### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Limits of Computation 22C 131

UI

GPA 3.87

### View Full Document

## 9

## 0

## Popular in Course

## Popular in ComputerScienence

This 22 page Class Notes was uploaded by Tamia Bernhard on Friday October 23, 2015. The Class Notes belongs to 22C 131 at University of Iowa taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/228055/22c-131-university-of-iowa in ComputerScienence at University of Iowa.

## Popular in ComputerScienence

## Reviews for Limits of Computation

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/23/15

Lecture Notes developed by Teodor Rus a ruscs uiowa edu The University of Iowa Department of Computer Science aThis notes have been developed by Teodor Rus They are copyrighted materials and may not be used in other course settings outside of the University of Iowa in their current form or modified form without the express written permission of one of the copyright holders During this course students are prohibited from selling notes to or being paid for taking notes by any person or commercial firm without the express written permission of one of the copyright holders Computation Theory p15 0 History 39 Current trends of computation theory 0 Problem solving methodology a Polya Four Steps MethodOIOQY 0 Problem Classification 0 probIem Solving and Areas of Computation Theory 0 Problem Solving Tools 0 ReIationship to Theory of Computation o How to Approach lt comPUtation Theory p25 The three sources of theory of computation are 1 Works performed by mathematicians such as Leibnitz and Pascal trying to mechanize calculus and logical deduction 2 Work performed by logicians such as Kurt Godel Alfred Tarski Alan Turing Alonzo Church A A Markov toward the development of a formal concept of algorithm 3 Development of computer based problem solving methodology Computation Theory p35 Gottfried Wilhelm Leibnitz German mathematician 1646 1716 Invented Calculus independent of Newton Leibnitz s notation is still used Discovered binary system Blaise Pascal French mathematician 1623 1662 Invented mechanical calculators Worked on Projective geometry and Probability Theory with Fermat Since 1654 to the end he did philosophy and theology Known to us through quotPascal languagequot Developed by Nicholas Wirth 1970 Kurt Godel Austrian American Logician 1906 BrUn Bruno Czech 1978 Princeton NJ Proved Incompleteness theorem thus challenging Hilbert s Program 1900 Alfred Tarski Polish American MathematicianLogician 1901 Warsaw Poland 1983 Berkeley Ca Invented the formal concept of truth and model theory Alan Turing English Mathematician 1912 1954 known as the father of CS Invented the formal concept of an algorithm Turing Machine Invented Enigma machine a codebreaker during Second World War Alonzo Church American Logician 1903 1995 Invented the Acalculus Known for Church s thesis everything that is computable is computable by a recursive functions TM Andrey Andreevich Markov Russian Mathematician 1903 1979 sun of AA Markov 1856 1922 Developed Russian school of constructive mathematics and logic Invented normal algorithms and proved NAZRFETMZAC Current trends Algorithm development and information computation technology IT Solving problems related to computation complexity Putting information technology on firm mathematical basis Developing domain specific languages DLS to express computations 0 Developing domain specific computer based problem solving methodology 1 Most of the current texts dedicated to the theory of computation disregard the influence computer based problem solving methodology hasd on the development of theory of computation 2 Provide please rationale for this situation 3 We will try to correct this in this offering of 220131 by choosing a textbook that can be best used to connect the theory of computation with problem solving methodology Unfortunately following tradition this class will have no programming component compmation Theory p125 Problem solving methodology 39 Problem paraphrasing GPoya Stanford 1956 to have a problem means to search consciously for some action appropriate to attain a given aim Solution to solve a problem means to find such an action See G Polya How To Solve It 1956 compmation Theory p135 Observations A problem is characterized by three principal components unknowns 0 data and 0 conditions To solve a problem means to find a way of determining the unknowns from the given data such that the conditions of the problem are satisfied compmation Theory p145 Example problem Find all real numbers 1 that for a given triple a b c of real numbers satisfy the relation 5132 951 C 0 Unknown real numbers 1 Data real numbers abc Conditions a 0 and 035132 bx c 0 Solving the problem Use the properties of the data and conditions to deduce a relation 1 fa b c a x 2 b x c O by problem statement a x 2 b x c by adding c to both terms of equality x 2 ba X ca by dividing both term by a x b2a 2 b 2 4ac4a 2 by using binomial identity x b2a sqrtb 2 4ac2a by taking square root x b sqrtb 2 4ac2a by adding b2a to equality Solutions 131 b bZ 4ac2a x2 b bZ 4ac2a compmation Theory p165 Dif culties in solving a problem In finding a way of determining unknowns this belongs to the very notion of a problem Citing Polya where there is no difficulty there is no problem It seems that what best characterizes human activity is solving problems by finding ways around or out of difficulties compmation Theory p175 Two classes of dif culties Difficulties that pertain to finding the action Difficulties that pertain to performing the ac on Example solving linear systems of equations 1 One can use Cramer s rule or Gaussian elimination method 2 One may know how and one can do it for small systems system size lt 10 3 One could do it for large systems too system size gt 1000 but perhaps she will not finish during her entire life compmation Theory pig5 Distinction between dif culties The distinction between the two classes of difficulties is in solution mechanisms Finding the way around difficulties in discovering the action seems to be a characteristic of intelligent human behavior What could one use to help this Finding the way around difficulties of performing the action can be done both creatively and mechanically What could one use to help this Mathematical methodology Polya s four steps methodology 1 Formalize the problem 2 Develop an algorithm to solve the problem 3 Perform the algorithm on the data characterizing the problem 4 Validate the solution Question is there any difference between this and computer based methodology compmation Theory p205 Computerbased methodology How do we solve problems using computers Computation Theory p215

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.