$a^ib^jc^k | (i = j)$ then k is even?I can write it as$a^ib^ic^k$ where k is evenOR$a^ib^jc^k where (i != j)$Both are DCFL and union of DCFL may be DCFL, but I think because of OR operator it gives a sense of parallelism and hence NCFL.I haven't tried to make a DPDA for it, because in exam I might not be have much time to draw.I don't think it is DCFL.Theoretically, is this approach right ?
Is the given language DCFL?
context free;finite automata;nondeterminism
You can construct a DPDA for your language as follows. When reading $a$s, the machine pushes $A$s onto the stack. When reading $b$s, the machine pops them, noting to itself if there are more $b$s than $a$s. When it reads the first $c$, it can use the top-of-stack to tell if the number of $a$ was equal to the number of $b$s; if so, it transfers control to a DFA for $(cc)^*$, and otherwise it transfers control to a DFA for $c^*$.