1. CS 3240: Languages and Computation
Course Overview

2. Course Staff Instructor: Prof. Alberto Apostolico TA: Akshay Wadia
Office: KLAUS 1310
Office Hours:
Tue. & Thur. at 4-5pm
Or by appointment
TA: Akshay Wadia
Office: KLAUS 2124
Tue. & Thur. at am,

3. Required Textbook
Introduction to Automata Theory, Languages, and Computation
(3rd Edition) by John E. Hopcroft , Rajeev Motwani , Jeffrey D. Ullman Hardcover Addison Wesley; 3 edition (July 8, 2006) ISBN-10: ISBN-13:

4. Required Textbook
Introduction to Automata Theory, Languages, and Computation
(3rd Edition) by John E. Hopcroft , Rajeev Motwani , Jeffrey D. Ullman Hardcover Addison Wesley; 3 edition (July 8, 2006) ISBN-10: ISBN-13:
This book is complemented by an online resource found at
Go to this site, register using the student access code provided with your copy of the book, then login and enter the following class token at the prompt: 71E4F530
PLEASE DO NOT DISTRIBUTE THIS TOKEN OUTSIDE THE CLASS

5. Course Objectives Formal languages Theory of computation
Understand definitions of regular and context-free languages and their corresponding “machines”
Understand their computational powers and limitations
Theory of computation
Understand Turing machines
Understand decidability
Applications Basics
Lexical Analysis & Compiler
Text searching
Finite state device design

6. Outline Regular expressions, DFAs, NFAs and automata
Limits on regular expressions, pumping lemma
Practical parsing and other applications
Context-free languages, grammars, Chomsky Hierarchy
Pushdown automata, deterministic vs. non-deterministic
Attribute grammars, type inferencing
Context-free vs. context-sensitive grammars
Turing machines, decidable vs. undecidable problems, reducibility

7. Grading Homework: 20% Mini-project: 25% Tests: 30% Final: 25%
Homework will try to exploit Gradiance resource with final version due in class
No late homework or assignments without prior approval of instructor
Homework should be concise, complete, and precise
Tests will be in class. Closed book, closed notes, but one-page cheat-sheet allowed.

8. Collaboration Policy
Students must write solutions to assignments completely independently
General discussions are allowed on assignments among students, but names of collaborators must be reported

9. Resources Check often for announcements and schedule changes.
Class webpage
GRADIANCE webpage
Check often for announcements and schedule changes.

10. Introduction & Motivation

11. Automata & Formal Languages
Turing Machines
Automata & Grammars
Compilers
Text & Web applications

12. Compilers What is a compiler? Why compilers?
A program that translates an executable program from source language into target language
Usually source language is high-level language, and target language is object (or machine) code
Related to interpreters
Why compilers?
Programming in machine (or assembly) language is tedious, error prone, and machine dependent
Historical note: In 1954, IBM started developing FORTRAN (FORmula TRANslation) language and its compiler

13. How Does Compiler Work? Scanner Start Parser
Request
Token
Get
Token
Start
Parser
Front End: Analysis of program syntax and semantics
Semantic
Action
Semantic
Error
Checking
Intermediate
Representation

14. Parts of Compilers Focus of this class. 1. Lexical Analysis Front End
2. Syntax Analysis
3. Semantic Analysis
Synthesis
Back
End
4. Code Generation
5. Optimization

15. Basic Concepts
Computational problems can be posed ultimately as decision (yes-no) problems
Yes-No problems can be posed ultimately as language recognition problems
A language is any set of strings over some alphabet
Deciding a language means being able to discriminate the strings belonging to it against all others
There are two basic ways to ‘’decide’’ a language: Automata & Grammars
An Automaton discriminates whether a given input string is in the language or not
A Grammar generates all and only the strings in the language
There is a subtle correspondence between an automaton and a corresponding grammar
Some languages are easy to decide, some are harder, some are ‘’impossible’’
We can build a hierarchy of automata , and a corresponding one of grammars based on the complexity of the languages we wish to decide

16. Limits of Computation
Three easy functions defined on the decimal development of Greek Pi p …
The ratio of the circumference to the diagonal of the unit circle
f(n) = 1, if 4 appears before the nth decimal digit of p
f(n) = 0 otherwise
g(n) = 1, if 4 appears as the nth decimal digit of p
g(n) = 0 otherwise
h(n) = 1, if 4 appears after the nth decimal digit of p
h(n) = 0 otherwise
Do we have an algorithm for f? for g? for h?

17. Computable, Undecidable, Untractable
Questions of decidability revolve around whether there is an algorithm to solve a certain problem
Questions of untractability revolve around whether there is a practically viable algorithm to solve a certain problem
Most of the algorithms we design and use are have low computational complexity

18. Proofs Deductive proofs Inductive proofs If-and-only-if proofs
Proofs by contradiction
Proofs by counterexample
Etc.

19. Deductive Proofs
A chain of statements implying each the next one, leading from the first one (hypothesis) to the last (thesis or conclusion)
For integer x = 4 or higher 2x is not smaller than x2
Try for few values of parameter x, e.g., x=4 or x=6
What happens to the left side and right side when x becomes larger than 4?
Left side doubles with unit increase,
right side grows by not more than [(x+1)/x]2 , which is for x=4
Exercise 1: generalize to non-integers
Exercise 2: give an inductive proof (see next)

20. Inductive Proofs
Prove a basis statement and an inductive step providing a propagation rule
Let S(n) be a statement about integer n
Basis: prove S(i) for some fixed value i
Inductive step: prove that for any m > i – 1, S(m) implies S(m+1)

21. Inductive Proofs
Prove a basis statement and an inductive step providing a propagation rule
Let S(n) be a statement about integer n
Basis: prove S(i) for some fixed value i
Inductive step: prove for m > i-1 S(m) implies S(m+1)
E.g.1, prove that for any positive n the sum of the first n integers equals n(n+1)/2 (btw did you know how Pitagoras did it?)
E.g. 2 Let a binary tree be defined as ‘a single node or a node with having two trees as its children . Prove that any binary tree with n leaves (nodes without children) has precisely n-1 internal nodes (nodes with children)

22. The structure of Inductive Proofs
Prove the basis statement : check the validity of the claim for initial values of the parameter
Prove inductive step :
assume statement is true for all values of the parameter up to n-1 providing a propagation rule
Take instance associated with value n
Decompose this instance into instances involving smaller values of the parameter
Force inductive hypothesis on these instances
Re-assemble the instance for value n
Strange things happen when we are not careful
E.g.: for any positive n, all horses in a group of n have the same mantel

23. Additional Proofs Proofs by contradiction
Assume the opposite of hypothesis, show thesis cannot follow
Proofs by counterexample
All primes are odd – Exhibit the even prime 2
(are there also proofs ‘’by example’’?)
If-then-else proofs

24. Automata Finite Automata model many design and analysis tasks, e.g.
Lexical analyzer in a compiler
Digital cicuit design
Keywork searching in texts or on the web.
Software for verifying finite state systems,
such as communication protocols.
Etc.