Logic in computer science | Computational complexity theory
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit. Boolean circuits provide a model for many digital components used in computer engineering, including multiplexers, adders, and arithmetic logic units, but they exclude sequential logic. They are an abstraction that omits many aspects relevant to designing real digital logic circuits, such as metastability, fanout, glitches, power consumption, and propagation delay variability. (Wikipedia).
Canonical forms for logic circuits | Math Foundations 263 | N J Wildberger
A key problem in circuit analysis is to associate to a logical circuit, typically made of logic gates such as AND, OR, NOT, XOR, NAND and NOR, an algebraic expression that captures the effect of that circuit on all possible inputs. Such an effect is called a Boolean function, and it acts o
From playlist Boole's Logic and Circuit Analysis
Boole polynumbers and equivalent circuits | Math Foundations 264 | N J Wildberger
We want to explain how to associate algebraic expressions to logic circuits which encode their values on various input values, in other words which encode the Boolean functions of circuits. We first review the idea of a polynumber, as opposed to a polynomial, which allows us to concentrat
From playlist Boole's Logic and Circuit Analysis
From playlist Week 1 2015 Shorts
How the Algebra of Boole simplifies circuit analysis (I) | Math Foundations 262 | N J Wildberger
Engineers and computer scientists create complicated circuits from the basic logic gates, typically NOT, AND, OR, XOR, NAND, NOR, XNOR and sometimes others. Such a circuit typically has a number of inputs, say A,B,C,etc and yields a single output. [More complicated circuits will have seve
From playlist Boole's Logic and Circuit Analysis
The Algebra of Boole is not Boolean algebra! (III) | Math Foundations 257 | N J Wildberger
We continue discussing George Boole's original algebra which can be framed as arithmetic over the bifield B_2={0,1} and vector spaces/algebra over it. We have seen how to reformulate Aristotle's syllogistic construction in terms of Boole's algebra, and use simple algebra to prove his syllo
From playlist Boole's Logic and Circuit Analysis
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
The Algebra of Boole is not Boolean Algebra! (I) | Math Foundations 255 | N J Wildberger
We begin to introduce the Algebra of Boole, starting with the bifield of two elements, namely {0,1}, and using that to build the algebra of n-tuples, which is a linear space over the bifield with an additional multiplicative structure. This important abstract development played a key role
From playlist Boole's Logic and Circuit Analysis
Construct a Circuit for the Boolean Expression (~P ^ Q) V ~Q
Construct a Circuit for the Boolean Expression (~P ^ Q) V ~Q If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There are several ways that you can
From playlist Digital Logic Circuits
How the Algebra of Boole simplifies circuit analysis (III) | MathFoundations 266 | N J Wildberger
How can you tell whether two given circuits are equivalent? One way is to create a table representing the Boolean function: all possible outputs for all possible input sets. A much more efficient way is to determine the unique Boole polynumber encoded by a circuit. Along the way we get to
From playlist Boole's Logic and Circuit Analysis
Amortized circuit complexity, formal complexity measures, and catalytic algorithms - Jeroen Zuiddam
Computer Science/Discrete Mathematics Seminar II Topic: Amortized circuit complexity, formal complexity measures, and catalytic algorithms Speaker: Jeroen Zuiddam Affiliation: New York University - Courant Institute of Mathematical Sciences Date: March 23, 2021 For more video please visi
From playlist Mathematics
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
MIT 6.004 Computation Structures, Spring 2017 Instructor: Chris Terman View the complete course: https://ocw.mit.edu/6-004S17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62WVs95MNq3dQBqY2vGOtQ2 4.2.1 Sum of Products License: Creative Commons BY-NC-SA More informati
From playlist MIT 6.004 Computation Structures, Spring 2017
Monotone Arithmetic Circuit Lower Bounds Via Communication Complexity - Arkadev Chattopadhyay
Computer Science/Discrete Mathematics Seminar I Topic: Monotone Arithmetic Circuit Lower Bounds Via Communication Complexity Speaker: Arkadev Chattopadhyay Affiliation: Tata Institute of Fundamental Research Date: February 15, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
mod-25 lec-26 Introduction to Fluid Logic
Fundamentals of Industrial Oil Hydraulics and Pneumatics by Prof. R.N. Maiti,Department of Mechanical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Fundamentals of Industrial Oil Hydraulics and Pneumatics (CosmoLearning Mechanical Engineering)
Lower bounds for subgraph isomorphism – Benjamin Rossman – ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.3 Lower bounds for subgraph isomorphism Benjamin Rossman Abstract: We consider the problem of determining whether an Erdős–Rényi random graph contains a subgraph isomorphic to a fixed pattern, such as a clique or cycle of consta
From playlist Mathematical Aspects of Computer Science
Live CEOing Ep 90: Quantum Computing in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Quantum Computing in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Proof and Circuit Complexity - Robert Robere
Short talks by postdoctoral members Topic: Proof and Circuit Complexity Speaker: Robert Robere Affiliation: Member, School of Mathematics For more video please visit http://video.ias.edu
From playlist Mathematics
Live CEOing Ep 74: Quantum Computing in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Quantum Computing in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
(May 16, 2012) David Dill discusses how a continuing improvement of computing technology is making it possible to digitally model some biological systems. Stanford University: http://www.stanford.edu/ Stanford School of Engineering: http://soe.stanford.edu/ Stanford Computer Systems Co
From playlist Engineering
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