The Ackermann function. a theoretical, computational, and formula manipulative study

@article{Sundblad1971TheAF,
  title={The Ackermann function. a theoretical, computational, and formula manipulative study},
  author={Yngve Sundblad},
  journal={BIT Numerical Mathematics},
  year={1971},
  volume={11},
  pages={107-119}
}
  • Y. Sundblad
  • Published 1 March 1971
  • Computer Science
  • BIT Numerical Mathematics
Ackermann's function is of highly recursive nature and of two arguments. It is here treated as a class of functions of one argument, where the other argument defines the member of the class. The first members are expressed with elementary functions, the higher members with a hierarchy of primitive recursive functions. The number of calls of the function needed in a straightforward recursive computation is given for the first members. The maximum depth in the recursion during the evaluation is… 
Depth of recursion and the ackermann function
TLDR
It is shown that the recursive use parameter of the Ackermann function contributes to the depth of recursion, and that this contribution may be reduced by rearranging the order of the parameters.
A programming technique for recursive procedures
A programming technique is described for ALGOL-like recursive procedures in which parameters and local variables are replaced by variables global to the recursive procedure and declared in a
Ackermann's function in Ada
TLDR
This paper largely summarises the main papers concerned with the use of Ackermann's functio n as a performance measure, but interprets the significance of the results in an Ada context.
The far side of recursion
TLDR
This paper looks at how three lesser known algorithms of recursion can be used in teaching behavioral aspects of recursions: The Josephus Problem, the Hailstone Sequence and Ackermann’s Function.
From folklore to fact: comparing implementations of stacks and continuations
TLDR
An ``apples-to-apples'' comparison of six different approaches to implementing call stacks and continuations, with the only differences being those required by the differences in implementation strategy.
Ackermann's function: A study in the efficiency of calling procedures
A six line recursive procedure is used to assess the efficiency of the procedure calling mechanism in ALGOL-like languages. The results from some 40 systems varying from ALGOL 68 and PL/I to System
A heap‐based implementation of the programming language Pascal
  • C. Marlin
  • Computer Science
    Softw. Pract. Exp.
  • 1979
TLDR
The implementation of Pascal known as Pascal ‘P’ was modified so that activation records for blocks (procedures and functions) were no longer allocated on a stack, but were instead allocation on a heap, to assess the efficiency of implementing Pascal procedures and functions in this way.
Constraint programming algorithms and models for scheduling applications
TLDR
This thesis proves that CP is able to solve large instances of real-world scheduling problems in short amounts of time and designs new abstractions and techniques to enrich the set of tools CP can use to solve Scheduling problems.
BiGO: A Toolset to Support CS Students to Learn to Analyze Time Complexities of Algorithms
TLDR
BiGO is presented, a tool to support the students to understand and learn to analyze the time complexity of algorithms in rigorous manner and the pedagogical goals of the tool and the system implementation architecture are outlined.
A Calculus of Chaos in Stochastic Compilation - Engineering in the Cause of Mathematics
TLDR
This calculus quantifies the entropy introduced into run-time program traces by a compiler that aims for the maximal possible entropy, furnishing a definition and proof of security for encrypted computing (Turing-complete computation in which data remains in encrypted form throughout), where the status was formerly unknown.
...
...

References

SHOWING 1-3 OF 3 REFERENCES
Formula Manipulation—The User’s Point of View
For a number of years, formula manipulation has been a prosperous member of the large family of computer applications. It has already facilitated the solution of problems too lengthy and
Zum Hilbertschen Aufbau der reellen Zahlen
Um den Beweis fiir die yon Cantor aufgestellte Vermutung zu e~bringen, dal~ sich die Menge der ree|len Zahlen, d. h. der zaMentheoretischen I~unktionen, mi~ Hilfe der Zahlen de~ zweiten Zahlklasse
A Programming Language.