9. Let Li and L2 be arbitrary languages, subject to the specification in either (i) or (ii). Consider the following four questions: (Q2) Is L1-L2 empty? (Q4) Is L1ņL2 empty? For each of these four questions explain with reasons whether the general problem is (Q1) Does L1-L2 contain a given fixed word w? (Q3) Does LINL2 contain a given fixed word w? recursive, not recursive but r. e., or non-r. e., provided (i) Both Li and L2 are recursive. (ii) Li is r. e., but not recursive and L2 is recursive. Note that there are eight different questions to be answered.

9. Let Li and L2 be arbitrary languages, subject to the specification in either (i) or (ii). Consider the following four questions: (Q2) Is L1-L2 empty? (Q4) Is L1ņL2 empty? For each of these four questions explain with reasons whether the general problem is (Q1) Does L1-L2 contain a given fixed word w? (Q3) Does LINL2 contain a given fixed word w? recursive, not recursive but r. e., or non-r. e., provided (i) Both Li and L2 are recursive. (ii) Li is r. e., but not recursive and L2 is recursive. Note that there are eight different questions to be answered.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(ii) L₁ is r. e., but not recursive and L₂ is recursive.

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