which tasks can simple perceptron perform? - artificial-intelligence

Question

I'm trying to teach simple single neuron perceptron to recognize repetitive sequences of 1.
here is data I use to teach it:
learning_signals = [
[[1, 1, 0, 0], 1],
[[1, 1, 0, 1], 1],
[[1, 1, 1, 0], 1],
[[0, 1, 1, 0], 1],
[[0, 1, 1, 1], 1],
[[0, 0, 1, 1], 1],
[[1, 0, 1, 1], 1],
[[0, 0, 0, 0], 0],
[[1, 0, 0, 0], 0],
[[0, 1, 0, 0], 0],
[[0, 0, 1, 0], 0],
[[0, 0, 0, 1], 0],
[[1, 0, 1, 0], 0],
[[1, 0, 0, 1], 0],
# [[0, 1, 0, 1], 0],
This is the array of learning templates each of them are array of data and correct result for that data.
As you see. last row commented - if I do uncomment it - perceptron will fail to learn. without it perceptron does not work right in case with "0101". So the question is:
Is this task can be solved with single neuron perceptron or should I use few layered perceptron?
How can I determine which tasks can be solved with such a simple perceptron? Are there any rule that I can apply to my task and say that it could be done with simple perceptron?
here is the code of perceprton written in coffeescript:
class window.Perceptron
weights: []
calc: (signal) ->
#neuron.calc signal
adjust: ->
foo: 0.1
calc: (signal) ->
sum = 0
for s, i in signal
sum += s*#weights[i]
if sum>0.5 then return 1 else return 0
sum
learn: (templates) ->
#weights = []
for i in [1..templates[0][0].length]
#weights.push Math.random()
li = 0
max_li = 50000
console.log #weights
while true
gerror = 0
li++
for template, i in templates
res = #calc template[0]
# console.log "result: #{res}"
error = template[1] - res
gerror += Math.abs error
for weight, i in #weights
#weights[i] += #foo*error*template[0][i]
if ((gerror == 0) || li > max_li) then break
if gerror == 0
console.log "Learned in #{li} iterations"
else
console.log "Learning failed after #{max_li} iterations"
console.log #weights