TL;DR
The paper introduces the tree machine, a new computational model replacing the tape with a manipulable tree, facilitating easier machine construction and better modeling of functional programming complexity.
Contribution
It presents the tree machine, a novel variant of Turing machines that models functional programming complexity more precisely.
Findings
Enables explicit constructions of machines more easily than traditional Turing machines.
Models the asymptotic complexity of functional programming languages.
Provides a framework to analyze inherent problem complexity in functional languages.
Abstract
A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be leveraged to write explicit constructions of machines much more easily than with Turing machines. Second, this new kind of machines models finely the asymptotic complexity of functional programming languages, and may allow to answer questions such as "is this problem inherently slower in functional languages".
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Logic, programming, and type systems