Skip to main content Link Menu Expand (external link) Document Search Copy Copied

Lecture Notes : Midterm Study

Outline

This class we’ll discuss:

  • Prep for the Midterm

A Slideshow:

GUIDED NOTES (Optional)

Prep For Midterm

Topics

  1. Regular Languages
    • Regular Expressions: from set description to RE
    • Regular Expressions: from RE to set description
    • Finite Automata: Interpreting an FA (parts, equivalent RE, and accepted Language)
    • Finite Automata: Building a FA given a language set description
  2. Regular vs Non-Regular Languages
    • Short Proofs: using definitions
    • Short Proofs: using closure
    • Short Proofs: finding a simple RE or FA
  3. Non-Regular Languages (NRLs)
    • Understand the difference/relation between regular and non-regular languages
    • Prove a given Language is NOT regular (Pumping Lemma is useful here)
  4. Context-Free Languages (CFLs)
    • Understand the definition of CFGs and Push-Down Automata
    • Understand the difference/relation between regular and CFG-languages
    • Understand the relation between Push-Down Automata and CFG-languages
    • Prove a given Language IS context free
    • Understand how one WOULD Prove a given Language is NOT context free
    • Short Proofs: using definitions
    • Short Proofs: using closure
    • Short Proofs: finding a simple CFG or PDA
  5. Turing-Decidable Languages (TDLs)
    • Understand the definition of Turing Machines
    • Understand the difference/relation between regular, CFG-languages, and TDLs
    • Prove a given Language IS Decidable
    • Short Proofs: using definitions
    • Short Proofs: using closure
    • Short Proofs: finding a simple TM

Exam Info

  • Where/How to take the exam:
    Please read the full instructions in self-scheduled-exams

  • Cheat-Sheet

    • A single approved cheatsheet will be distributed. You can ONLY bring that single page AND you must submit it with your exam at the end!

    Note that the exam is designed so that you must use your reasoning rather than memory or copied notes.

  • Exam Structure and Requirements

    • The exam will have 7 questions covering the topics mentioned above
    • it is graded on 50 points but there are 60 points available to you (you keep any extra points you earn towards HW grades)
    • It is designed to be completed in 1 hour and 30 minutes but you’ll have up to 3 hours to complete it
    • You may scribble notes and practice answers anywhere in the exam but MUST indicate your final reply clearly, otherwise the whole scribbling will be taken as your reply
    • You MUST use clear sentences and logic. Rambling answers do not grant partial credit so be concise and precise (think before you answer)

General tips

  • See the examples solved in class and those solved in the Problem Sets. Any questions that come in the exam will be VERY similar to those.

  • You will be asked to do proofs, but they will be rather straightforward.
    Examples:

    • show an example of an RE that disprooves a statement that there can be none
    • use a Pumping Lemma proof on a question that is VERY similar to one seein in class (HALF)
    • show a CFG to generate a certain Language

Tips on Proofs

If you want to prove a statement like “This $ something $ is NOT in the category $ category $” (Like this Language L is NOT a Regular Language), you can use the following approaches:

  • by contradiction (assume it IS and find a contradiction. . . for example, using the Pumping Lemma)
  • by construction (show all elements follow some structure that precludes them from falling inside the $ category $)

If you want to disprove a statement like

“There is NO $something$ that has the property $\text{some property}$”

Example: there is no Regular Expression that can describe language

\[L = {w \vert w \text{ has alternating 1s and 0s} }\]
  • you only need to find an example.

If you want to prove that a set of elements follows some property (like saying “these two languages are equivalent” or “This language L is Context-Free”), you might want to use one of the following approaches:

  • using closure properties
  • by construction (show how you can generate the rules that produce the set)
  • by induction