tailieunhanh - Lecture note Theory of automata - Lecture 26

Lecture Theory of automata - Lecture 26 includes contents: Example of nonregular language, pumping lemma version I, proof, examples. | Lecture note Theory of automata - Lecture 26 Lecture 2 Theory Of Automata By Dr. MM Alam Lecture 1 Recap Definition of the word Automata Types of languages empty Null String Alphabets words length of strings Palindromes How to form palindromes of even and odd length. Question Q Prove that there are as many palindromes of length 2n defined over Σ a b c as there are of length 2n-1 n 1 2 3 . Determine the number of palindromes of length 2n defined over the same alphabet as well. Example - L aa ab ac bb ba bc cc ca cb 9 words. Solution Since the number of symbols are 3 in the alphabet therefore the length of 2n palindromes will be 3n. As 2n means that palindromes are of even length. Solution Cont d Similarly for palindromes of length 2n-1 we need to calculate their number for each respective symbol in the alphabet that is the required number of palindromes are 3n- 1 for symbol a Similarly the number of palindromes of length 2n-1 with b or c as middle letter will be 3n-1 as well. Hence the total number of palindromes of length 2n-1 will be 3n-1 3n-1 3n-1 3 3n-1 3n . Consider the language of Palindrome over the alphabet a b . Prove that if x is in PALINDROME then so is xn for any n. Example suppose x aba and is a palindrome and xr aba r aba Then aba 5 aba aba aba aba aba aba r aba aba aba aba aba which is again a palindrome Proof. It is true for n 0 by assumption xn is palindrome. Assume that it is true for n-1 namely xn-1 is in palindrome and xn-1 r xn-1. Now as we know that xy r yrxr . xn r xn-1x r xr xn-1 r x xn-1 xn. Thus xn is in palindrome Kleene Star closure In order to further generalize the notation of any combination of strings the famous logician kleene and founder of the Theory of Automata subject has introduced a notation called kleene closure. It is denoted by Σ and represent all collection of strings defined over Σ including Null string. The language produced by Kleene closure is infinite. It contains infinite words however each word has finite length. .

• Tự động hoá
• Theory of automata
• Lecture Theory of automata
• Computer theory
• Theory of computation
• Example of nonregular language
• Pumping lemma version I
• Formal Languages & Automata
• Pushdown Automata
• Finite Automata
• Non deterministic Pushdown Automata
• Instantaneous Description
• Language accepted by NPDA
• Deterministic Finite Automata (DFA)
• Operational Manner
• Transition Graphs
• Extended Transition Function
• Automata theory
• Automata theory languages
• Automata theory computation
• Context Free grammars
• Regular languages
• Automata hữu hạn
• Đoán nhận ngôn ngữ
• Biểu diễn automata
• Xây dựng automata
• xây dựng DFA
• Automata Model
• Settlement Development
• Automata Framework
• Cellular Automata
• Transport Equations
• Population Dynamics
• isaster Areas
• Bus Dynamics
• A Hierarchy of Formal Languages and Automata
• ecursively Enumerable Languages
• Recursive Languages
• Unrestricted Grammars
• Context Sensitive Grammars
• Tin học lý thuyết
• Bài giảng Tin học lý thuyết
• Automata đẩy xuống
• Push Down Automata
• PDA đơn định
• PDA không đơn định
• Additional classes
• Intractable problems
• Properties of context free languages
• Introduction to automata theory languages and compution
• Regular expressions
• Properties of regular sets
• chương trình đồ họa
• giáo trình thiết kế
• thiết kế đồ họa
• lý thuyết automata
• tài liệu về automata
• tài liệu về pushdown automata
• ngôn ngữ lập trình
• Logical Computation
• Quantum Computations
• Automata Application
• Organizing Networks
• Molecular Orbitals
• Disordered Cellular automata
• Traffic flow models
• Automata traffic
• Nagel Schreckenberg
• Deceleration terms
• Cellular Automata in transportation
• Evaluating Dynamic
• Three Basic Concepts
• Languages Grammars Automata
• Input file
• Control unit
• String in L
• Introduction Formal Languages & Automata
• A formal language
• An automaton
• Fundamental ideas
• Models underlying computing
• Văn phạm phi ngữ cảnh
• Ngôn ngữ hình thức
• Văn phạm hình thức và các Automata
• Trình biên dịch
• Solution of the task
• Polish notation
• Total language tree
• Null production
• Nullable production
• Theorem regarding CNF
• The START state
• Nondeterministic PDA
• Equivalent PDA
• PDA corresponding to CFG
• STACK alphabet
• Computer science
• CFG corresponding