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This document provides an introduction to the theory of computation, including definitions of key concepts like automata theory, symbols, alphabets, strings, languages, and sets. It discusses how automata theory deals with formal models of computation and is used in areas like text processing and programming languages. Mathematical terminology is introduced, such as symbols, alphabets, strings, languages, sets, and the power and Cartesian product of alphabets. Examples are given to illustrate concepts like strings, languages, and valid versus invalid computations based on whether a string is contained within a language.
This document provides an overview of constraint satisfaction problems (CSPs). It defines a CSP as a problem where variables must be assigned values from their domains to satisfy constraints. Examples of CSPs include the n-queens puzzle, map coloring, Boolean satisfiability, and cryptarithmetic problems. A CSP is represented as a constraint graph with nodes as variables and edges as binary constraints. The goal is to assign values to each variable to satisfy all constraints.
This document provides an introduction to theory of computation from Dr. Hussien Sharaf. It discusses how TC emerged from mathematicians' efforts to model machines that can think and do calculations. TC gives answers about capabilities and limitations of computing machines. It explains that TC consists of automata theory, computability theory, and complexity theory. The document also introduces some basic mathematical notations and terminology used in TC like sets, sequences, tuples, relations, functions, graphs, strings, and languages. It includes examples and exercises to illustrate these concepts.
11.a new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known continuous triangular fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of "positive fuzzy number," "negative fuzzy number," and "half-positive and half-negative fuzzy number." Several propositions and theorems are presented along with proofs to show that the solution to such a fuzzy equation can be a positive, negative, or half-positive/half-negative fuzzy number, depending on the values of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations
A new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of positive, negative, and half-positive/half-negative fuzzy numbers. Propositions and theorems are presented to show that the solution to such an equation can be a positive, negative, or half-positive/half-negative fuzzy number depending on the properties of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations in solving equations where X is an unknown fuzzy number.
This document discusses regular expressions (RE) and how they can be used with the grep command. It covers the basic RE character subset used by grep by default, including wildcards like *, ., [], ^, and $. It then explains the extended RE character subset used with grep's -E option, including quantifiers like + and ?, alternation with |, and grouping with (). Finally, it provides examples of using grep with both basic and extended REs to search files for matching patterns.
This document provides an introduction to the Theory of Computation course offered at Mutah University. The course will cover three main topics: automata, computability theory, and complexity theory. It will examine fundamental capabilities and limitations of computers. Required reading includes Sipser's textbook Introduction to the Theory of Computation. Key concepts to be discussed include formal models of computation, problems that cannot be solved by computers, and distinguishing between easy and hard computational problems.
This document discusses context-free grammars and regular grammars. It defines regular grammars and shows that the class of regular languages, deterministic finite automata, regular expressions, and regular grammars are equivalent. Regular grammars can generate regular languages, and any regular language can be generated by a regular grammar. The document provides examples and proofs of these properties.
This document provides an introduction to the theory of computation, including definitions of key concepts like automata theory, symbols, alphabets, strings, languages, and sets. It discusses how automata theory deals with formal models of computation and is used in areas like text processing and programming languages. Mathematical terminology is introduced, such as symbols, alphabets, strings, languages, sets, and the power and Cartesian product of alphabets. Examples are given to illustrate concepts like strings, languages, and valid versus invalid computations based on whether a string is contained within a language.
This document provides an overview of constraint satisfaction problems (CSPs). It defines a CSP as a problem where variables must be assigned values from their domains to satisfy constraints. Examples of CSPs include the n-queens puzzle, map coloring, Boolean satisfiability, and cryptarithmetic problems. A CSP is represented as a constraint graph with nodes as variables and edges as binary constraints. The goal is to assign values to each variable to satisfy all constraints.
This document provides an introduction to theory of computation from Dr. Hussien Sharaf. It discusses how TC emerged from mathematicians' efforts to model machines that can think and do calculations. TC gives answers about capabilities and limitations of computing machines. It explains that TC consists of automata theory, computability theory, and complexity theory. The document also introduces some basic mathematical notations and terminology used in TC like sets, sequences, tuples, relations, functions, graphs, strings, and languages. It includes examples and exercises to illustrate these concepts.
