Given L1 is Deterministic context free languages & L2 is Regular language. L1 U L2 results DCFL or regular?
please give some examples with the context
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hint: a simple example `a^nb^c^n` U `x^ny^x^n`, now what is it?? – Grijesh Chauhan Jan 12 '15 at 04:42
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@GrijeshChauhan Neither of those languages are regular, though, unless I'm mistaken. – templatetypedef Jan 16 '15 at 00:36
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@templatetypedef yes, you are correct, my comment is not useful :( to question. – Grijesh Chauhan Jan 16 '15 at 04:29
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The resulting language must be a DCFL. Intuitively, you could check if a string is in the union of a DCFL and a regular language by getting a DPDA for the DCFL, a DFA for the regular language, then running the two in parallel and seeing if either accept. You can simulate that process by using a variation of the product construction that shows that the regular languages are closed under union: build a DPDA with one state for each combination of a DFA state and a DPDA state, then structure the transitions so that they simulate following a transition from the DPDA and the DFA in parallel. You only need one stack for this, so the construction should work just fine.
Hope this helps!
templatetypedef
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l2=sigma* and L1=a^nb^n l1 is dcfl and l2 is regular.but L1 union l2=l1 is dcfl but not regular
Anurag Semwal
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Correct me if I'm wrong, but isn't the union of those two languages Sigma*, which is indeed regular? – templatetypedef Apr 29 '19 at 19:34