'Primitive recursive' presentation slideshows

::ICS 804:: Theory of Computation - Ibrahim Otieno - iotieno@uonbi.ac.ke +254-0722-429297

::ICS 804:: Theory of Computation - Ibrahim Otieno - iotieno@uonbi.ac.ke +254-0722-429297 SCI/ICT Building Rm. G15. Course Outline. Mathematical Preliminaries Turing Machines Recursion Theory Markov Algorithms Register Machines Regular Languages and finite-state automata

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Other Models of Computation

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Thresholds for Ackermannian Ramsey Numbers

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Lecture 18 Various TMs

Lecture 18 Various TMs. Allow the head not move. Theorem . If the head is allowed to stay at the cell in each move, then every function computed by the DTM is still Turing-computable. Proof. Consider DTM M=(Q, ? , ? , ? ,s) where ? : Q x ? ? Q x ? x {R, L, H} and H means

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????? II ?????

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Numerical Representation of Strings

Numerical Representation of Strings. First, we define two primitive recursive functions. where R(x, y) and ?x / y? are defined as in Section 3.7.

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Numerical Representation of Strings

Numerical Representation of Strings. 2.) g(u, v) = CONCAT n (u, v) This function is primitive recursive because it is defined by the following equation: CONCAT n (u, v) = u?n |v| + v Example: Alphabet A = {1, 2, 3, 4, 5, 6, 7, 8, 9, X}: CONCAT 10 (13, 478) = 13?1000 + 478 = 13478.

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Lecture 1-4 Recursive Functions

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Some Primitive Recursive Functions

Some Primitive Recursive Functions. Example 3: h(x) = x! Here are the recursion equations: h(0) = 1 h(t + 1) = h(t) ? s(t) This can be rewritten as: h(0) = s(n(t)) h(t + 1) = g(t, h(t)) where g(x 1 , x 2 ) = s(x 1 ) ? x 2 , which can be written as:

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Recursively Enumerable Sets

Recursively Enumerable Sets. Definition: We write: W n = {x ? N | ?(x, n) ?}. Theorem 4.6 (Enumeration Theorem): A set B is r.e. if and only if there is an n for which B = W n . This is an immediate consequence of the definition of ?(x, n).

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