11.a new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known continuous triangular fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of "positive fuzzy number," "negative fuzzy number," and "half-positive and half-negative fuzzy number." Several propositions and theorems are presented along with proofs to show that the solution to such a fuzzy equation can be a positive, negative, or half-positive/half-negative fuzzy number, depending on the values of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations
A new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of positive, negative, and half-positive/half-negative fuzzy numbers. Propositions and theorems are presented to show that the solution to such an equation can be a positive, negative, or half-positive/half-negative fuzzy number depending on the properties of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations in solving equations where X is an unknown fuzzy number.
This document discusses regular expressions (RE) and how they can be used with the grep command. It covers the basic RE character subset used by grep by default, including wildcards like *, ., [], ^, and $. It then explains the extended RE character subset used with grep's -E option, including quantifiers like + and ?, alternation with |, and grouping with (). Finally, it provides examples of using grep with both basic and extended REs to search files for matching patterns.
This document provides an introduction to the Theory of Computation course offered at Mutah University. The course will cover three main topics: automata, computability theory, and complexity theory. It will examine fundamental capabilities and limitations of computers. Required reading includes Sipser's textbook Introduction to the Theory of Computation. Key concepts to be discussed include formal models of computation, problems that cannot be solved by computers, and distinguishing between easy and hard computational problems.
This document discusses context-free grammars and regular grammars. It defines regular grammars and shows that the class of regular languages, deterministic finite automata, regular expressions, and regular grammars are equivalent. Regular grammars can generate regular languages, and any regular language can be generated by a regular grammar. The document provides examples and proofs of these properties.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
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Call us at : 08263069601
Kahler Differential and Application to Ramification - Ryan Lok-Wing PangRyan Lok-Wing Pang
This document discusses the application of Kähler differentials to the study of ramification in algebraic number theory. It defines Kähler differentials and constructs the module of relative differentials. Properties like exact sequences are proven. The concept of the different ideal is introduced, which encodes ramification data in field extensions. It is shown that the different ideal is the annihilator of the module of Kähler differentials, providing a geometric characterization of ramification.
This document provides information about getting fully solved assignments by emailing or calling a provided contact. It then provides sample answers to 6 questions related to computer science topics like recursive functions, proof techniques, trees, finite state machines, and grammars. The answers discuss recursive functions versus growth functions, direct and indirect proof techniques, walks and paths in trees, deterministic finite automata and their transition systems, the differences between Moore and Mealy machines, and defines context-free grammars and ambiguous grammars with examples.
This document provides information about an assignment for the subject Foundations of Mathematics. It lists the subject code, credit hours, and evaluator ID. It then provides 5 questions related to the course content, such as defining Cauchy's theorem and verifying it for a given function. It also asks students to define logical concepts like tautology, contradiction, negation, and to verify theorems like Lagrange's mean value theorem. The last question asks students to define set theory concepts like the set, null set, subset, power set, and union set. Students are instructed to answer all questions, with 10 mark questions being approximately 400 words each.
The document discusses formal languages and grammars. It defines key concepts such as alphabets, strings, languages, and regular expressions. Some key points:
- An alphabet is a set of symbols. A string is a finite sequence of symbols from an alphabet.
- A formal language is a set of strings over a given alphabet. Languages can be constructed using operations like union.
- Regular expressions are used to define regular languages recursively, using operators like concatenation and Kleene star.
- A formal grammar is a 4-tuple that can be used to generate a formal language. The language generated by a grammar is the set of strings derived from the start variable using the production rules.
This document discusses solving polynomial equations by factoring. It provides examples of factoring polynomials, including factoring the difference and sum of cubes. Factoring by substitution is also introduced as a method for factoring polynomials of degree 4 or higher. The document demonstrates solving polynomial equations by factoring the expressions and setting each factor equal to 0. Both real and imaginary solutions may be obtained depending on whether the factors are real or complex numbers. Graphing is presented as an alternative method to find real solutions of a polynomial equation.
This document summarizes a lecture on database design theory that covered topics like database design problems, functional dependencies, decomposition, and normalization. It began with an overview of the concepts of redundancy, anomalies, and functional dependencies. It then discussed decomposition rules, lossless joins, dependency preservation, and normal forms. The lecture aimed to explain how to model databases and design relational schemas to minimize redundancy and avoid anomalies.
This document provides an introduction to the basics of formal language theory for the course CIS511 Introduction to the Theory of Computation. It discusses key concepts such as alphabets, strings, languages, operations on languages, and models of computation including finite automata, pushdown automata, and Turing machines. The document outlines the Chomsky hierarchy of formal grammars and their corresponding families of languages. It aims to provide students with an understanding of formal languages and how they are defined and manipulated.
Theory of automata and formal languageRabia Khalid
KleenE Star Closure, Plus operation, recursive definition of languages, INTEGER, EVEN, factorial, PALINDROME, languages of strings, cursive definition of RE, defining languages by RE,Examples
Dear students get fully solved assignments
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This document provides an overview of formal languages and properties. It discusses two types of languages - informal languages which do not strictly follow grammar rules, and formal languages which must follow predefined syntactic rules. Descriptive definition is introduced as a method to define formal languages by describing the conditions imposed on words. Several examples of languages defined descriptively are provided to illustrate this concept.
The document describes simplifying variable expressions. It defines terms, like terms, and coefficients in an expression. Expressions can be simplified by combining like terms using the distributive property. Examples show identifying parts of expressions, simplifying expressions, and writing and simplifying an expression to describe calories burned during a workout involving jogging and swimming for different time periods.
This document provides an introduction to First Order Predicate Logic (FOPL). It discusses the differences between propositional logic and FOPL, the parts and syntax of FOPL including terms, atomic sentences, quantifiers and rules of inference. The semantics of FOPL are also explained. Pros and cons are provided, such as FOPL's ability to represent individual entities and generalizations compared to propositional logic. Applications include using FOPL as a framework for formulating theories.
The document presents a method for incremental evolving fuzzy grammar fragment learning with independent-order feature. It discusses background, existing approaches, learning fuzzy grammar fragments, issues in grammar variety and derivation, a fuzzy approach for text pattern learning, grammar similarity, a minimal combination algorithm, experiments on parsing coverage and independent-order grammar learning, and conclusions.
First-order logic (FOL) is a formal system used in mathematics, philosophy, linguistics, and computer science to represent knowledge about domains involving objects and relations. FOL extends propositional logic with quantifiers and predicates to describe properties of and relations between objects. Well-formed formulas in FOL involve constants, variables, functions, predicates, quantifiers, and logical connectives. The meaning and truth of FOL statements is determined with respect to a structure called a model that specifies a domain of objects and interpretations of symbols. FOL can be used to represent knowledge about many different domains and perform logical inference.
This document provides an introduction and outline for a course on Formal Language Theory. The course will cover topics like set theory, relations, mathematical induction, graphs and trees, strings and languages. It will then introduce formal grammars including regular grammars, context-free grammars and pushdown automata. The course is divided into 5 chapters: Basics, Introduction to Grammars, Regular Languages, Context-Free Languages, and Pushdown Automata. The Basics chapter provides an overview of formal vs natural languages and reviews concepts like sets, relations, functions, and mathematical induction.
Theory of automata and formal languageRabia Khalid
The document discusses theory of automata and formal languages. It defines key concepts like abstract machines, automata, alphabets, strings, words, languages and provides examples to describe them. Abstract machines are theoretical models of computer systems used to analyze how they work. Automata are self-operating machines that follow predetermined sequences of operations. Alphabets are sets of symbols, strings are concatenations of symbols, and words are strings belonging to a language. Languages can be defined descriptively or recursively and examples are given to illustrate different ways of defining languages.
