Lecture Notes 20: Midterm Review
Outline
This class we'll discuss:
- Topics covered in the midterm
- Exam Info and General Recommendations
- Overview of topics and problems
- Q&A
Topics
- Logic and Reasoning
- Predicate logic and simple logic proofs
- 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
- Regular vs Non-Regular Languages
- Short Proofs: using definitions
- Short Proofs: using closure
- Short Proofs: finding a simple RE or FA
- Non-Regular Languages (NRLs)
- Understand the difference/relation between regular and non-regular languages
- Prove a given Language is NOT regular
- 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
- 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
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 9 questions covering the topics mentioned above
- It is designed to be completed in 1 hour and 15 minutes but you'll have up to 4 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.
- No Question will be as hard as the Problem-5 questions in the Problem sets.
- 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 <some property>” (Like there is no Regular Expression that can describe language L = {w | w 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
Full Review
Q & A
Next class: Review of Practice Midterm Answers
Homework
Complete the practice exam! (Pablo should publish it in Moodle!)
Study!
[Optional]
TODO
