Everything about Ackermann function
Quickly growing function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. It is essentially constructed by diagonalizing a sequence of primitive recursive functions selected from the Grzegorczyk hierarchy. This makes the Ackermann function the first limit point of the fast-growing hierarchy. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Ackermann functionA 5-minute orientation
- Skim a recent paper: Analytical Construction of Koopman EDMD Candidate Functions for Optimal Control of Ackermann-Steered VehiclesInfluential work since 2022
- Pick up a classic book: HypergigantonThe most-reprinted book on the subject
- Read the landmark paper: The Ackermann function. a theoretical, computational, and formula manipulative studyCited 22 times
- Go sideways: HyperoperationA closely related topic
- Go sideways: Primitive recursive functionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Ackermann function. a theoretical, computational, and formula manipulative study
Borel Partitions of Products of Finite Sets and the Ackermann Function
Some interesting connections between the slow growing hierarchy and the Ackermann function
Depth of recursion and the ackermann function
GOODSTEIN SEQUENCES BASED ON A PARAMETRIZED ACKERMANN–PÉTER FUNCTION
The Inverse of Ackermann Function is Computable in Linear Time
The Ackermann function in APL
The inverse of Ackermann function is computable in linear time
🆕 Influential since 2022
đź“š Books worth reading
Hypergiganton · 2024
HypernullarionIvan Futurologic Petrov · 2024
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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