This document provides an overview of the Prolog programming language. It begins with an outline of the topics that will be covered, including syntax of terms, simple programs, terms as data structures, the cut operator, and writing real programs. It then defines Prolog as a logic programming language that uses logical variables and unification. The rest of the document explains key aspects of Prolog like clauses, facts, rules, queries, compound terms, and unification through examples. It also discusses how Prolog programs are executed and how clauses can be read both declaratively and procedurally.
Mh0054 finance, economics and planning in healthcare.smumbahelp
This document provides information about an assignment for the subject MH0054 - Finance, Economics and Planning in Healthcare Services. It lists the semester, specialization name, subject code and name, credits, and marks. It also contains 6 questions related to the subject matter, asking students to answer all questions and noting that 10-mark questions should be around 400 words. Students are instructed to send their semester and specialization details to an email address or call a phone number to get fully solved assignments.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
Kahler Differential and Application to Ramification - Ryan Lok-Wing PangRyan Lok-Wing Pang
This document discusses the application of Kähler differentials to the study of ramification in algebraic number theory. It defines Kähler differentials and constructs the module of relative differentials. Properties like exact sequences are proven. The concept of the different ideal is introduced, which encodes ramification data in field extensions. It is shown that the different ideal is the annihilator of the module of Kähler differentials, providing a geometric characterization of ramification.
This document provides information about getting fully solved assignments by emailing or calling a provided contact. It then provides sample answers to 6 questions related to computer science topics like recursive functions, proof techniques, trees, finite state machines, and grammars. The answers discuss recursive functions versus growth functions, direct and indirect proof techniques, walks and paths in trees, deterministic finite automata and their transition systems, the differences between Moore and Mealy machines, and defines context-free grammars and ambiguous grammars with examples.
This document provides information about an assignment for the subject Foundations of Mathematics. It lists the subject code, credit hours, and evaluator ID. It then provides 5 questions related to the course content, such as defining Cauchy's theorem and verifying it for a given function. It also asks students to define logical concepts like tautology, contradiction, negation, and to verify theorems like Lagrange's mean value theorem. The last question asks students to define set theory concepts like the set, null set, subset, power set, and union set. Students are instructed to answer all questions, with 10 mark questions being approximately 400 words each.
The document discusses formal languages and grammars. It defines key concepts such as alphabets, strings, languages, and regular expressions. Some key points:
- An alphabet is a set of symbols. A string is a finite sequence of symbols from an alphabet.
- A formal language is a set of strings over a given alphabet. Languages can be constructed using operations like union.
- Regular expressions are used to define regular languages recursively, using operators like concatenation and Kleene star.
- A formal grammar is a 4-tuple that can be used to generate a formal language. The language generated by a grammar is the set of strings derived from the start variable using the production rules.
This document discusses solving polynomial equations by factoring. It provides examples of factoring polynomials, including factoring the difference and sum of cubes. Factoring by substitution is also introduced as a method for factoring polynomials of degree 4 or higher. The document demonstrates solving polynomial equations by factoring the expressions and setting each factor equal to 0. Both real and imaginary solutions may be obtained depending on whether the factors are real or complex numbers. Graphing is presented as an alternative method to find real solutions of a polynomial equation.
This document summarizes a lecture on database design theory that covered topics like database design problems, functional dependencies, decomposition, and normalization. It began with an overview of the concepts of redundancy, anomalies, and functional dependencies. It then discussed decomposition rules, lossless joins, dependency preservation, and normal forms. The lecture aimed to explain how to model databases and design relational schemas to minimize redundancy and avoid anomalies.
This document provides an introduction to the basics of formal language theory for the course CIS511 Introduction to the Theory of Computation. It discusses key concepts such as alphabets, strings, languages, operations on languages, and models of computation including finite automata, pushdown automata, and Turing machines. The document outlines the Chomsky hierarchy of formal grammars and their corresponding families of languages. It aims to provide students with an understanding of formal languages and how they are defined and manipulated.
