Show using a cross-product construction that the class of regular languages is closed under intersection. You do not need an inductive proof, but you should convincingly explain why your construction works.

Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF  {wct | t ∈ {a,b}* ∧ w is a substring of t}

2. Consider the language DOUBLE-SAT, all of the boolean expressions with at least two satisfying assignments. (a) What would a possible DOULBE-SAT solution look like for an expression? (b) Is DOUBLE-SAT in NP?

Problem 1. Consider the regular expression (0|1)*1 over the alphabet {0, 1} What language does the regular expression describe? Use the Thompson's construction method to derive a non-deterministic finite automaton (NFA) that recognizes L. It is enough to draw the final NFA Use the powerset construction method to derive an equivalent deterministic finite automaton (DFA). You must show the computation of e-closures and draw the DFA Use the partitioning method to derive an equivalent, minimal DFA. You must show the partitioning steps and draw the minimal DFA