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Class Notes for FIT2014 at Monash University

Theory of computation

FIT2014 Lecture Notes - Lecture 19: Invertible Matrix, Euclidean Algorithm, Lexicographical Order
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Lecture 19: Polynomial time, and the class P Decidable languages Solvable in principle Doesnt matter which computer you are using or the hardware etc How we are trying to talk about the time Time Complexity The time ta...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 18: If And Only If, Recursively Enumerable Language, Universal Turing Machine
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Lecture 18: : Recursively Enumerable A language L is decidable if and only if there exists a Turing Machine T such that Definition: recursively enumerable A language L is recursively enumerable if there exists a Turing mac...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 20: Finite-State Machine, Vertex Cover, Turing Machine
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Lecture 20 Deciding if a string belongs to a language or not VS Verifying that a string belongs to a language P is intended to contain languages which are efficiently decidable. P is the set of languages for which there is...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 17: If And Only If, Halting Problem, Turing Machine
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Lecture 17 Undecidability Halting Problem Input: Turing Machine P, input x Question if P is run with input x, does it eventually halt? Theorem: The halting problem is undecidable. Proof is by contradiction and includes a m...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture 14: Turing Machine
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Lecture 14: Turing Machine Turing Machine Setup: Infinitely long tape divided into cells Each cell may contain a symbol from a finite alphabet Head scans one tape cell at a time. The machine is in some state Program: F...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 15: Universal Turing Machine, Turing Machine, Regular Language
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Lecture 15 Variation on Turing Machines: Direction: stay still, as well as left or right Two way infinite tape Multiple tape Separate input output tape, work tape Turing Machines for computing functions: So far Turing ...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 16: Terminal And Nonterminal Symbols, Natural Number, L(R)
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Lecture 16 Decidability Decision Problem: Input: an integer Question : Is It even? Input: a string. Question: Is it a palindrome? Input: an expression in propositional logic Question: Is it ever True? Input: a graph G, and...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 12: Context-Free Grammar, Lr Parser, Parse Tree
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Lecture 12 Parsing. Suppose you have a context free grammer (e.g. S aX) and a string of letter, Parsing is the task of determining whether the string is a word in the language and if it is finding a parse tree for it How...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 13: Binary Tree, Parse Tree, Longest Path Problem
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Lecture 13 : Chomsky Normal Forum CNF is a special type of context free grammar Nonterminal Nonterminal Nonterminal (live production) Or Nonterminal terminal (dead production) For any context free language L, the on empty ...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 11: Context-Free Grammar, Pushdown Automaton, Regular Grammar
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Lecture 11 Regular Grammars and pushdown Automata NFA to CFG 1. Name all states in NFA by a symbol a. Call the start State S 2. For each edges 3. For each edge Write X Y 4. write X aX 5. Fo each final state X write X Semi ...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 10: Context-Free Grammar, Terminal And Nonterminal Symbols
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Lecture 10 Context Free Grammar Context Free Grammer: 1. An alphabet a. The letters are called Terminals 2. A set of symbols a. We call these symbols nonterminals b. One of these symbols are statrt symbol(usually S) 3. A f...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 9: Regular Language, Regular Expression, Concatenation
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Lecture 9 Pumping Lemma Closures Properties If doing some operation on regular languages always produces another regular language, then we say that regulars are closed under that operation. 1. Complement 2. Union 3. Inters...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 6: Deterministic Finite Automaton, Regular Expression
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Lecture 6: Finite Automata Finite Automaton FA is also as know as Deterministic Finite Automaton Used to determining whether a word does or does not belong to a Regular Langing Used to defining Regular Language Used in...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 7: Regular Expression
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Lecture 7 Kleenes Theorem Any language can be defined by Regular Expression Finite Automata NFA GNFA Can be defined by any of the other methods. Converting a Regular Expression to NFA Converting NFA to FA In FA : Any ...

Information Technology
FIT2014
Graham Farr
FIT2014 Lecture Notes - Lecture 8: Lexeme, Regular Expression
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Lecture 8 : Terminology A token is a name of pattern o It may also have an attribute value associated with it A lexeme is a sequence of characters that matches the pattern corresponding to a token A pattern is a descrip...

Information Technology
FIT2014
Graham Farr

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