Create PDA (deterministic or non-deterministic) for the following languages. For each one, begin with a brief, high-level, English description of your overall plan, centered on how the stack will be used. On each language, give three or more good strings and three or more bad strings. For each test string (good or bad), state its category (good string examples: minimum string with two as, contains one each of a, b, and c ; bad string examples: too many as, length is not even); each category should be different. Draw the PDA.

a, L1 = { w | w = x#y, x, y ( 0 U 1 )⁺, |x| = |y|, |w| > 1, = { 0, 1, # } }

b, L2 = { w | w = aⁿb^mx^myⁿ, n, m > 0, = { a, b, x, y } }

c, L3 = { w | w ( x U y )* and w has exactly 2 more xs than ys,

xs and ys may be in any order, = { x, y } }

d, L4 = { w | w x⁺y⁺z⁺, number of xs != number of zs, = { x, y, z } }