Loop variant

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Practical considerations

Integers Unbounded iteration Recursive function call Μ-recursion Primitive recursion

14 related topics

Every loop that terminates has a variant

Axiom of choice Partial order Descending chain condition Identity function First uncountable ordinal

7 related topics

Rule of inference for total correctness

Rule of inference Floyd–Hoare logic Universally quantified

3 related topics

Overview

Computer science Mathematical function State space Well-founded relation While loop

11 related topics

Topics to explore

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Overview

Computer science
Mathematical function Function (mathematics)
State space State (computer science)
Well-founded relation
While loop
Invariant conditions Loop invariant
Ensuring its termination Termination analysis
Transfinite Transfinite number
Well-founded descent Transfinite induction
Infinite descending chains Infinite descending chain
Partially correct Partial correctness

Rule of inference for total correctness

Rule of inference
Floyd–Hoare logic
Universally quantified Universal quantification

Every loop that terminates has a variant

Practical considerations

Integers Integer
Unbounded iteration Μ operator
Recursive function call Recursion (computer science)
Μ-recursion Μ-recursive function
Primitive recursion Primitive recursive function
Ackermann's function
Loop with an integer variant For loop
Computational complexity Computational complexity theory
Tractable Tractable problem
Turing machine
Kurt Gödel
Incompleteness theorem Gödel's incompleteness theorems
Halting problem
Pseudocode

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Map overview Semantic statistics

Nodes40

Edges39

Triples11

Avg. degree1.95

Density0.05

Components1

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Loop variant

Top relations

related to Practical considerations · 7

Loop variant → Ackermann's, And, Considering, In, So, Turing, Unless

is a · 1

Loop variant → mathematical function defined on the state space of a computer program whose value is monotonically decreased with respect to a

Important terminology Word statistics

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Important terminology

loop variant terminates termination well-founded invariant state function computer program relation iteration number correctness every successor time may existence transfinite

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Loop variant	is a	mathematical function defined on the state space of a computer program whose value is monotonically decreased with respect to a	0.90	text
a recursive function call	instance of	language allows a transfinite proof of termination for some other equally powerful construct	0.80	text
it is no longer capable of full μ-recursion	instance of	language allows a transfinite proof of termination for some other equally powerful construct	0.80	text
but only primitive recursion	instance of	language allows a transfinite proof of termination for some other equally powerful construct	0.80	text
Loop variant	related to Practical considerations	In	0.60	section
Loop variant	related to Practical considerations	Unless	0.60	section
Loop variant	related to Practical considerations	Ackermann's	0.60	section
Loop variant	related to Practical considerations	Considering	0.60	section
Loop variant	related to Practical considerations	And	0.60	section
Loop variant	related to Practical considerations	Turing	0.60	section
Loop variant	related to Practical considerations	So	0.60	section

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Min side: 3

Research this topic

Explore this topic

Practical considerations

Every loop that terminates has a variant

Rule of inference for total correctness

Overview

Key facts & relationships

Topics to explore

Overview

Rule of inference for total correctness

Every loop that terminates has a variant

Practical considerations

Advanced semantic analysis

Map overview Semantic statistics

Loop variant

How this topic connects Entity context

Loop variant

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges