**its a DCFL.** how?

lets break it..

let the required states be *q0,q1=non final states* and**q2****,q4=final ****states**(*given that states with value 1 = non final , value=0 final state*).

**case 1**:

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**.**

**case 2:**

(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 a**^{n}b^{n } : where n>=1

so we conclude that the given pda accepts ε , a^{n}b^{n } : 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.**