slike bài giảng môn automata and formal language

Languages Grammars Automata Automata and Formal language Huynh Viet Linh vietlinh@cse.hcmut.edu.vn Ngày 13 tháng 9 năm 2009 Huynh Viet Linh Automata and Formal language Languages Grammars Automata Course Overview An introduction to the fundamental theories and algorithms for computing on digital computer. Automation: A model producing output from acceptable input based on self-made decision Formal Language: An abstraction of programming language syntax. Huynh Viet Linh Automata and Formal language Languages Grammars Automata 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 Huynh Viet Linh Automata and Formal language Languages Grammars Automata Reading Materials Hồ Văn Quân, Giáo trình lý thuyết automat và ngôn ngữ hình thức. Peter Linz, An introduction to formal languages and automata. John Hopcroft and Jeffrey Ullman, Introduction to automata theory, languages, and computation. Course website: 505012-CSE-06-Fall 2009 Huynh Viet Linh Automata and Formal language Languages Grammars Automata Assessment Mid term: ??? Final exam: ??? Presentation Huynh Viet Linh Automata and Formal language Languages Grammars Automata Related Issues Digital Circuit Design Compiler Programming Languages Huynh Viet Linh Automata and Formal language Languages Grammars Automata Required Background Set and Graph Theory Induction and Contradiction-based Methods Huynh Viet Linh Automata and Formal language Languages Grammars Automata Three Basic Concepts Languages Grammars Automata Huynh Viet Linh Automata and Formal language Languages Grammars Automata Languages Alphabet: a finite and nonempty set of symbols, denoted by  Example 1:  = {a,b}  = {0,1} Roman alphabet  = {A,B, ,Z} Greek alphabet  = {α, β, } Huynh Viet Linh Automata and Formal language Languages Grammars Automata Languages String: finite sequence of symbols from  λ: empty string  ∗ : the set of all strings on  (  + =  ∗ −{λ}) Example 2:  = {a,b}  ∗ = {λ,a,b,aa,ab,aaa,abb, } w = abaaabba is a string of  Huynh Viet Linh Automata and Formal language [...]... Linh Automata and Formal language Languages Grammars Automata Formal Grammar Productions: x → y, x ∈ (V ∪ T )+ , y ∈ (V ∪ T )∗ Example 5: G = ({S}, {a,b},S,P) P: S → aSb S→λ Huynh Viet Linh Automata and Formal language Languages Grammars Automata Directly Derive w =uxv derives z = uyv if x → y is a production w⇒z w1 ⇒∗ wn w1 ⇒+ wn Huynh Viet Linh Automata and Formal language Languages Grammars Automata. .. Linh Automata and Formal language Languages Grammars Automata Generated Language G = (V,T,S,P) L(G) = {w ∈ T ∗ : S ⇒∗ w } Example 7: For the grammar G in example 5, L(G ) = {an bn : n ∈ N} Huynh Viet Linh Automata and Formal language Languages Grammars Automata Derivation S ⇒ w1 ⇒ w2 ⇒ ⇒ wn ⇒ w ∈ L(G) Example 8: S ⇒ aSb ⇒ aaSbb ⇒ aabb is a derivation Huynh Viet Linh Automata and Formal language Languages...Languages Grammars Automata Language Language: a subset L of ∗ Sentence: a string in L Example 3: L = {an bn : n ∈ N} is a language on = {a,b} w = aabba is a string of but not a sentence of L Huynh Viet Linh Automata and Formal language Languages Grammars Automata Language concatenation L1 L2 = {xy : x ∈ L1 , y ∈ L2 } Ln = LL L (n times) L0 = {λ} Huynh Viet Linh Automata and Formal language Languages... Grammars Automata Language concatenation L = {an bn : n ∈ N} L2 = {an bn am bm : m, n ∈ N} L1 = {an b2n } and L2 = {bn a2n } → L1 L2 =? Huynh Viet Linh Automata and Formal language Languages Grammars Automata Closure Operators Star-Closure: L∗ = L0 ∪ L1 ∪ L2 Positive-Closure: L+ = L1 ∪ L2 Huynh Viet Linh Automata and Formal language Languages Grammars Automata Grammar Grammar for a natural language: ... Grammars Automata 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) An abstract model of digital computer Huynh Viet Linh Automata and Formal language Languages Grammars Automata Automaton Structure Huynh Viet Linh Automata and Formal language. .. alphabet as the input one) The automaton can read and change the storage cells Huynh Viet Linh Automata and Formal language Languages Grammars Automata Control Unit Having a finite set of internal states Can be any one of its internal states Can change from one internal state to other Huynh Viet Linh Automata and Formal language Languages Grammars Automata Automation Operations Transition function:... info Move: current configuration → next configuration Huynh Viet Linh Automata and Formal language Languages Grammars Automata Automaton Types Accepter: yes/no output Transducer: string of symbols as output Deterministic: single possible move at one point Non-deterministic: multiple possible moves Huynh Viet Linh Automata and Formal language ... natural language: a set of rules to construct vocabulary and sentences Example 4: A simple English grammar → → → → a | the → boy | dog → runs | walks Huynh Viet Linh Automata and Formal language Languages Grammars Automata Formal Grammar Formal grammar: G = (V , T , S, P) V: finite set of variables... Linh Automata and Formal language Languages Grammars Automata Input File Input file: is Divided into squares or cells, each of which holds a symbol of the alphabet The symbols are to be read from left to right The end of input file is detectable The automaton cannot change the contents of the input file Huynh Viet Linh Automata and Formal language Languages Grammars Automata Storage A device consisting . Linh Automata and Formal language Languages Grammars Automata Three Basic Concepts Languages Grammars Automata Huynh Viet Linh Automata and Formal language Languages Grammars Automata Languages Alphabet:. Languages Grammars Automata Automata and Formal language Huynh Viet Linh vietlinh@cse.hcmut.edu.vn Ngày 13 tháng 9 năm 2009 Huynh Viet Linh Automata and Formal language Languages Grammars Automata Course. Linh Automata and Formal language Languages Grammars Automata Assessment Mid term: ??? Final exam: ??? Presentation Huynh Viet Linh Automata and Formal language Languages Grammars Automata Related