lect17-tm3

# lect17-tm3 - 1 Decidability Turing Machines Coded as Binary...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Decidability Turing Machines Coded as Binary Strings Diagonalizing over Turing Machines Problems as Languages Undecidable Problems 2 Binary-Strings from TM’s ◆ We shall restrict ourselves to TM’s with input alphabet {0, 1}. ◆ Assign positive integers to the three classes of elements involved in moves: 1. States: q 1 (start state), q 2 (final state), q 3 , … 2. Symbols X 1 (0), X 2 (1), X 3 (blank), X 4 , … 3. Directions D 1 (L) and D 2 (R). 3 Binary Strings from TM’s – (2) ◆ Suppose δ (q i , X j ) = (q k , X l , D m ). ◆ Represent this rule by string i 10 j 10 k 10 l 10 m . ◆ Key point : since integers i, j, … are all > 0, there cannot be two consecutive 1’s in these strings. 4 Binary Strings from TM’s – (2) ◆ Represent a TM by concatenating the codes for each of its moves, separated by 11 as punctuation. ◗ That is: Code 1 11Code 2 11Code 3 11 … 5 Enumerating TM’s and Binary Strings ◆ Recall we can convert binary strings to integers by prepending a 1 and treating the resulting string as a base-2 integer. ◆ Thus, it makes sense to talk about “the i-th binary string” and about “the i-th Turing machine.” ◆ Note : if i makes no sense as a TM, assume the i-th TM accepts nothing. 6 Table of Acceptance 1 2 3 4 5 6 . . . TM i 1 2 3 4 5 6 . . . String j x x = 0 means the i-th TM does not accept the j-th string; 1 means it does. 7 Diagonalization Again ◆ Whenever we have a table like the one on the previous slide, we can diagonalize it....
View Full Document

{[ snackBarMessage ]}

### Page1 / 27

lect17-tm3 - 1 Decidability Turing Machines Coded as Binary...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online