Lua table.toString(tableName) and table.fromString(stringTable) functions?

I am using the following code in order to serialize tables:

function serializeTable(val, name, skipnewlines, depth)
    skipnewlines = skipnewlines or false
    depth = depth or 0

    local tmp = string.rep(" ", depth)

    if name then tmp = tmp .. name .. " = " end

    if type(val) == "table" then
        tmp = tmp .. "{" .. (not skipnewlines and "\n" or "")

        for k, v in pairs(val) do
            tmp =  tmp .. serializeTable(v, k, skipnewlines, depth + 1) .. "," .. (not skipnewlines and "\n" or "")
        end

        tmp = tmp .. string.rep(" ", depth) .. "}"
    elseif type(val) == "number" then
        tmp = tmp .. tostring(val)
    elseif type(val) == "string" then
        tmp = tmp .. string.format("%q", val)
    elseif type(val) == "boolean" then
        tmp = tmp .. (val and "true" or "false")
    else
        tmp = tmp .. "\"[inserializeable datatype:" .. type(val) .. "]\""
    end

    return tmp
end

the code created can then be executed using loadstring(): http://www.lua.org/manual/5.1/manual.html#pdf-loadstring if you have passed an argument to 'name' parameter (or append it afterwards):

s = serializeTable({a = "foo", b = {c = 123, d = "foo"}})
print(s)
a = loadstring(s)()

The code lhf posted is a much simpler code example than anything from the page you linked, so hopefully you can understand it better. Adapting it to output a string instead of printing the output looks like:

t = {
{11,12,13},
{21,22,23},
}

local s = {"return {"}
for i=1,#t do
  s[#s+1] = "{"
  for j=1,#t[i] do
    s[#s+1] = t[i][j]
    s[#s+1] = ","
  end
  s[#s+1] = "},"
end
s[#s+1] = "}"
s = table.concat(s)

print(s)

The general idea with serialization is to take all the bits of data from some data structure like a table, and then loop through that data structure while building up a string that has all of those bits of data along with formatting characters.

How about a JSON module? That way you have also a better exchangeable data. I usually prefer dkjson, which also supports utf-8, where cmjjson won't.