Formal methods | Logic in computer science | Boolean algebra | NP-complete problems | Satisfiability problems
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable. SAT is the first problem that was proved to be NP-complete; see Cook–Levin theorem. This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization problems, are at most as difficult to solve as SAT. There is no known algorithm that efficiently solves each SAT problem, and it is generally believed that no such algorithm exists; yet this belief has not been proved mathematically, and resolving the question of whether SAT has a polynomial-time algorithm is equivalent to the P versus NP problem, which is a famous open problem in the theory of computing. Nevertheless, as of 2007, heuristic SAT-algorithms are able to solve problem instances involving tens of thousands of variables and formulas consisting of millions of symbols, which is sufficient for many practical SAT problems from, e.g., artificial intelligence, circuit design, and automatic theorem proving. (Wikipedia).
Boolean Algebra: Sample Problems
In this video, I work through some sample problems relating to Boolean algebra. Specific, I work through examples of translating equivalences from logical or set notation to Boolean notation, and also a derivation using Boolean equivalences.
From playlist Discrete Mathematics
From playlist Week 1 2015 Shorts
Analysis of Boolean Functions on Association Schemes - Yuval Filmus
Yuval Filmus Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
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A Quick Overview of BOOLEAN ALGEBRA (symbols, truth tables, and laws)
Error in Video (9:32, 11:30): When talking about the last laws in the columns for equivalences, I say "DeMorgan's Law" when I mean to say "Distributive Law". In this video on #Logic, we learn the basics of #BooleanAlgebra and compare the notation for propositional logic with it. We cover
From playlist Logic in Philosophy and Mathematics
Boolean Algebra 2 – Simplifying Complex Expressions
This video follows on from the one about the laws of Boolean algebra. It explains some useful interpretations of the laws of Boolean algebra, in particular, variations of the annulment and distributive laws. It goes on to demonstrate how Boolean algebra can be applied to simplify comple
From playlist Boolean Algebra
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Discussed the arithmetization of Boole
From playlist MIT 18.404J Theory of Computation, Fall 2020
PMSP - Quasi-random boolean functions, and inapproximability - Ryan O'Donnell
Ryan O'Donnell Carnegie Mellon University June 17, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
Bob Hearn - How Martin Gardner Inspired an Area of Theoretical Computer Science - CoM Oct 2021
Reconfiguration: How Martin Gardner Inspired an Area of Theoretical Computer Science A popular area in theoretical computer science for the past ten or fifteen years is known as “combinatorial reconfiguration”, or just “reconfiguration”. What is not widely appreciated is the debt this fie
From playlist Celebration of Mind 2021
NP Completeness II & Reductions - Lecture 16
All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c
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Unique and 2:2 Games, Grassmannians, and Expansion - Irit Dinur
Hermann Weyl Lectures Topic: Unique and 2:2 Games, Grassmannians, and Expansion Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor Affiliation: School of Mathematics Date: November 20, 2019 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
The Remarkable BEST-SAT Algorithm
A dive into the remarkable BEST-SAT approximation algorithm. Created as a part of SoME2: https://www.youtube.com/watch?v=hZuYICAEN9Y ------------------ Timetable: 0:00 - Introduction 2:21 - RAND-SAT 3:35 - LP-SAT 8:49 - BEST-SAT 10:11 - Outro ------------------ Source code: https://gi
From playlist Summer of Math Exposition 2 videos
Boolean Algebra 1 – The Laws of Boolean Algebra
This computer science video is about the laws of Boolean algebra. It briefly considers why these laws are needed, that is to simplify complex Boolean expressions, and then demonstrates how the laws can be derived by examining simple logic circuits and their truth tables. It also shows ho
From playlist Boolean Algebra
Seminar on Applied Geometry and Algebra (SIAM SAGA): Timo de Wolff
Date: Tuesday, March 9 at 11:00am EST (5:00pm CET) Speaker: Timo de Wolff, Technische Universität Braunschweig Title: Certificates of Nonnegativity and Their Applications in Theoretical Computer Science Abstract: Certifying nonnegativity of real, multivariate polynomials is a key proble
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)
Replacing truth tables and Boolean equivalences | MathFoundations274 | N J Wildberger
While Propositional Logic is a branch of philosophy, concerned with systematizing reasoning using connectives such as AND, OR, NOT, IMPLIES and EQUIVALENT, the Algebra of Boole provides a mathematical framework for modelling some of this. With this approach we ignore the issue of the mean
From playlist Boole's Logic and Circuit Analysis
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Covered NP-completeness; SAT and 3SAT;
From playlist MIT 18.404J Theory of Computation, Fall 2020
Strong refutation of semi-random Boolean CSPs - Venkatesan Guruswami
Computer Science/Discrete Mathematics Seminar I Topic: Strong refutation of semi-random Boolean CSPs Speaker: Venkatesan Guruswami Affiliation: Carnegie Mellon University Date: March 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Boole Reduction: A challenge for programmers | MathFoundations 269 | N J Wildberger
Moving from Boolean algebra to the more powerful and direct Algebra of Boole for circuit analysis opens up some unique challenges for programmers. This will be especially relevant for those with interest and experience in Maple, Mathematica, Matlab, Sage, Mupad and other Computer Algebra S
From playlist Boole's Logic and Circuit Analysis
Product Free Sets in Groups - Noam Lifshitz
Workshop on Additive Combinatorics and Algebraic Connections Topic: Product Free Sets in Groups Speaker: Noam Lifshitz AffiliationL Member, School of Mathematics Date: October 28, 2022 A subset of a group is said to be product free if it does not contain the product of two elements in it
From playlist Mathematics