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  • Groundbreaking treatise on state machines, paxos, specification
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Paxos demystified

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vy October 6, 2019January 13, 2022 archived, theory Read more

The halting problem has nothing to do with computers

  “Turing’s work was of course a great contribution to the world of mathematics, but there is a question of exactly how it is related to the world of computing. – Wilkes The undecidability of the halting problem for Turing

vy July 12, 2019March 19, 2021 theory Read more

Von Neumann’s critique of automata theory and logic in computer science

These remarks from “THE GENERAL AND LOGICAL THEORY OF AUTOMATA” 1947 are, not surprisingly, enormously insightful. Von Neumann essentially predicts the emergence of the field of analysis of algorithms and algorithmic complexity.  Not only does he point out the importance

vy February 20, 2019September 25, 2023 theory Read more

Judea Pearl’s mysterious claim

Pearl: Of course, but you cannot see this noble aspiration in scientific equations. The language of algebra is symmetric: If x tells us about y, then y tells us about x. I’m talking about deterministic relationships. There’s no way to write in mathematics a simple fact—for example,

vy May 21, 2018May 21, 2018 academics, theory Read more

Trees in informal methods

What’s a tree? First define a sequence or length n> 0 as a total map s: {1,.. n}→ X. Let Nil be the empty sequence.  If s is a sequence of length n, and x is an element, then u

vy May 5, 2018August 23, 2019 state maps Read more

Linked lists

What’s a linked list?  Let V be a set of values and A be a set of “addresses”. Say a map f is a “linked list element” compatible with values V  and addresses A if and only if f(value)∈ V

vy May 2, 2018August 23, 2019 state maps Read more

informal methods applied to networks and timeouts

Distributed computation involves many interesting issues concerning shared data. Here I want to sketch out what networks look like using applied (informal) mathematics so we can look at some algorithms for consensus and data consistency. No  formal methods or category

vy January 16, 2018August 23, 2019 academics, state maps, systems Read more

Sorting and groups

I can’t find much reference to this in the literature (see Maus for some hints and an interesting paper) , but surely people have looked at sorting as a problem in group theory? Given a sequence $latex s=[x_1\dots x_n] $

vy July 22, 2017August 23, 2019 state maps Read more

Basic math for basic algorithms

It’s odd that all the descriptions of basic programming operations, such as sorting, rely on pseudo code or complex formal logic. All we are doing is modifying finite sequences so it seems like we should be able to use ordinary

vy June 9, 2017November 21, 2017 academics, theory Read more

circularity problems in distributed consensus

Distributed consensus involves organizing a collection of independent agents – processes or network sites – to agree on some value or sequence of values.  Many distributed consensus methods depend on a leader-follower scheme in which the leader is an agent

vy August 25, 2016January 13, 2022 academics, archived, systems, theory Read more
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