Automata and Formal Language Quan Thanh Tho qttho@dit.hcmut.edu.vn Course Overview  An introduction to the fundamental theories and algorithms for computing on digital computer. – Automation: A model producing input from acceptable output based on self-made decision – Formal Language: An abstraction of programming language syntax. Course Outline  Chapter 1: Introduction  Chapter 2: Finite Automata  Chapter 3: Regular Language and Regular Grammar  Chapter 4: Properties of Regular Language  Chapter 5: Context-Free Grammar  Chapter 6: Simplification of Context-Free Grammar  Chapter 7: Pushdown Automata Reading Materials • Giáo trình lý thuyết automat và ngôn ngữ hình thức. Hồ Văn Quân • An introduction to formal languages and automata. Peter Linz • Introduction to automata theory, languages, and computation. John Hopcroft & Jeffrey Ullman Assessment  Assignment: 30%  Final Exam: 70% Related Issues  Digital Circuit Design  Compiler  Programming Languages Required Background  Set and Graph Theory  Induction and Contradiction-based Methods Three Basic Concepts  Languages  Grammars  Automata Languages • Alphabet: a finite and nonempty set of symbols Σ = {a, b} • Example 1.1 • Roman Alphabet: A,B,C, ,Z. • Greek Alphabet: α,β,… Language (cont’d) • String: finite sequence of symbols from Σ λ: empty string Σ*: the set of all strings on Σ (Σ+ = Σ* − {λ})  Example 1.2: Given Σ = {a,b} => Σ* = {λ, a, b, aa, ab, ba, aaa, } w = abaaa is a string of Σ L = {anbn | n ≥ 0} = {λ, ab, aabb, } is a set of strings of Σ [...].. .Language (cont’d) • Language: a subset L of Σ* • Sentence: a string in L • Example 1.3: In Example 1.2, L is a language on Σ, w is a string of Σ but not a sentence in L Language Concatenation L L = {xy | x∈L , y∈L } 1 2 1 2 Ln = L L L L0 = {λ} (n times) Language Concatenation (cont’d) • Example 1.4: L = {anbn | n ≥ 0} L2 = {anbnambm... Grammar for a natural language: a set of rules to construct vocabulary and sentences  Example 1.5: A simple English grammar → → → → a | the → boy | dog → runs | walks Hands-on Exercise 1.1:  Find all of possible sentences of the grammar given in Example 1.5 Formal Grammar • Formal grammar: G =... productions Formal Grammar (cont’d) • Productions: x → y, x∈(V ∪T )+, y∈(V ∪T )* • Example 1.6: G = ({S}, {a, b}, S, P) P: S → aSb S→λ Directly Derive • w = uxv derives z = uyv if xy is a production w⇒z w ⇒* w (w ⇒ w ⇒ ⇒ w | w = w ) 1 n 1 2 n 1 n w ⇒+ w 1 n Directly Derive (cont’d) • Example 1.7: Take into consideration the grammar given in Example 1.6: S ⇒ aSb ⇒ aaSbb ⇒ aabb S ⇒* aabb Generated Language. .. aabb Sequential Forms • S, w1, w2, , wn (containing variables) with S ⇒ w1 ⇒ w2 ⇒ ⇒ wn ⇒ w is a derivation • Example 1.10: S ⇒ aSb ⇒ aaSbb ⇒ aabb aabb: sentence aaSbb: sentential form Automata  “An automaton (plural: automata) is a self-operating machine The word is sometimes used to describe a robot, more specifically an autonomous robot Used colloquially, it refers to a mindless follower.” (Wiki)... contents of the input file Storage  A device consisting of unlimited cells  Each cell hold a symbol from an alphabet (it is not necessary to be the same alphabet as the input one)  The automaton can read and change the storage cells Control Unit  Having a finite set of infernal states  Can be any one of its infernal states  Can change from one infernal state to other Automation Operations • Transition . Pushdown Automata Reading Materials • Giáo trình lý thuyết automat và ngôn ngữ hình thức. Hồ Văn Quân • An introduction to formal languages and automata. Peter Linz • Introduction to automata. abstraction of programming language syntax. Course Outline  Chapter 1: Introduction  Chapter 2: Finite Automata  Chapter 3: Regular Language and Regular Grammar  Chapter 4: Properties of Regular Language  Chapter. Automata and Formal Language Quan Thanh Tho qttho@dit.hcmut.edu.vn Course Overview  An introduction