Course Content and Goals
نویسنده
چکیده
The basic question: what can and cannot be computed? Hilbert’s 10th problem, 1900. (CANNOT) Error testing (a.k.a. the Halting Problem). (CANNOT) Godel’s Theorem. (CANNOT) Tools: Well specified models. Mathematical arguments (convincing and unassailable) — analogous to geometry in high school. Important goal of the course: Have you better able to recognize when an argument is mathematically convincing and to write such arguments. Course timeline: Today: introduction, notation review, proof by contradiction, halting problem. Thursday: Review of induction and recursion. Weeks 2-4: Finite automata, regular languages, the (first) Pumping Lemma. Weeks 5-7: Pushdown Automata (pda), Context Free Languages (CFLs), the (second) Pumping Lemma. Week 8 (one day): Midterm. Weeks 8-11: Computability and non-computability. Weeks 11-14: NP Completeness. Final lecture: Review.
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