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For Cybersecurity, Computer Science Must Rely on Strongly-Typed Actors

Hewitt, Carl (2019) For Cybersecurity, Computer Science Must Rely on Strongly-Typed Actors. [Preprint]

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Abstract

This article shows how fundamental higher-order theories of mathematical structures of computer science (e.g. natural numbers [Dedekind 1888] and Actors [Hewitt et. al. 1973]) are categorical meaning that they can be axiomatized up to a unique isomorphism thereby removing any ambiguity in the mathematical structures being axiomatized. Having these mathematical structures precisely defined can make systems more secure because there are fewer ambiguities and holes for cyberattackers to exploit. For example, there are no infinite elements in models for natural numbers to be exploited. On the other hand, the 1st-order theories and computational systems which are not strongly-typed necessarily provide opportunities for cyberattack.
Cyberattackers have severely damaged national, corporate, and individual security as well causing hundreds of billions of dollars of economic damage. [Sobers 2019] A significant cause of the damage is that current engineering practices are not sufficiently grounded in theoretical principles. In the last two decades, little new theoretical work has been done that practically impacts large engineering projects with the result that computer systems engineering education is insufficient in providing theoretical grounding. If the current cybersecurity situation is not quickly remedied, it will soon become much worse because of the projected development of Scalable Intelligent Systems by 2025 [Hewitt 2019].
Kurt Gödel strongly advocated that the Turing Machine is the preeminent universal model of computation. A Turing machine formalizes an algorithm in which computation proceeds without external interaction. However, computing is now highly interactive, which this article proves is beyond the capability of a Turing Machine. Instead of the Turing Machine model, this article presents an axiomatization of a strongly-typed universal model of digital computation (including implementation of Scalable Intelligent Systems) up to a unique isomorphism. Strongly-typed Actors provide the foundation for tremendous improvements in cyberdefense.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Hewitt, Carl
Keywords: uniquely categorical theories, strong types, Scalable Intelligent Systems, Actor Model of Computation, Alonzo Church, Haskell Curry, Richard Dedekind, Kurt Gödel, Thomas Kuhn, Martin Löb, Gordon Plotkin, Bertrand Russell, Alan Turing, Ludwig Wittgenstein, John Woods, Stephen Yablo
Subjects: Specific Sciences > Computation/Information > Classical
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Proof
Specific Sciences > Computer Science
General Issues > Determinism/Indeterminism
General Issues > Science and Policy
Depositing User: Prof. Carl Hewitt
Date Deposited: 22 Jun 2019 18:11
Last Modified: 22 Jun 2019 18:11
Item ID: 16133
Subjects: Specific Sciences > Computation/Information > Classical
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Proof
Specific Sciences > Computer Science
General Issues > Determinism/Indeterminism
General Issues > Science and Policy
Date: 19 June 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16133

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