects. They may be useful for Spectral, Orion and CUDA projects1

Student work from previous year. SEBASTIAN SCHUEPPEL. Image Processing. Fast Fourier and Matching.
Student work from previous year. Fast Fourier and Matching. From Satya Nekkalapu
Student work from previous year. SEBASTIAN SCHUEPPEL. Fast Fourier and Matching.
Information about boards.
ADD FINAL REPORTS FROM SEBASTIAN.
MAKE LINK TO FFT LECTURES.

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PROJECT NUMBER 2. PROJECT "FRACTAL"

Fractal Images Based on Higher Order Algebras.
Scott Blakely.
Vishwanath Kusugal.
Tobias Oerstein.

report from Jessie Armagost. 2007.
Full data from Jessie Armagost. ZIPPED. 2007.
Find about octonions and quaternions.
Find about Clifford algebras.
Graphics11-3DObjectRepresentations2.pptx

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PROJECT NUMBER 3. PROJECT "CUDA"

GPU and CUDA
Scott Storms,
Sagar Raj,
one out of class,
one more from class Vijy.
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PROJECT NUMBER 4. PROJECT "ORION"

Constraints Satisfaction problem interface to Adiabatic Quantum Conmputer.
Dmitriy Labunsky.
Boshra Samy.
Yasuda.
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PROJECT NUMBER 5. PROJECT "REVERSIBLE"

Testing Reversible Circuits.
Carlos Nieva.
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PROJECT NUMBER 6. PROJECT "SENSORS"

LEGO NXT/TETRIX ROBOT WITH MANY SENSORS.
Quincy Chiu.
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PROJECT NUMBER 7. PROJECT "DANCING"

Emotion Learning and Mimicking Robot.
Mathias Sunardi.
Dancing and fighting humanoid robot KHR-1 is used in this project.
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PROJECT NUMBER 8. PROJECT "HAND"

Realistic Hand Motion Generation for a Humanoid Robot.
Aditya Bhutada.
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WEEK FOUR OF THE CLASS. FALL 2008. FPGAS AND CAD SOFTWARE FOR THEM.

MANDATORY LECTURES

Lecture 1.1. Introduction, class information, grading. PDF Format. Review of basic logic design from previous classes. Please review logic circuits using the textbook that you used in the previous classes.
Lecture 1.2. What is the class about. From De Micheli. PDF Format. VLSI design. Microelectronics. Array-based design. Technologies. Design space and evaluation space.
Lecture 1.3. What is the class about. Additional material for review and illustration IC design tools. Design, verification, simulation. Physical design. Design methodologies. PLA.

You should be able to solve any problem related to the material of these lectures. Please review Karnaugh Maps, covering problems, Sum of Products, prime implicants and various binary gates. PDF Format.

CHAPTER 2. BASIC COMBINATORIAL PROBLEMS

Read chapters 1, 2 and 7 of the De Micheli texbook.

Lecture 2.1. Review and formalism to be used. From Yonsei University. Design styles. Design trade-offs. Bit-serial adder. Logic equations. Optimization and technology mapping. Testing. Delay optimization. Graph models and algorithms. Backtracking. Asymptotic complexity.
Lecture 2.2. Graph Coloring of Hypergraphs for combinatorial Problems. From De Micheli. PDF Format. Shortes path problem. Longest path problem. Vertex cover. Heuristics. Graph Coloring. Interval graphs. Clique partitioning. Covering and satisfiability.

CHAPTER 3. BASIC CONSTRAINT SATISFACTION PROBLEMS AND PROGRAMMING. HOMEWORK ONE

3.1. Homework 1. Instruction what to do. PPT Format.
3.2. Dongsoo Lee - Maximum Cliques in the graph

3.3. Donghyun Kim - Maximum Cliques in the graph using Kerbosh method

3.4. Ahn, Ki-yong, A graph coloring algorithm in Chapter 2.4.3 of text book. (Page 62 ALGORITHM 2.4.6)

file graph.c

3.5. Hyungock Kim - Graph Coloring in Java

3.6. Seon Pil Kim - Shortest and Longest Path in a Directed Graph.

3.7. Hwangbo Woong - Vertex covering

3.8. HeeJun Shim Unix C program

CHAPTER 4. COMBINATORIAL PROBLEMS AND DATA STRUCTURES IN LOGIC SYNTHESIS

Lecture 4.1. Combinatorial Problems and Branch and Bound from De Micheli. PDF Format. The essence of Branch and Bound and Backtracking. Bounding functions. Unate and Binate cover.
Lecture 4.2. Boolean Algebra. PDF Format. Set theory and notation. Sets, Cartesian Products and Relations. Functions. Posets and Hasse Diagrams. Lattices. Boolean Algebras. Boolean Functions. Cofactors. Boole/Shannon Expansion Theorem. Minterm Canonical Forms. Boolean Difference. Don't cares.
Lecture 4.3. Introduction to Multiple-Valued Logic and Its Applications. PDF Format. Multi-valued signals. Why is multiple-valued logic important. History. Post Literals. Min and Max gates. Maps for multiple-valued logic and their use in synthesis. Expressions versus maps. Decision Trees and Diagrams.
Lecture 4.4. Review of graph coloring, set covering, cliques and decomposition. Part 1. This review includes more examples, some new algorithms, new applications, industrial importance and some additional discussion. PDF Format.
Lecture 4.5. Review of graph coloring, set covering, cliques and decomposition. Part 2. PDF Format. Functional Decomposition as a general problem-solving idea. Decomposition of multiple-valued relations.
Lecture 4.6. Review of graph coloring, set covering, cliques and decomposition. Part 3. PDF Format. Decomposition of functions and relations based on graph coloring.
Lecture 4.7. Symmetry of Boolean Functions and Decision Diagrams. Part 1. PDF Format. Lattice Diagrams. Switching structures. Recognizing symmetry. Generalized symmetries.
Lecture 4.8. Symmetry of Boolean Functions and Decision Diagrams. Part 2. PDF Format. Networks of multiplexers. Shannon Lattices. Types of Decision Diagrams. Graphic methods to create Shannon and Davio lattices. Joining operations on maps and expressions.
Lecture 4.9. Decomposition of Multi-valued relations and its application in data mining. Part 1. PDF Format. The machine learning problem. Data Mining. Logic formulation of learning. Various reductions of decomposition problems to basic combinational problems. Decomposition of multiple-valued relations. Generalizations of Ashenhurst-Curtis Model. Applications of decomposition in VLSI, FPGA and Data Mining.
Lecture 4.10. Decomposition of Multi-valued relations and its application in data mining. Part 2. PDF Format. Benchmarking and applications of decomposition.

CHAPTER 5. HOMEWORK TWO

REMOVED AS DIFFERENT HOMEWORKS ARE ASSIGNED FOR THIS PART EVERY YEAR.

CHAPTER 6. MIDTERM EXAMINATION

6.1. Problems to review - Midterm Exam. PDF Format. We present here all topics and problems that may occur in the midterm exam. The is an inclusive list of topics for the rehearsal meetings on Fridays, that will be held before the midterm exam.
6.2. Problems from Midterm Exam. After the exam, please solve them all as additional homework. This homework will be graded separately from the midter, so if you have done a mistake, you can fix it in the homework. PDF Format.
6.3. Solutions to Midterm Exam. PDF Format.

CHAPTER 7. PROJECT

REMOVED AS NEW PROJECTS ARE DIFFERENT.

CHAPTER 8. MODELING AND ARCHITECTURE

The material for this part is included in chapters 3 and 4 of the De Micheli texbook.

Lecture 8.1. Modeling Circuit Modeling, Hardware Description Languages - examples. Structural and behavioral views. Silage and Data Flow Graphs. VHLD and Verilog. Simple retiming and transformations on design data. Data Flow examples. Hierarchies. Estimation of costs.
Lecture 8.2. Architectural issues and tools Synthesis. Trade-offs. Pareto Points. Architectural Level synthesis. Design procedures. Compilation transformations. Constraints and resources. Hardware Modeling. Binding. Design trade-offs.
Lecture 8.3. Control Data Flow Graphs and FSMs. PDF Format. Place of Finite State Machines in Design methodologies. Examples. Specification of FSMs. Mealy. Moore. Non-deterministic. Probabilistic. Reductions. Equivalence and Minimization. Decomposition. Composition.
Lecture 8.4. Data Flow Graph and Scheduling. PDF Format. The concept of Data Flow Graph. Examples. Transformations. Allocation. Scheduling and Mapping concepts. Constraints. Various algorithms that operate on CDFGs.
Lecture 8.5. Petri Nets. PDF Format. Petri Net examples. Uses of Petri Nets. Equivalence. Parallelism. Verification. Reachability. Liveness. Persistence and other properties.

