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Computer Science and Mathematical Basics

Computer Science and Mathematical Basics. Chap. 3. 발표자 : 김정집. Introduction. Fundamental notions of computer science and mathematics necessary for understanding the GP approach leading question What are the mathematical and information-processing contexts of GP?

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Computer Science and Mathematical Basics

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  1. Computer Science and Mathematical Basics Chap. 3 발표자 : 김정집

  2. Introduction • Fundamental notions of computer science and mathematics necessary for understanding the GP approach • leading question • What are the mathematical and information-processing contexts of GP? • What are the tools from these contexts that GP has to work with

  3. 3.1 The Importance of Randomness in Evolutionary Learning • Evolution in Nature vs. Evolution in Computers • in nature, mutation is basically “free” • The Costs of Variation • in nature, sexual reproduction is not “free” • GP as a General Search Process • “non-deterministic” algorithm • depend on randomness

  4. 3.2 Mathematical Basics • Randomness and Probability • random events play such a prominent role in GP

  5. 3.2.1 Combinatorics and the Search Space • Permutation • N different elements constituting the set E can be ordered in N! different permutations • Combination • Variation

  6. 3.2.2 Random numbers • Quasi-random number generator • Linear Congruential Method

  7. Randomness test • X2 Test • randomness test • if X2 is near to k, then the random number generator is good

  8. 3.2.3 Probability • Elementary Events • random experiments - flip a coin • events - “heads” or “tails” • Relative Frequency • Probability

  9. Random Variables and Probability Distributions • probability distribution p(x) of random variable x

  10. Expectation Value and Variance • moment quantity • Expectation value • Variance

  11. Bernoulli Process and the Binomial Distribution • Probability Density Functions • Normal Distribution

  12. Multiplicative Variation and the Log-Normal Distribution

  13. Three distributions

  14. 3.3 Computer Science Background and Terminology • 3.3.1 The Turing Machine, Turing Completeness, and Universal Computation

  15. Turing Completeness • a programming language allows to write a program that emulates the behavior of a certain arbitrary TM • Structure and Function of a TM • Universal TM and Universal Computation • A Universal TM U can emulate any TM T • U is said to be able to perform universal computation

  16. 3.3.2 The Halting Problem • Halting Theorem • there is no problem that can determine the termination properties of all programs • time bounded excution of GP

  17. 3.3.3 Complexity • Complexity measure • # of nodes, # of bits needed to express a program in linear form, or # of instructions • Kolmogorov Complexity and Generalization • Kolmogorov Complexity • “complexity of a computable object” • the shortest program that produces the object upon execution • if two programs model the same data, the shorter one can be argued to have a higher probability of being general

  18. Different complexity measures

  19. 3.4 Computer Hardware • Von Neumann machine • a computer where the program resides in the same storage as the data used by that program

  20. 3.4.1 Von Neumann Machines • The Processor • RISC/CISC • RISC(SPARC or PowerPC) • extensive use of registers • CISC(Pentium)

  21. Schematic view of CPU

  22. 3.4.2 Evolvable Hardware • FPGAs • EHW • When HW has failures, there is no need to discard the entire HW; instead one simply reprogram the chip

  23. 3.5 Computer Science • Elementary representation of software • machine language, assembly language • higher language • data structures

  24. 3.5.1 Machine Language and Assembler Language • Machine Language • A sequence of integers • impractical to use numbers for instructions • not natural to remember • Assembly • very simple grammar

  25. 3.5.2 Higher Languages • Imperative Language • BASIC, C, FORTRAN, Pascal, SIMULA • program statements explicitly order (Latin imperare) the computer how to perform a certain task • Functional, Applicative Language • LISP, LOGO, ML, BETA • a program represents a function that maps input data and internal data into output data • using a function on its arguments is called application, so a functional language is also called applicative

  26. Predictive Language • PROLOG • programming means describing to the computer what is wanted as result • Objective-Oriented Languages • SMALLTALK-80, C++, JAVA • the principle behind these languages is modeling a system by objects

  27. Language classes

  28. 3.5.3 Data Structures

  29. Aggregation • cartesian product of structures • Generalization • unites structures • Recursion • Graph, Tree, List • Power Set • Function Space • Selector

  30. 3.5.4 Manual versus Genetic Programming • From Bits to Memo Code • From Assembler to High-Level Languages • From High-Level Languages to Algebraic Specification • A Programmer’s Heuristics • “cut and paste” strategy • cut and paste <-> crossover • generation of new segments <-> mutation • debugging and testing <-> selection • unused code <-> introns

  31. The main difference • GP can afford to evolve a population of programs simultaneously • a programmer only work in this way if • the environments changed only slightly between applications or • the programming language was hard to handle • hard for GP system to generate code • without any idea of what a given argument or function could mean to the output

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