Theory of automata and formal languageRabia Khalid
KleenE Star Closure, Plus operation, recursive definition of languages, INTEGER, EVEN, factorial, PALINDROME, languages of strings, cursive definition of RE, defining languages by RE,Examples
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
This document provides an overview of formal languages and properties. It discusses two types of languages - informal languages which do not strictly follow grammar rules, and formal languages which must follow predefined syntactic rules. Descriptive definition is introduced as a method to define formal languages by describing the conditions imposed on words. Several examples of languages defined descriptively are provided to illustrate this concept.
The document describes simplifying variable expressions. It defines terms, like terms, and coefficients in an expression. Expressions can be simplified by combining like terms using the distributive property. Examples show identifying parts of expressions, simplifying expressions, and writing and simplifying an expression to describe calories burned during a workout involving jogging and swimming for different time periods.
This document provides an introduction to First Order Predicate Logic (FOPL). It discusses the differences between propositional logic and FOPL, the parts and syntax of FOPL including terms, atomic sentences, quantifiers and rules of inference. The semantics of FOPL are also explained. Pros and cons are provided, such as FOPL's ability to represent individual entities and generalizations compared to propositional logic. Applications include using FOPL as a framework for formulating theories.
The document presents a method for incremental evolving fuzzy grammar fragment learning with independent-order feature. It discusses background, existing approaches, learning fuzzy grammar fragments, issues in grammar variety and derivation, a fuzzy approach for text pattern learning, grammar similarity, a minimal combination algorithm, experiments on parsing coverage and independent-order grammar learning, and conclusions.
First-order logic (FOL) is a formal system used in mathematics, philosophy, linguistics, and computer science to represent knowledge about domains involving objects and relations. FOL extends propositional logic with quantifiers and predicates to describe properties of and relations between objects. Well-formed formulas in FOL involve constants, variables, functions, predicates, quantifiers, and logical connectives. The meaning and truth of FOL statements is determined with respect to a structure called a model that specifies a domain of objects and interpretations of symbols. FOL can be used to represent knowledge about many different domains and perform logical inference.
This document provides an introduction and outline for a course on Formal Language Theory. The course will cover topics like set theory, relations, mathematical induction, graphs and trees, strings and languages. It will then introduce formal grammars including regular grammars, context-free grammars and pushdown automata. The course is divided into 5 chapters: Basics, Introduction to Grammars, Regular Languages, Context-Free Languages, and Pushdown Automata. The Basics chapter provides an overview of formal vs natural languages and reviews concepts like sets, relations, functions, and mathematical induction.
Theory of automata and formal languageRabia Khalid
The document discusses theory of automata and formal languages. It defines key concepts like abstract machines, automata, alphabets, strings, words, languages and provides examples to describe them. Abstract machines are theoretical models of computer systems used to analyze how they work. Automata are self-operating machines that follow predetermined sequences of operations. Alphabets are sets of symbols, strings are concatenations of symbols, and words are strings belonging to a language. Languages can be defined descriptively or recursively and examples are given to illustrate different ways of defining languages.
This document provides an overview of the Prolog programming language. It begins with an outline of the topics that will be covered, including syntax of terms, simple programs, terms as data structures, the cut operator, and writing real programs. It then defines Prolog as a logic programming language that uses logical variables and unification. The rest of the document explains key aspects of Prolog like clauses, facts, rules, queries, compound terms, and unification through examples. It also discusses how Prolog programs are executed and how clauses can be read both declaratively and procedurally.
Mh0054 finance, economics and planning in healthcare.smumbahelp
This document provides information about an assignment for the subject MH0054 - Finance, Economics and Planning in Healthcare Services. It lists the semester, specialization name, subject code and name, credits, and marks. It also contains 6 questions related to the subject matter, asking students to answer all questions and noting that 10-mark questions should be around 400 words. Students are instructed to send their semester and specialization details to an email address or call a phone number to get fully solved assignments.
