Theory
536 posts in category “Theory”.
Abstract Interpretation: Cousot's Galois Connection Framework, Widening/Narrowing, and Sound Static Analysis by Construction
2021-12-29A deep exploration of abstract interpretation—the mathematical theory of sound approximation that underpins every modern static analyzer, from the Astrée system to the Rust borrow checker.
The Complexity Of The Network Simplex Algorithm For Minimum Cost Flow
2021-12-23A comprehensive technical exploration of the complexity of the network simplex algorithm for minimum cost flow, covering key concepts, practical implementations, and real-world applications.
Domain Theory: Scott's D∞ Construction, Solving Recursive Domain Equations, and the Foundations of Denotational Semantics
2021-12-19An in-depth exploration of domain theory—Scott's construction of a universal domain D∞ isomorphic to its own function space, continuous lattices, and how these ideas gave birth to denotational semantics.
A Deep Dive Into The Hat Trie: Array Compressed Trie With Efficient Cache Locality
2021-12-18A comprehensive technical exploration of a deep dive into the hat trie: array compressed trie with efficient cache locality, covering key concepts, practical implementations, and real-world applications.
Implementing A Van Emde Boas Tree For Predecessor Queries In O(Log Log U) Time
2021-12-13A comprehensive technical exploration of implementing a van emde boas tree for predecessor queries in o(log log u) time, covering key concepts, practical implementations, and real-world applications.
The Algorithm For Building A Fibonacci Heap With Decrease Key And Meld In Logarithmic Time
2021-12-06A comprehensive technical exploration of the algorithm for building a fibonacci heap with decrease key and meld in logarithmic time, covering key concepts, practical implementations, and real-world applications.
Building A Self Balancing Binary Search Tree With Weighted Average Rotation (Wavl) For Better Worst Case Balance
2021-12-01A comprehensive technical exploration of building a self balancing binary search tree with weighted average rotation (wavl) for better worst case balance, covering key concepts, practical implementations, and real-world applications.
The Performance Of Binary Search Trees: Treap, Splay Tree, Red Black Tree, And Avl Tree Under Random And Sequential Access
2021-11-18A comprehensive technical exploration of the performance of binary search trees: treap, splay tree, red black tree, and avl tree under random and sequential access, covering key concepts, practical implementations, and real-world applications.
A Detailed Analysis Of The Quickunion Disjoint Set Union Data Structure With Path Compression And Union By Rank
2021-11-04A comprehensive technical exploration of a detailed analysis of the quickunion disjoint set union data structure with path compression and union by rank, covering key concepts, practical implementations, and real-world applications.
Implementing An Exact Cover Solver Using Dancing Links (Knuth’S Algorithm X)
2021-10-30A comprehensive technical exploration of implementing an exact cover solver using dancing links (knuth’s algorithm x), covering key concepts, practical implementations, and real-world applications.
The Complexity Of The Isomorphism Problem For Graphs: Subgraph Isomorphism Via Color Refinement
2021-10-19A comprehensive technical exploration of the complexity of the isomorphism problem for graphs: subgraph isomorphism via color refinement, covering key concepts, practical implementations, and real-world applications.
Game Semantics: Fully Abstract Models of PCF, AJM Games, and Strategies as Sheaves
2021-09-30A rigorous exploration of game semantics—the technique that cracked the full abstraction problem for PCF by modeling computation as dialogue between Player and Opponent.
Linear Logic: Girard's Resource-Sensitive Logic, Exponential Modalities, and Linear Types in Rust
2021-09-29A comprehensive exploration of linear logic's resource-conscious foundations, proof nets, the ! and ? modalities translating intuitionistic to linear, and how Rust's ownership system mirrors these ideas.
A Rigorous Proof Of The No Free Lunch Theorem In Optimization: Convex Vs. Non Convex Landscapes
2021-09-28A comprehensive technical exploration of a rigorous proof of the no free lunch theorem in optimization: convex vs. non convex landscapes, covering key concepts, practical implementations, and real-world applications.
Building A Distributed Sampler From Scratch: Parallel Mcmc With Consensus And Mode Seeking
2021-09-24A comprehensive technical exploration of building a distributed sampler from scratch: parallel mcmc with consensus and mode seeking, covering key concepts, practical implementations, and real-world applications.
The Mathematical Foundations Of The Metropolis Hastings Algorithm For Markov Chain Monte Carlo
2021-09-17A comprehensive technical exploration of the mathematical foundations of the metropolis hastings algorithm for markov chain monte carlo, covering key concepts, practical implementations, and real-world applications.
Implementing A Finger Table For Consistent Hashing With Replication And Fault Tolerance
2021-09-11A comprehensive technical exploration of implementing a finger table for consistent hashing with replication and fault tolerance, covering key concepts, practical implementations, and real-world applications.
The Performance Of Minimal Perfect Hashing: Chd Algorithm, Empirical Hash Seeds, And Space Efficiency
2021-09-06A comprehensive technical exploration of the performance of minimal perfect hashing: chd algorithm, empirical hash seeds, and space efficiency, covering key concepts, practical implementations, and real-world applications.
A Deep Dive Into The Cuckoo Filter: Lower Memory Footprint Than Bloom Filters And Deletion Support
2021-08-28A comprehensive technical exploration of a deep dive into the cuckoo filter: lower memory footprint than bloom filters and deletion support, covering key concepts, practical implementations, and real-world applications.
The Design Of A Probabilistic Skip List With Path Compression And Concurrency Support
2021-08-24A comprehensive technical exploration of the design of a probabilistic skip list with path compression and concurrency support, covering key concepts, practical implementations, and real-world applications.
Optimizing Distributed Consensus: Comparing Fast Paxos, Epaxos, And Multi Paxos In Wan Deployments With Latency Benchmarks
2021-08-20A comprehensive technical exploration of optimizing distributed consensus, comparing Fast Paxos, Epaxos, and Multi Paxos in WAN deployments with latency benchmarks, covering key concepts, practical implementations, and real-world applications.
Implementing A Bloom Filter Cascade For Efficient Set Intersection And Summarization
2021-08-16A comprehensive technical exploration of implementing a bloom filter cascade for efficient set intersection and summarization, covering key concepts, practical implementations, and real-world applications.
A Thorough Explanation Of The Hyperloglog Algorithm: Counting Cardinalities With Log Log Estimation And Bias Correction
2021-08-12A comprehensive technical exploration of a thorough explanation of the hyperloglog algorithm: counting cardinalities with log log estimation and bias correction, covering key concepts, practical implementations, and real-world applications.
Homotopy Type Theory: The Univalence Axiom, Higher Inductive Types, and ∞-Groupoids
2021-08-11A deep dive into the univalent foundations of mathematics, where equality is homotopy, types are spaces, and the universe mirrors the ∞-groupoid of all ∞-groupoids.