Curriculum
- 4 Sections
- 55 Lessons
- 10 Weeks
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- MODULE 112
- 1.1MOTIVATION FOR STUDYING COMPUTABILITY
- 1.2NEED FOR MATHEMATICAL MODELING
- 1.3AUTOMATA: INTRODUCING AUTOMATA THROUGH SIMPLE MODELS
- 1.4THREE BASIC CONCEPTS: ALPHABET, STRINGS, AND LANGUAGES
- 1.5FORMAL DEFINITION OF A FINITE AUTOMATA
- 1.6DETERMINISTIC FINITE AUTOMATA(DFA)
- 1.7NON DETERMINISTIC FINITE AUTOMATA
- 1.8NFA WITH EPSILON TRANSITIONS
- 1.9EQUIVALENCE OF NFAs AND DFAs
- 1.10THE SUBSET CONSTRUCTION
- 1.11DFA STATE MINIMIZATION
- 1.12APPLICATIONS OF FINITE AUTOMATA: TEXT SEARCH, KEYWORD RECOGNITION
- MODULE 217
- 2.1REGULAR EXPRESSIONS: THE FORMAL DEFINITION OF A REGULAR EXPRESSION
- 2.2BUILDING REGULAR EXPRESSIONS
- 2.3CONVERTING FA TO REGULAR EXPRESSIONS
- 2.4CONVERTING REGULAR EXPRESSIONS TO FA
- 2.5PATTERN MATCHING AND REGULAR EXPRESSION
- 2.6REGULAR GRAMMAR: CONVERTING RG TO FA
- 2.7CONVERTING FA TO RG
- 2.8CLOSURE AND DECISION PROPERTIES OF REGULAR LANGUAGES
- 2.9THE PUMPING LEMMA FOR REGULAR LANGUAGES
- 2.10PUMPING LEMMA AS A TOOL TO PROVE NON REGULARITY OF LANGUAGES
- 2.11FORMAL DEFINITION OF A CONTEXT FREE GRAMMAR
- 2.12DESIGNING CONTEXT FREE GRAMMARS
- 2.13LEFTMOST AND RIGHTMOST DERIVATIONS USING A GRAMMAR
- 2.14PARSE TREES
- 2.15AMBIGUOUS GRAMMARS
- 2.16RESOLVING AMBIGUITY
- 2.17INHERENT AMBIGUITY
- MODULE 312
- 3.1FORMAL DEFINITION OF A PUSHDOWN AUTOMATA
- 3.2DPDA AND NPDA
- 3.3EXAMPLES OF PUSHDOWN AUTOMATA
- 3.4CONVERTING PDA TO CFG
- 3.5CONVERTING CFG TO PDA
- 3.6ELIMINATION OF USELESS SYMBOLS AND PRODUCTIONS
- 3.7ELIMINATING EPSILON PRODUCTIONS
- 3.8ELIMINATING UNIT PRODUCTIONS
- 3.9CHOMSKY NORMAL FORM
- 3.10GREIBACH NORMAL FORM
- 3.11THE PUMPING LEMMA FOR CONTEXT FREE LANGUAGES
- 3.12CLOSURE AND DECISION PROPERTIES OF CONTEXT FREE LANGUAGES
- MODULE 414
- 4.1THE FORMAL DEFINITION OF A TURING MACHINE
- 4.2EXAMPLES OF TURING MACHINES
- 4.3TURING MACHINE AS LANGUAGE ACCEPTORS
- 4.4TURING MACHINES AS COMPUTERS OF FUNCTIONS
- 4.5VARIANTS OF TURING MACHINES
- 4.6RECURSIVE AND RECURSIVELY ENUMERABLE LANGUAGES
- 4.7CHOMSKIAN HIERARCHY
- 4.8LINEAR BOUNDED AUTOMATON AS A RESTRICTED TM
- 4.9CHURCH TURING THESIS
- 4.10ENCODING OF TMs
- 4.11UNIVERSAL MACHINE AND DIAGONALIZATION
- 4.12DECIDABLE AND UNDECIDABLE PROBLEMS
- 4.13HALTING PROBLEMS
- 4.14POST CORRESPONDENCE PROBLEM