The document provides information about getting fully solved assignments for the Bachelor of Business
Administration (BBA) Semester 1. It includes 6 questions and evaluation schemes for an assignment on
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Mh0053 hospital & healthcare information managementsmumbahelp
This document provides information about an assignment for a Master of Business Administration in Healthcare Services Management course. It includes 6 questions related to health information systems and hospital management. The questions cover topics like issues with existing health management systems in India, the significance of health information systems in nursing education, defining medical audits and describing the audit process, categories of information systems in hospitals, modules of hospital information systems, and helping a hospital management choose between continuing manual medical records or automating with an electronic medical records system. Students are instructed to answer all questions and send their semester and specialization details to receive fully solved assignments.
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This document provides information about obtaining fully solved assignments for the MBA semester 4 course MI0039 – E-Commerce. It includes 6 questions related to electronic payment systems, EDI standards, marketing mix (4Ps), website structure, online catalogs, and m-commerce. Students are instructed to send their semester and specialization details to the provided email or call the phone number to receive assistance with their assignments.
This document summarizes findings from time use surveys conducted in Finland. It finds that:
1) Response rates were higher for telephone interviews (62%) than face-to-face interviews (58%), but total non-response was lower for telephone interviews.
2) There were no significant differences in diary quality or number of activities reported between face-to-face and telephone interviews.
3) A light paper diary pilot survey had a very low response rate of 17.4% and differences compared to full surveys, suggesting interviewer assistance is needed for quality and response.
This document provides information about getting fully solved assignments from an assignment help service. It includes their contact email and phone number. Students can send their semester and specialization to get solved assignments. The document then provides sample answers to 6 questions related to topics like discounting principle, demand forecasting, isoquants, break-even analysis, oligopolistic competition, product differentiation, equi-marginal principle, and price elasticity of demand.
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This document provides information about getting fully solved assignments. It instructs students to send their semester and specialization name to an email address or call a phone number to receive solved assignments. It then provides details about assignment programs for various semesters and subjects, including codes, credits, and evaluation criteria. Questions are included about quality management tools like flow diagrams, value stream mapping, and causal loop diagrams.
Life is full of ups and downs, challenges and triumphs. While difficulties will come, having faith, hope and love can help one endure all things. Appreciate each day as a gift, treat people with kindness, and live intentionally without regret.
Dear students get fully solved SMU MBA Fall 2014 assignments
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This document provides information about getting fully solved assignments. It gives a mail ID and phone number to contact to get assignments for various semesters and specializations in MBA programs. It lists subject codes, names, credits and marks for the Project Finance subject. It also provides instructions for answering questions and notes that 10-mark questions should be around 400 words.
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The document provides an overview of machine learning and artificial intelligence concepts:
- Machine learning allows intelligent agents to autonomously discover knowledge from experience. It involves learning from examples without being explicitly programmed.
- Explanation-based learning systems generate explanations for training examples and generalize these to apply to new examples. Case-based learning directly applies previous cases to new problems.
- Connectionist models like neural networks are inspired by the brain and use interconnected nodes that are activated based on input signals to learn complex functions.
This document provides information about an assignment for the subject Fundamental of Algorithms for the 4th semester of the BSc IT program. It includes 6 questions about algorithms topics like insertion sort, divide and conquer strategy, knapsack problem, trees and graphs, spanning trees, and Hamiltonian circuits and paths. Students are instructed to send their semester and specialization details to a provided email or call a phone number to get fully solved assignments.
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1. The document proposes Granulated LDA (GLDA), a regularized version of LDA, to improve topic modeling stability.
2. It introduces measures like Kullback-Leibler divergence and Jaccard coefficient to evaluate topic similarity and modeling stability across runs.
3. An experiment applies LDA, SLDA, and GLDA to a large Russian text corpus, finding that GLDA produces more stable topics across multiple runs according to these measures.
The document discusses approximation algorithms for NP-hard optimization problems. It provides examples of approximation algorithms for problems like set cover, vertex cover, traveling salesman problem (TSP), and knapsack. For set cover, it shows that a greedy algorithm provides a (1+ln n)-approximation. For vertex cover and TSP, it describes 2-approximation algorithms. It also presents a fully polynomial-time approximation scheme (FPTAS) for knapsack that provides a solution within (1-eps) of optimal.
