The Rice theorem states that any non-trivial property of the languages recognized by Turing machines is undecidable. This includes properties like whether the language is regular, context-free, empty, or includes palindromes. The theorem also shows that any non-monotonic property of recursively enumerable languages is unrecognizable. The document discusses the Rice theorem and its implications, including that many Turing machine-related decision problems are undecidable.

1. RICE THEOREM

2. Rice theorem for some
undecidable languages
Any non-trivial property of the
language recognizable by a Turing
machine (recursively enumerable
language) is undecidable.

3. Rice theorem for some
unrecognizable language
Any non-monotonic property of the language
recognizable by a Turing machine
(recursively enumerable language) is
unrecognizable

4. Cont…

5. Cont….

6. Applications of Rice’s
Theorem
• From Rice’s theorem, we can
conclude that a whole host of TM-
related problems are undecidable,
including:
Is L(M)L(M) a regular language?
Is L(M)L(M) a CFL?
Is L(M)L(M) empty?
Does L(M)L(M) include any
palindromes?

7. Rice Theorem ( Part 1 )
Unit 5 / SRMIST / KTR 7

8. Rice Theorem – The reduction
Unit 5 / SRMIST / KTR 8

9. Rice Theorem ( Part 2 )
Unit 5 / SRMIST / KTR 9

10. Rice Theorem (Part 2) – The reduction
Unit 5 / SRMIST / KTR 10