CHAPTER 9. FINITE STATE MACHINES AND SEQUENTIAL CIRCUITS

Lecture 9.1. JK flip-flops and flowcharts. PDF Format. Structures of FSMs. Flowcharts and their transformations. Converto Flowchart to table and graph. Types of flip-flops and creation of equations. Please review all material about basic flip-flops and state machines. It will be used in homeworks and exams.
Lecture 9.2. MSI Building Blocks. PDF Format. Multiplexers, demultiplexers, applications in control and data path. Synthesis with Muxes. Active levels. ROMs. Decoders.
Lecture 9.3. Memory. PDF Format. RAM, ROM, timing. Memory systems.
Lecture 9.4. Introduction to minimization of completely specified Finite State Machines. PDF Format. Basic ideas of FSM minimization. Graph and tabular algorithms for flowcharts and completely specified machines.
Lecture 9.5. Advanced methods for Finite State Machine Minimization. PDF Format. Detailed examples of graphical methods that will be tested on the exam. Closed and complete graphs.
Lecture 9.6. Advanced Algorithms for FSM minimization. From U.C. Berkeley. PDF Format. More examples, formalization.
Lecture 9.7. State assignment methods for synchronous machines based on rules. PDF Format. Relations between excitation equations and state assignment rules for FSMs. You have to understand the origin of the rules and illustrate how they relate to hardware minimization after realization of the machine.
Lecture 9.8. State assignment methods based on multiline and partition pair methods. PDF Format. This is an advanced material that is not neccessary for the exam. Any state assignment method is allowed. However, these methods give you a better understanding of partitions and partition pairs which are the fundamental concepts in structural theory of machines by Hartmanis and Stearns, Rhodes, etc.
Lecture 9.9. Retiming and pipelines. PDF Format.
Retiming and resynthesis. Pipelines. Retiming and resynthesis of pipelines. This is useful for many final exam problems. Links to scheduling and allocation.

ADDITIONAL MATERIALS

A.9. REVIEW AND ADDITIONAL MATERIAL ABOUT FINITE STATE MACHINES.

A.9.1. Bus and Memory. PDF Format. Auxiliary materials only, related to some of your questions from Friday meetings. You should be able to link this information to register-transfer level synthesis.
A.9.2. Example of controller design - Manchester Encoder. PDF Format. A complete design example that includes simple state machine for control and simple data path, but illustrates timing and composition of machines. Related to exams.
A.9.3. Turing Machine as an example of a controller. PDF Format. Just to show you that Turing machine is also a controller and can be designed as other controllers using methods developed in this class. Useful as exercise in designing controllers.
A.9.4. Waveform generator. PDF Format. Another complete design example of a system with controller and data path.
A.9.5. Example of using both rule based and multiline method to find a good assignment. PDF Format.
A.9.6. Additional material on state assignment based on methods developed at University of California, Berkeley, USA. PDF Format. Comparison of methods on a simple FSM. More on state assignment and encoding. Various CAD tools. You can find more detailed information on these topics in the De Micheli book.
A.9.7. Additional material on sequential circuits, state minimization and state assignment from Yonsei University, Korea. PDF Format. This material is more algorithmic and you can find complete examples of solutions. All problems from this set of slides can be solved of course with any of the methods presented in the class or in the slides from section A.9.
A.9.8. Additional material on modern methods for state assignment from Eindhoven University in Netherland. PDF Format. The short review of state assignment algorithms and systems. Can be used as a guide to literature for those who want to go into depth of structural synthesis of automata.
A.9.9. Additional Material: Concurrent state-minimization in two dimensions and decomposition of a finite state machine. PDF Format. A paper by M.A. Perkowski, L. Jozwiak and W. Zhao, "Symbolic Two-Dimensional Minimization of Strongly Unspecified Finite State Machines". A new advanced approach to synthesis of machines with many don't cares. Example of non-standard approaches to FSM synthesis. This is given only for those who have deep interest in FSM design. Not required for exams.

CHAPTER 10. SCHEDULING, ALLOCATION AND HIGH LEVEL SYNTHESIS.

MANDATORY LECTURES AND READINGS.

Read chapters 5 and 6 of the De Micheli texbook.

Lecture 10.1. Scheduling I. PDF Format. Scheduling. Taxonomy. ASAP and ALAP scheduling. Mobility. Constraint graphs. Scheduling under timing constraints. Integer Linear Programming approach to scheduling.
Lecture 10.2. Scheduling II. PDF Format. Hu's algorithm. List scheduling. Force-directed scheduling. Scheduling with chaining.
Lecture 10.3. Resource Sharing. PDF Format. Allocation and binding. Compatibility graphs and conflict graphs. Algorithms and heuristics. Perfect graphs. Interval graphs. Left-Edge algorithm. ILP algorithm. Register binding problem. Register sharing data-flow graphs. Memory binding. Bus sharing. Module selection approaches.
Lecture 10.4. Scheduling and Allocation example. PDF Format. Various practical examples of complete solutions to allocation and scheduling of simple controllers. Exam-related.
Lecture 10.5. One more scheduling example. PDF Format. Similar but simpler problem may occur on final.
Lecture 10.6. More examples of scheduling and allocation. PDF Format.

ADDITIONAL MATERIALS.

A.10. REVIEW AND ADDITIONAL MATERIALS ABOUT SCHEDULING AND ALLOCATION. HIGH-LEVEL SYNTHESIS AND RELATED ISSUES.

All material given here will not occur on the final. They are given here only to illustrate better some of the concept and examples introduced in mandatory lectures.