This document discusses recursion and recursive algorithms. It begins with definitions of recursion and recursive thinking. Examples of recursively defined concepts and recursively structured algorithms are provided, such as defining a list recursively and recursively searching all subfolders of a folder. The document then covers implementing recursion in programming through recursive methods and functions. Examples of recursively implemented algorithms like factorial and power functions are analyzed. Tracing the execution of recursive methods is discussed through activation records and recursion stacks. Finally, searching algorithms like binary search are described, which can be implemented recursively.
Machine Learning: Decision Trees Chapter 18.1-18.3butest
The document discusses machine learning and decision trees. It provides an overview of different machine learning paradigms like rote learning, induction, clustering, analogy, discovery, and reinforcement learning. It then focuses on decision trees, describing them as trees that classify examples by splitting them along attribute values at each node. The goal of learning decision trees is to build a tree that can accurately classify new examples. It describes the ID3 algorithm for constructing decision trees in a greedy top-down manner by choosing the attribute that best splits the training examples at each node.
Operations management chapter 03 homework assignment use thisPOLY33
This document contains homework assignments related to operations management, machine learning algorithms, and product life cycles. It includes questions about breaking even on a new product line, calculating process velocity and efficiency, analyzing the Perceptron algorithm and stochastic gradient descent, weak learners for concept classes, and AdaBoost iterations. The key details are calculating metrics like break even point, profit/loss, process velocity and efficiency based on given costs, sales, time estimates. It also involves explaining relationships between algorithms, finding weak learners to approximate complex concepts, and ensuring classifiers have 50% accuracy for AdaBoost iterations.
The document discusses concepts related to supervised machine learning and decision tree algorithms. It defines key terms like supervised vs unsupervised learning, concept learning, inductive bias, and information gain. It also describes the basic process for learning decision trees, including selecting the best attribute at each node using information gain to create a small tree that correctly classifies examples, and evaluating performance on test data. Extensions like handling real-valued, missing and noisy data, generating rules from trees, and pruning trees to avoid overfitting are also covered.
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The document discusses greedy algorithms and their use for optimization problems. It provides examples of how greedy algorithms can find optimal solutions for counting coins to make a certain amount of money and designing Huffman codes to compress data. Specifically, it explains that greedy algorithms make locally optimal choices at each step to hopefully find a global optimum. While this works for coin counting, it may not find the optimal solution for other problems like scheduling tasks.
The document provides summaries of several coding interview questions at different difficulty levels:
- Easy questions include Two Sum, Valid Parentheses, Merge Two Sorted Lists, etc.
- Medium questions include 3Sum, Clone Graph, Course Schedule, Coin Change, etc.
- Hard/expert level questions are also mentioned but not summarized.
The document aims to help candidates prepare for coding interviews at top tech companies with examples of commonly asked problems.
Mit203 analysis and design of algorithmssmumbahelp
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Mca 4040 analysis and design of algorithmsmumbahelp
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The document provides a summary of 30 most commonly asked coding interview questions organized by difficulty level. It includes questions related to data structures and algorithms like binary tree, linked list, array, string, sorting, and searching. It also provides information about courses offered by Tutort on data science, machine learning, full stack development, and benefits of joining their programs like 1:1 mentorship and job assistance.
Mathematics is the study of patterns and quantities. It is used in many fields and is everywhere in daily life. Some key concepts in mathematics include geometric patterns found in nature, Fibonacci numbers, problem solving techniques, and graph theory. Mathematics uses formal language and symbols to express ideas and relationships precisely. Common tools in mathematics include logic, sets, functions, and statistical analysis of data. Mathematicians develop and apply logical reasoning to understand mathematical concepts and solve problems.
