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Here's the list of topics covered in the exam:

Regular expressions
- Definition
- Extensions in practice
- The languages they define
Formal languages and their relationship to decision problems
Regular languages and their relationship to regular expressions
Finite automata
- Definition, deterministic, non-deterministic
- Language defined by a finite automaton
Equivalence of NFA, DFA, regular expressions/languages
- Including the proof of this equivalence
DFA minimization
Pumping Lemma
- Proof and application
Context-free grammars, definition and the languages they define
Parse trees and derivations, leftmost and rightmost derivation
Push-down automata, modes of acceptance, and equivalence of modes of acceptance
Relationship between PDA and context-free grammars/languages
Recursive-descent parsing and shift-reduce parsing (the ideas; we did not discuss the details of how to choose when to shift or reduce for example)
Deterministic PDAs
Turing machines and RAMs (definition, how do they work), variations of Turing machines and their (in)significance
Recognizable languages, decidable languages, computable functions
Church-Turing thesis
Existence of undecidable, unrecognizable languages, existence of non-computable functions
- How do we use reductions to prove this
Definitions of P and NP

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