diff --git a/metadata/entries/Lovasz_Local.toml b/metadata/entries/Lovasz_Local.toml --- a/metadata/entries/Lovasz_Local.toml +++ b/metadata/entries/Lovasz_Local.toml @@ -1,29 +1,30 @@ title = "General Probabilistic Techniques for Combinatorics and the Lovasz Local Lemma" date = 2023-09-20 topics = [ "Mathematics/Probability theory", "Mathematics/Combinatorics", ] abstract = "This entry aims to formalise several useful general techniques for using the probabilistic method for combinatorial structures (or discrete spaces more generally). In particular, it focuses on bounding tools for combinatorics, such as the union and complete independence bounds, and the first formalisation of the pivotal Lovász local lemma. The formalisation focuses on the general lemma, however also proves several useful variations, including the more well-known symmetric version. Both the original formalisation and several of the variations used dependency graphs, which were formalised using Noschinski's general directed graph library. Additionally, the entry provides several useful existence lemmas, required at the end of most probabilistic proofs on combinatorial structures. Finally, the entry includes several significant extensions to the existing probability libraries, particularly for conditional probability (such as Bayes theorem) and independent events. The formalisation is primarily based on Alon and Spencer's textbook \"The Probabilistic Method\", as well as Zhao's course notes on the subject." license = "bsd" note = "" [authors] [authors.edmonds] email = "edmonds_email" [contributors] [notify] edmonds = "edmonds_email" [history] [extra] [related] pubs = [ "https://dl.acm.org/doi/book/10.5555/3002498", - "https://yufeizhao.com/pm/probmethod_notes.pdf", + "Lecture notes by Yufei Zhao", + "Wikipedia" ] diff --git a/web/entries/Lovasz_Local.html b/web/entries/Lovasz_Local.html --- a/web/entries/Lovasz_Local.html +++ b/web/entries/Lovasz_Local.html @@ -1,171 +1,173 @@ General Probabilistic Techniques for Combinatorics and the Lovasz Local Lemma - Archive of Formal Proofs

General Probabilistic Techniques for Combinatorics and the Lovasz Local Lemma

Chelsea Edmonds 📧

September 20, 2023

Abstract

This entry aims to formalise several useful general techniques for using the probabilistic method for combinatorial structures (or discrete spaces more generally). In particular, it focuses on bounding tools for combinatorics, such as the union and complete independence bounds, and the first formalisation of the pivotal Lovász local lemma. The formalisation focuses on the general lemma, however also proves several useful variations, including the more well-known symmetric version. Both the original formalisation and several of the variations used dependency graphs, which were formalised using Noschinski's general directed graph library. Additionally, the entry provides several useful existence lemmas, required at the end of most probabilistic proofs on combinatorial structures. Finally, the entry includes several significant extensions to the existing probability libraries, particularly for conditional probability (such as Bayes theorem) and independent events. The formalisation is primarily based on Alon and Spencer's textbook "The Probabilistic Method", as well as Zhao's course notes on the subject.

License

BSD License

Topics

Related publications

Session Lovasz_Local

\ No newline at end of file diff --git a/web/entries/Paraconsistency.html b/web/entries/Paraconsistency.html --- a/web/entries/Paraconsistency.html +++ b/web/entries/Paraconsistency.html @@ -1,193 +1,194 @@ Paraconsistency - Archive of Formal Proofs

Paraconsistency

Anders Schlichtkrull 🌠and Jørgen Villadsen ðŸŒ

December 7, 2016

Abstract

Paraconsistency is about handling inconsistency in a coherent way. In classical and intuitionistic logic everything follows from an inconsistent theory. A paraconsistent logic avoids the explosion. Quite a few applications in computer science and engineering are discussed in the Intelligent Systems Reference Library Volume 110: Towards Paraconsistent Engineering (Springer 2016). We formalize a paraconsistent many-valued logic that we motivated and described in a special issue on logical approaches to paraconsistency (Journal of Applied Non-Classical Logics 2005). We limit ourselves to the propositional fragment of the higher-order logic. The logic is based on so-called key equalities and has a countably infinite number of truth values. We prove theorems in the logic using the definition of validity. We verify truth tables and also counterexamples for non-theorems. We prove meta-theorems about the logic and finally we investigate a case study.

License

BSD License

Topics

Session Paraconsistency

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Real-Time Double-Ended Queue

Balazs Toth 📧 and Tobias Nipkow ðŸŒ

June 23, 2022

Abstract

A double-ended queue (deque) is a queue where one can enqueue and dequeue at both ends. We define and verify the deque implementation by Chuang and Goldberg. It is purely functional and all operations run in constant time.

License

BSD License

Topics

Related publications

  • - Chuang, T.-R., & Goldberg, B. (1993). Real-time deques, multihead Turing machines, and purely functional programming. Proceedings of the Conference on Functional Programming Languages and Computer Architecture. https://doi.org/10.1145/165180.165225 + Chuang, T.-R., & Goldberg, B. (1993). Real-time deques, multihead Turing machines, and purely functional programming. Proceedings of the Conference on Functional Programming Languages and Computer Architecture - FPCA ’93. https://doi.org/10.1145/165180.165225
  • Wikipedia

Session Real_Time_Deque

\ No newline at end of file diff --git a/web/entries/Relational_Disjoint_Set_Forests.html b/web/entries/Relational_Disjoint_Set_Forests.html --- a/web/entries/Relational_Disjoint_Set_Forests.html +++ b/web/entries/Relational_Disjoint_Set_Forests.html @@ -1,185 +1,187 @@ Relational Disjoint-Set Forests - Archive of Formal Proofs

Relational Disjoint-Set Forests

Walter Guttmann ðŸŒ

August 26, 2020

Abstract

We give a simple relation-algebraic semantics of read and write operations on associative arrays. The array operations seamlessly integrate with assignments in the Hoare-logic library. Using relation algebras and Kleene algebras we verify the correctness of an array-based implementation of disjoint-set forests with a naive union operation and a find operation with path compression.

License

BSD License

History

-
June 19, 2021
+
August 10, 2023
+
added matrix model of Peano structures and order-embedding from nat +(revision 9933c1ff260f)
June 19, 2021
added path halving, path splitting, relational Peano structures, union by rank (revision 98c7aa03457d)

Topics

Session Relational_Disjoint_Set_Forests

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Statistics

- + - +
765 Entries
466 Authors
~244,400~244,500 Lemmas
~3,964,200~3,964,700 Lines of Code

Most used AFP entries:

Name Used by ? entries
1. List-Index 23
2. Collections 19
3. Show 16
4. Jordan_Normal_Form 15
5. Coinductive 13
6. Deriving 13
7. Polynomial_Factorization 12
8. Regular-Sets 12
9. Landau_Symbols 11
10. Abstract-Rewriting 10
11. Automatic_Refinement 10
12. Native_Word 10

Growth in number of entries:

Growth in lines of code:

Growth in number of authors:

Size of entries:

\ No newline at end of file diff --git a/web/theories/paraconsistency/index.html b/web/theories/paraconsistency/index.html --- a/web/theories/paraconsistency/index.html +++ b/web/theories/paraconsistency/index.html @@ -1,83 +1,84 @@ Paraconsistency - Archive of Formal Proofs

Paraconsistency

-

Paraconsistency

+

Paraconsistency

+

Paraconsistency_Validity_Infinite

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