CMPS 260 Spring 2022
Mid-term Test Preview

Be prepared to solve problems of the following varieties on the test. You will not be expected to solve every problem.

• Given a binary relation on a set A (i.e., a set R ⊆ A×A), identify which properties among reflexivity, symmetry, transitiivity, etc., that it possesses.
• Given a set A, 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.
• Present a DFA that accepts a language described intensionally (e.g., { x ∈ {a,b}^* | x satisfies properties ... }).
• 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 obtain an equivalent minimized DFA.
• Given an FA (possibly nondeterministic), devise an equivalent regular expression.
• Regarding the language described by a given regular expression, distinguish between members and non-members (e.g., by identifying a shortest string that is a member (or perhaps a non-member) or by describing those characteristics of a string that would make it a member).
• Present a regular expression that denotes a language described intensionally.
• 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.