CMPS 260 Spring 2020
Mid-term Test Preview

Expect problems of the following varieties on the test. You will not be expected to solve all of them.

• Given a "universe" A of elements, present a binary relation on A that satisfies certain properties (e.g., symmetry, reflexivity, transitivity, or the absence of one or more of these).
• Prove a "theorem" using mathematical induction.
• Given a language described "intensionally" (e.g., { x ∈ {a,b}^* : x satisfies properties ... }), present a CFG that generates that language.
• Given a CFG G, describe the language it generates, show that G is ambiguous, and present an equivalent unambiguous grammar.
• Present a DFA that accepts a language described intensionally.
• Present an NFA that accepts a language described intensionally.
• Convert a given NFA into an equivalent DFA using the subset construction algorithm.
• Given a DFA, identify the equivalence classes of "indistinguishable" states and use those to compute a minimal equivalent DFA.
• Given an FA (possibly nondeterministic), use your intuition to devise an equivalent regular expression.
• Present a regular expression that denotes a specified language.
• Given an operator on languages, determine whether or not the class of regular languages is closed with respect to that operator, and justify your conclusion.