one.lua

-- match regex /a*b/
print('/a*b/')

-- Lua wrapper to extract a character from a string
-- at the indexth position (starting from 0)
-- This is just a helper since Lua is 1-indexed which
-- is insane. You can just copy this out.
function charat (str, index)
	return string.sub(str, index + 1, index + 1)
end

-- our generated function that corresponds to our input regex. return true if a string matches
function doesmatch (str)
	local index = 0

	-- a*
	while index < #str do
		if charat(str, index) == 'a' then
			index = index + 1
		else
			break
		end
	end

	-- b
	if charat(str, index) ~= 'b' then
		return false
	else
		index = index + 1
	end

	-- make sure we've matched the whole string by comparing index with length of string
	if index < #str then
		return false
	end

	return true
end

print(doesmatch('aaaaaab'), 'should equal', true)
print(doesmatch('ab'), 'should equal', true)
print(doesmatch('b'), 'should equal', true)
print(doesmatch('bb'), 'should equal', false)

two.lua

-- match regex /(b|c*d)/
print('/(b|c*d)e/')

-- Lua wrapper to extract a character from a string
-- at the indexth position (starting from 0)
-- This is just a helper since Lua is 1-indexed which
-- is insane. You can just copy this out.
function charat (str, index)
	return string.sub(str, index + 1, index + 1)
end

-- our generated function that corresponds to our input regex. return true if a string matches
function doesmatch (str)
	local index = 0

	-- (
	local subexpr = false
	local subexprindex = index

	-- b
	if not subexpr then
		subexpr = true -- assume match until proven false

		if charat(str, subexprindex) == 'b' then
			subexprindex = subexprindex + 1
		else
			subexpr = false
		end
	end

	-- c*d
	if not subexpr then
		subexpr = true -- assume match until proven false

		-- c*
		while subexprindex < #str do
			if charat(str, subexprindex) == 'c' then
				subexprindex = subexprindex + 1
			else
				break
			end
		end

		-- d
		if charat(str, subexprindex) ~= 'd' then
			subexpr = false
			-- this would be "return false" on top-level
		else
			subexprindex = subexprindex + 1
		end
	end

	-- )
	if not subexpr then
		return false
	else
		-- update "top-level" index with our index in the subexpression
		index = subexprindex
	end

	-- e
	if charat(str, index) ~= 'e' then
		return false
	else
		index = index + 1
	end

	-- make sure we've matched the whole string by comparing index with length of string
	if index < #str then
		return false
	end

	return true
end

print(doesmatch('be'), 'should equal', true)
print(doesmatch('de'), 'should equal', true)
print(doesmatch('cccd'), 'should equal', false)
print(doesmatch('bbbde'), 'should equal', false)