its a DCFL. how?
lets break it..
let the required states be q0,q1=non final states andq2,q4=final states(given that states with value 1 = non final , value=0 final state).
we can goto final state without reading anything directly from qo to q4.
($,ε,ε) = means if stack empty we can goto final state.
at state q0 :
(a,ε,a) means a can be pushed into the state qo without reading anything from the input.
at state q4 : its a null statement as once stack is empty we will goto state q4 than how will we have a again..
(ε,a,ε) means pop a without reading anything from state q4.
conclusion for case 1 : it accepts ε.
(b,a,ε) : for every b pop each a and soon as we have loop for state q1 .
($,ε,ε) means if stack empty goto state q3(final state).
conclusion : it can accept strings of anbn : where n>=1
so we conclude that the given pda accepts ε , anbn : where n>=0 (including ε also). = (DCFL)
so the required languauge is a DCFL overall.
the question has asked for complement of L. which is also a dcfl.