Question
Download Solution PDFConsider the following statements:
S1 : These exists no algorithm for deciding if any two Turing machines M1 and M2 accept the same language.
S2: Let M1 and M2 be arbitrary Turing machines. The problem to determine L(M1) ⊆ L(M2) is undecidable.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFS1 : These exists no algorithm for deciding if any two Turing machines M1 and M2 accept the same language.
Equivalence problem for recursive enumerable language is undecidable which means there does not exist any algorithm to decide if two Turing machine accept the same language or not. If it were decidable, there will be algorithm to decide the acceptance of a string by a Turing machine and problem of whether the language accepted by Turing machine is empty.
S2: Let M1 and M2 be arbitrary Turing machines. The problem to determine L(M1) ⊆ L(M2) is undecidable.
It is correct. Subset problem for Turing machine is undecidable. There can exists a problem which is accepted by Turing machine M2 but not by Turing machine M1. The problem to determine L(M1) ⊆ L(M2) is undecidable.
Last updated on Jul 7, 2025
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