1. C Sc 132 Computing Theory Professor Meiliu Lu Computer Science Department

2. Introduction An introductory course on formal languages and automata Three basic concepts: languages, grammar, & automata Purposes: to provide the foundation and basic principle of CS, to teach material that will be useful in subsequent work, and to strengthen students’ ability to use formal methods

3. Agenda Part I (before midterm): Basic concepts, Finite Automata, Regular Languages, Context Free Grammars, Parsing. Part II (after midterm): Push Down Automata, Turing Machines, and Chomsky Hierarchy, NP-complete problems Perl Regular expressions

4. 3 Major Concepts Languages -- 4 formal languages for design and implement programming languages – regular, context free, context sensitive, recursively enumerable Language generators -- 4 Grammars for 4 languages

5. 3 Major Concepts (cont.) Language recognizers -- 4 automata for 4 languages –finite automata, push down automata, bounded TM, Turing Machine (TM) Applications to reinforce the 3 concepts –Regular expressions in Perl –Parsing in compiler

6. Abstractions What is an abstraction? –A method and language for working with one aspect of a design. Examples: simulation, layout, specification, and models. All abstractions have limitations. We need different abstraction for different task in design and implementation of PL.

7. Class mailing list List name: csc132lu To subscribe the mailing list: –email to “majordomo@ecs.csus.edu” –leave subject open –body of the email: subscribe csc132lu Make sure you are using the list for class discussion only.

8. Summary Computing theory gives you the necessary background to understand others design and enable you to be a good designer of computer system. Abstraction makes powerful tools for you. What do you think of this course now?

9. Chapter 2. Languages Sets and Their operations Languages and Their operations

10. Sets and operations Sets, subsets, empty set, multiset Cartesian product of A and B Power set of A, 2 A, set of all subsets of A Cardinality of A, size of set A Sets operations: union, intersection, deference, universal set

11. Languages Alphabet: a finite, nonempty set S of symbols Strings: finite sequences of symbols from S Language: a set of strings from S S *, S +, empty string  and empty set  Language: a subset of S * Example: S = {a, b}. What are S * and S + ?

12. Language operations More languages on S –L = {a n b n : n >= 0} complement of L, S * - L concatenation (product) of languages –L 1 L 2 = {xy: x  L 1, y  L 2 } What is L 2 when L = {a n b n : n >= 0} ?

13. Language operations (cont.) Power of L –L 0 = { } –L n = L L n-1 –L * = L 0  L 1 … –L + = L 1  L 2 ...