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The Nature of Computing

The Nature of Computing. INEL 4206 – Microprocessors Lecture 2 Bienvenido V é lez Ph. D. School of Engineering University of Puerto Rico - Mayag ü ez. Some Inaccurate (Although Popular) Perceptions of Computing. Computing = (Electronic) Computers Computing = Programming

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The Nature of Computing

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  1. The Nature of Computing INEL 4206 – Microprocessors Lecture 2 Bienvenido Vélez Ph. D. School of Engineering University of Puerto Rico - Mayagüez

  2. Some Inaccurate (Although Popular) Perceptions of Computing • Computing = (Electronic) Computers • Computing = Programming • Computing = Software INEL 4206 - Microprocessors - Spring 2003

  3. A.K.A. The Computing Device View of Computing Computing = Computers Computing is about solving problems using computers INEL 4206 - Microprocessors - Spring 2003

  4. A.K.A. The Programming Language view of Computing Computing = Programming Computing is about writing programs for computers INEL 4206 - Microprocessors - Spring 2003

  5. A.K.A. The “Floppy Disk” view of Computing Computing = Software Computing is not concerned with hardware design INEL 4206 - Microprocessors - Spring 2003

  6. Outline • What is Computing? • Computing Models and Computability • Interpretation and Universal Computers • Abstraction and Building Blocks INEL 4206 - Microprocessors - Spring 2003

  7. What is computing then? Algorithmic Computation Function Input Information Output Information Computing is the study of Computation: the process oftransforming information INEL 4206 - Microprocessors - Spring 2003

  8. encode compute decode 011011001010100101… 011011001010100101… Problem Solution The Computation Process INEL 4206 - Microprocessors - Spring 2003

  9. Fundamental Questions Addressed by the Discipline of Computing • What is the nature of computation? • What can be computed? • What can be computed efficiently? • How to build practical computing devices? INEL 4206 - Microprocessors - Spring 2003

  10. encode compute decode 011011001010100101… 011011001010100101… Problem Solution Integer Integer Integer Function Computers as Integer Functions INEL 4206 - Microprocessors - Spring 2003

  11. IF ≠ CF All Integer Functions (IF) Halting Problem Computability IF ≟ CF Computable Integer Functions (CF) INEL 4206 - Microprocessors - Spring 2003

  12. The Halting Problem(Alan Turing 1936) Given a program P and an input I to Pdetermine if P stops on I Computer Program P P Halts on I? Input I We cannot build this machine … period INEL 4206 - Microprocessors - Spring 2003

  13. All Integer Functions (IF) We want to formally describe the set of computable functions. BUT HOW??? Halting Problem Computability IF ≠ CF IF ≟ CF Computable Integer Functions (CF) INEL 4206 - Microprocessors - Spring 2003

  14. Mathematical Computers:The Turing Machine (1936) 0 1 Infinite I/O TAPE Tape Head 0/{0,R} 0 1 FSM 1/{1,L} Alan Turing Turing demonstrated how to solve several problems using his LCM computing model INEL 4206 - Microprocessors - Spring 2003

  15. Mathematical Computers:The Turing Machine (1936) 0 1 Infinite I/O TAPE Tape Head 0/{0,R} 0 1 FSM 1/{1,L} Alan Turing Turing demonstrated how to solve several problems using his LCM computing model INEL 4206 - Microprocessors - Spring 2003

  16. A TM Machine Recognizing anbn Rutgers Turing Machine Example http://www.rci.rutgers.edu/~cfs/472_html/TM/anbnTM.html INEL 4206 - Microprocessors - Spring 2003

  17. Cannot build this … period The Halting Problem Proof Sketch (Blackboard) Given a program P and an input I to Pdetermine if P stops on I Computer Program P P Halts on I? Input I INEL 4206 - Microprocessors - Spring 2003

  18. FSM FSM FSM FSM FSM Sorting TM Sorting TM Sorting TM Sorting TM Searching TM FSM Integrating TM Ad-hoc Turing Machines We know we can build TM’s to solve many interesting problems. But building a TM is a lot of work Can we build ONE general purpose TM? INEL 4206 - Microprocessors - Spring 2003