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FALL 2014, ASSIGNMENT
PRIGRAM BCA(REVISED 2007)
SEMESTER 5TH
SUBJECT CODE & NAME BC0052 – THEORY OF COMPUTER SCIENCE
CREDIT 4
BK ID B0972
MAX. MARKS 60
Note:Answer all questions.Kindlynote that answersfor 10 marks questionsshouldbe approximately
of 400 words. Each questionis followedbyevaluationscheme.
1. What are the five ways used to describe a set? Describe the set containing all the nonnegative
integers less than or equal to 4.
Answer:A set isa collectionof objects,thingsorsymbolswhichareclearlydefined.
The individual objectsinasetare calledthe membersorelementsof the set.
A setmustbe properlydefinedsothatwe can findoutwhetheranobjectisa memberof the set.
There are twowaysof describing,orspecifyingthe membersof,aset.One wayis by intensional
definition,usingarule or semanticdescription:
A isthe set whose membersare the firstfourpositive integers.
B is the setof colorsof the Frenchflag.
2. What is Recursion Theorem? How do you define n! recursively and compute 5! recursively.
Answer: The Recursion Theorem simply expresses the fact that definitions by recursion are
mathematically valid, in other words, that we are indeed able correctly and successfully to define
2. functions by recursion. Mathematicians implicitly use this fact whenever they define a function by
recursion.
A more general version of the Recursion Theorem would allow the function f to use the argument n as
well as F(n). A still more general version of the Recursion Theorem, called course-of-values recursion,
allows f to use as an argument the entire restriction of the function F∣n to earlier values. (These more
complex versionsof the Recursiontheoremcanbe derivedsolelyfromthe single-value theoremyouhave
stated, by using a function f that takes a
3. State and prove Pigeonhole Principle.
Answer:Inmathematicsandcomputerscience,the pigeonholeprinciple statesthatif nitemsare put into
m pigeonholeswithn>m, thenat leastone pigeonholemust contain more than one item. This theorem
is exemplified in real-life by truisms like "there must be at least two left gloves or two right gloves in a
groupof three gloves".It is an example of a counting argument, and despite seeming intuitive it can be
used to demonstrate possibly unexpected results.
The first formalization of the idea is believed to have been made by Johann Dirichlet in 1834 under the
name Schubfachprinzip("drawerprinciple"or"shelf principle").Forthisreasonitisalso commonly called
Dirichlet's box principle or Dirichlet's drawer principle. In Russian and some other languages, it is
contracted to simply "Dirichlet
4. Prove that in Graph the number of vertices of odd degrees is always even.
Answer: 1. Each edge (including loops) contributes 2 to the vertex order total.
2. This means the vertex order total must be even because it increments by 2 for every edge.
3. For the vertex order total to be even, the number of vertices with odd orders must be even because:
(a) odd number + odd number = even number
(b) odd number + even number = odd number
(c) even number + even number = even number
5. What is Deterministic finite machine? What are the various components of DFA? Illustrate it using
the pictorial representation of DFA.
Answer:Inautomatatheory,a branch of theoretical computer science, a deterministic finite automaton
(DFA)—alsoknown as deterministic finite state machine—is a finite state machine that accepts/rejects
finite strings of symbols and only produces a unique computation (or run) of the automaton for each
input string. 'Deterministic' refers to the uniqueness of the computation.
3. In automatatheory(a branchof computerscience),DFA minimization is the task of transforming a given
deterministicfinite automaton(DFA) intoanequivalentDFA thathas a minimumnumber of states. Here,
two DFAs are called equivalent if they
Q.6 Prove that “A tree G with n vertices has (n–1) edges”
Answer:- We prove this theorem by induction on the number vertices n.
Basic step: If n = 1, then G contains only one vertex and no edge. So the number of edges in
G is n –1 = 1 – 1 = 0.
Inductionhypothesis:The statement is true for all trees with less than ‘n’ vertices. Induction step: Now
let us consider a tree with ‘n’ vertices. Let ‘ek ’ be any edge in T whose end vertices are vi and v j.
Since T is a tree, by there is no other path between vI and v j. So by removing ek from T , we get a
disconnected
graph. Furthermore, T - ek consists of exactly
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