Recursively Enumerable and Recursive Languages

Aug 11, 2012

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Recursively Enumerable and Recursive Languages

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1. 1 Recursively Enumerable and Recursive Languages

2. 2

Recursive and Iterative Algorithms

Recursive and Iterative Algorithms. What does the following algorithm do?. Algorithm what(n) (1) x:=1; y:=1; z:=0; (2) for int I:=1 to n-2 do (3) z := x +y; (4) y := x; (5) x := z; end for; (6) return z; End algorithm. Now this Algorithm?. Algorithm now-what (n)

606 views • 8 slides

Recursively Defined Sequences

Recursively Defined Sequences. Lecture 40 Section 8.1 Wed, Apr 11, 2007. Recursive Sequences. A recurrence relation for a sequence { a n } is an equation that defines each term of the sequence as a function of previous terms, from some point on.

1.02k views • 63 slides

Recursively Enumerable Languages

Recursively Enumerable Languages. A language is called Recursively Enumerable if there is a Turing Machine that accepts on any input within the language.

2.12k views • 8 slides

Recursive Procedures and Scopes

Recursive Procedures and Scopes. EOPL3 Sections 3.4 - 3.7. The LETREC Language. All of PROC, plus … Concrete: Expression :: = letrec Identiﬁer (Identiﬁer) = Expression in Expression AST: letrec-exp (proc-name bound-var proc-body letrec-body). value of a letrec expression.

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Recursive algorithms and more…

Recursive algorithms and more…. Dr. Jeyakesavan Veerasamy jeyv@utdallas.edu Dec 20 2012. We covered…. Recursion examples factorial fibonacci knapsack Contest problem: finding longest perfectly balanced (…) strings http://www.usaco.org/index.php?page=viewproblem2&cpid=189.

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Recursively Enumerable Sets

Recursively Enumerable Sets. As long as the G ö del numbering functions [x 1 , …, x n ] and (x) i are available, we only need to consider subsets of N instead of subsets of N m . Then we have: Theorem 4.2: Let C be a PRC class, and let B be a subset of N m , m  1.

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Recursive Definitions

Recursive Definitions. Recurrence Relations. Recursive Definitions. A recursive definition (or inductive definition) is used to define an object in terms of itself. Recursive definitions have two parts: a base case (basis) and an inductive step. . Recursive vs circular defns.

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Recursive Definitions: functions, structures, languages

Recursive Definitions: functions, structures, languages. Sections 5.3 & 5.4 Tuesday, 10 June. Recursively Defined Functions. A recursive definition (also called an inductive definition ) for a function from f : N  S: Specifies the initial value of the function (value at 0).

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Recursively Defined Sequences

Recursively Defined Sequences. Section 1.1. What is a Sequence?. Sequence. Example A. A square table seats 4 people. Two square tables pushed together seat 6 people. Three tables pushed together seat 8 people. How many people can sit at 10 tables pushed together?

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Recursive Definitions: functions, structures, languages

Recursive Definitions: functions, structures, languages. Sections 5.3 & 5.4 Tuesday, June 10. 1. Recursively Defined Sets. A set S can be defined recursively as follows: Specify one or more basis elements .

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Recursive Networks

Recursive Networks. Joe Touch Postel Center Director USC/ISI Research Assoc. Prof. USC CS and EE/Systems Depts. Active Research Areas. Virtual & recursive nets X-Bone, DynaBone, TetherNet*, RNA Optical IP networking OCDMA – MAC protocols, NIC design*

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Recursive

Recursive. Recursive Definitions. In a recursive definition , an object is defined in terms of itself. We can recursively define sequences , functions and sets. Recursively Defined Sequences. Example: The sequence {a n } of powers of 2 is given by a n = 2 n for n = 0, 1, 2, … .

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Computably Enumerable Semigroups, Algebras, and Groups

Computably Enumerable Semigroups, Algebras, and Groups. Bakhadyr Khoussainov The University of Auckland New Zealand Research is partially supported by Marsden Fund of New Zealand Royal Society. Plan. Equational presentations. The specification problem. A semigroup example.

688 views • 55 slides

Recursive Definitions: functions, structures, languages

Recursive Definitions: functions, structures, languages. Section 4.3. 1. Recursively Defined Functions. A recursive (or inductive) definition for a function from f : N  S : Specify the initial value of the function at n=0.

780 views • 62 slides

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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Undecidable problems for Recursively enumerable languages

Undecidable problems for Recursively enumerable languages. continued…. Take a recursively enumerable language. Decision problems:. is empty?. is finite?. contains two different strings of the same length?. All these problems are undecidable. Theorem:.

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Recursive and Iterative Algorithms

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Solving Problems Recursively

Solving Problems Recursively. Recursion is an indispensable tool in a programmer’s toolkit Allows many complex problems to be solved simply Elegance and understanding in code often leads to better programs: easier to modify, extend, verify (and sometimes more efficient!!)

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Recursively Defined Sequences

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Section 3.2 Recursively Defined Functions and Procedures

Section 3.2 Recursively Defined Functions and Procedures A function ƒ is recursively defined if at least one value ƒ( x ) is defined in terms of another value ƒ( y ), where x ≠ y . Similarly, a procedure P is recursively defined if the action of P ( x )

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