The document discusses examples of undecidable problems in computing. Specifically, it notes that determining whether a context-free language is ambiguous, or whether two context-free languages are equal, are undecidable because there is no algorithm that can always halt and provide a yes or no answer in finite time. It also states that problems like determining if a context-free grammar generates all possible strings of an input alphabet, or determining if a context-free language is regular, are undecidable for the same reason. Finally, it provides definitions of undecidable and semi-decidable problems in relation to decidable problems.

1. Examples of undecidable
problems and Problems

2. Undecidable
problems
• Examples
• The ambiguity of context-free
languages: Given a context-free language, there
is no Turing machine which will always halt in
finite amount of time and give an answer
whether language is ambiguous or not.
• Equivalence of two context-free
languages: Given two context-free languages,
there is no Turing machine which will always
halt in finite amount of time and give an answer
whether two context free languages are equal or
not.
A problem is undecidable if there is no
Turing machine which will always halt
in finite amount of time to give an
answer as ‘yes’ or ‘no’.
An undecidable problem has no
algorithm to determine the answer for a
given input.

3. Undecidable problem

6. Halting Problem

9. • Everything or completeness of CFG: Given a CFG and
input alphabet, whether CFG will generate all possible strings
of the input alphabet (∑*) is undecidable.
• Regularity of the CFL, CSL, REC and REC: Given a CFL,
CSL, REC or REC, determining whether this language is
regular is undecidable.

10. The relationship between semi-decidable, undecidable
and decidable problem