CSCI 301 L36 Notes

Lecture 36 - Notes

Goals

• Same as L35!

Announcements

• Final Exam Study Guide is out - find it here, or linked from the final exam row on the Schedule table.
• End-of-quarter special case for the homework resubmission policy:
  • Final deadline for resubmissions is 11:59pm Monday, December 9th.
• Friday’s class is optional. Ask me anything!
  • I’ll give priority to 301-related questions, but really, ask me anything!
• A9 and Week 9 survey due tonight
• I am recruiting students for my research group. Please fill out this form by the end of Friday and come talk to me with questions if you’re interested.

Notes

Mostly the same as L35!

A few things to address today:

• Why is the Church-Turing Thesis a thesis, not a theorem?
• (Re $\cup$ over)view of the Chomsky Hierarchy
• Are there any practical / applicable problems that are undecidable? Sure:
  • Equivalence of Turing machines (and therefore programs) - relevant for compilers, interpreters, etc.
  • Equivalence of context-free grammars - relevant for parsers, etc.
  • Halting problem - relevant for autograders (well, sort of)

Here’s a prettier picture of the Chomsky Hierarchy (credit to Logan Sizemore):

• A final distinction: undecidable languages can still be enumerable

A language is enumerable (sometimes called recursively enumerable) if there exists a Turing machine that can generate all strings in the language. We may be able to do this even if we can’t solve the decision problem (in particular, reject strings not in the language) in finite time.

Example: The set of halting turing machines