final-review.docx - CSCI 3236 Theoretical Foundations Final...

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CSCI 3236 Theoretical Foundations – Final Exam Review, Spring 2018 a. Chapter 1: Mathematical Foundations a. Set theory b. functions (total, onto, one-to-one) c. cardinality • how to prove a set is countably infinite, or denumerable • how to prove a set is uncountable (contradiction proof, using cantor’s diagonalization) d. recursive definition (basis, recursive step) e. mathematical induction (basis, inductive assumption, inductive step) f. graphs and trees (e.g. frontier of a tree) b. Chapter 2: Languages a. String: concatenation, reverse, length, kleene-star, empty string λ, substring, prefix/suffix, b. Language: Recursive definition, union, concatenation, kleene-star, Kleene-plus c. Regular sets and expressions: • Recursive definition of regular languages • Regular expressions: for a given regular expression, describing the regular set; finding a regular expression that represents the described regular language. c. Chapter 3: Context-Free Grammars (CFG) a. Leftmost derivations, rightmost derivations, derivation trees b.
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  • Spring '14
  • Greca,Ardian
  • Formal language, Context-free grammar

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