CS 81 Notes

  • Introduction to Logic
  • Propositional Logic

  • Well-Formed Formulas
  • Models of Classical Logic
  • Entailment
  • Abbreviating WFFs
  • English to WFFs
  • Proof Systems
  • Resolution
  • Propositional Natural Deduction
  • Metatheory
  • Predicate Logic

  • Syntax and Models
  • English to Predicate Formulas
  • Predicate Natural Deduction
  • Doing Proofs

  • Proofs for Humans
  • Bounded Quantifiers
  • Proofs with Implication and Equivalence
  • Proofs with Quantifiers
  • Proofs in Asymptotic Analysis
  • Mathematical Induction
  • Countable Sets
  • Uncountable Sets
  • Prolog

  • Prolog
  • Prolog to English
  • Unification
  • Depth-First Search
  • DFS Consequences
  • List Predicates
  • Generate-and-Test
  • (In)Equality in Prolog
  • Manipulating Lists
  • Negation
  • Computability

  • Introduction
  • String Theory
  • State Machines
  • Regular Languages
  • Kleene's Theorem
  • Closure Properties of Regular Languages
  • Extended Regular Expressions
  • Nonregular Languages and Distinguishable Strings
  • Nonregular Languages and the Pumping Lemma
  • Context-Free Languages (CFLs)
  • Context-Free Grammars (CFGs)
  • Parse Trees
  • Non-Context-Free Languages
  • The CYK Algorithm
  • Regular Grammars
  • Unrestricted Grammars
  • Turing Machines
  • Decidability
  • Reductions
  • Mapping Reductions
  • Rice's Theorem
  • Computation Histories
  • Post Correspondence Problem
  • And Back to Logic…

  • Preconditions, Postconditions, and Invariants