  19. Software • just bits • weightless • effective • computing • models • Hardware • heavy • expensive • cumbersome • computing • model The Universal Turing Machine (UTM)The Paradigm for Modern General Purpose Computers Encoded TM M Encoded Tape for M Universal TM • Capable of Emulating Every other TM • Shown computable by Alan Turing (1936) BIG IDEAS:INTERPRETATION & PROGRAMMABILITY!!! INEL 4206 - Microprocessors - Spring 2003

  20. Other Familiar Models of Computation • Combinational Circuits • Sequential Circuits (FSM’s) • Pentium Instruction Set Architecture • Lambda Calculus • Recursive Functions • C, C++, Java, C#, etc… Can you tell which ones areTuring Universal, or which ones can emulate any other Turing Machine? INEL 4206 - Microprocessors - Spring 2003

  21. Church’s Thesis “Any realizable computing device can be simulated by a Turing machine” “All the models of computation yet developed, and all those that may be developed in the future, are equivalent in power.” Alonso Church Issues not considered: Size, Programmability, Performance But they must be considered if one is to build … INEL 4206 - Microprocessors - Spring 2003

  22. ALU status control Practical Universal Computers(John) Von Neumann Architecture (1945) Memory CPU Program DataPaths AC This looks just like a TM Tape PC Data ABR Control Unit (FSM) CPU is a universal TM An interpreter of some programming language (PL) INEL 4206 - Microprocessors - Spring 2003

  23. All have embedded PL’s Multiple Coexisting Levels of Interpretation Computing in Perspective PSpice Excel MatLab Build Many Pascal C++ Fortran Assembler 1 Assembler 2 Assembler 3 ISA FSM Build One Gate CMOS Programming is the art/science of encoding algorithms INEL 4206 - Microprocessors - Spring 2003

  24. Computing in Perspective people Computer Human Interaction, User Interfaces CS1/CS2, Programming, Data Structures INEL 4206 Programming Languages, Compilers Computer Architecture Each abstraction layer implements an INTERPRETER of some computing/programming model computers People INEL 4206 - Microprocessors - Spring 2003

  25. Because we know of no other way of doing anything Why Abstraction Layers? • Resilience to change: • Each layer provides a level of indirection • Divide and Conquer Approach: • Can work on one small semantic gap at a time • Building Block Approach: • Can build many higher layer on same lower layer INEL 4206 - Microprocessors - Spring 2003

  26. Hardware Building Blocks A B A sel O SEL B O A 2-1 multiplexer Gate-Level Logic Provides a Computing Model INEL 4206 - Microprocessors - Spring 2003

  27. Software Building Blocks The function is one of the most ubiquitous abstraction tools // MUX – Implements a 2-1 binary multiplexer bool MUX(bool a, bool b, bool sel) { switch(sel) { case 0: return a; break; case 1: return b; break; } } Other abstraction tools include: structures, classes, modules INEL 4206 - Microprocessors - Spring 2003

  28. What Makes a Good Building Block • Provides a clear and simple contract • The contract hides irrelevant detail • The contract is general and orthogonal • The contract is easy to remember INEL 4206 - Microprocessors - Spring 2003

  29. Some Properties of a Good Programming Language • Does not hide expressive power of lower layers • Can be efficiently interpreted • Provides adequate higher level abstractions • Provides a variety of constructs for creating new abstractions, layers and modules • Achieves all of the above with minimal complexity INEL 4206 - Microprocessors - Spring 2003

  30. Summary • Computing = Information Transformation • Information Transformation = Integer Functions • Some integer functions are not computable • Turing Machine computations = All computations • Universal Computer = Universal TM • Interpretation => Programmability => Flexibility • Building blocks are abstract contracts INEL 4206 - Microprocessors - Spring 2003

  31. Summary "Computer Science is no more about computers than Astronomy is about telescopes" E. W. Dijkstra 1930-2002 1972 Turing Award INEL 4206 - Microprocessors - Spring 2003

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