Logic in computer science | Computational complexity theory

Boolean circuit

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).

Boolean circuit
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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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4.2.1 Sum of Products

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

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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

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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)

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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

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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

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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

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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

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Model Checking Cell Biology

(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

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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

Related pages

AC (complexity) | Functional completeness | Sequential logic | Decision problem | NAND gate | Unary operation | Binary function | NOT gate | Probabilistic Turing machine | Arithmetic logic unit | AND gate | Circuit complexity | Model of computation | Parallel algorithm | Logic gate | Boolean expression | Propositional formula | Combinational logic | Boolean function | Formal language | Fan-out | Circuit Value Problem | NC (complexity) | P-complete | Polynomial hierarchy | Advice (complexity) | OR gate | Turing machine | Bit | NP (complexity) | Directed acyclic graph | P/poly | Time complexity | Switching lemma | Computational complexity theory | Boolean algebra | P (complexity) | Adder (electronics) | String (computer science)