Logic in computer science | Temporal logic | Automata (computation)

Computation tree logic

Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one of which might be an actual path that is realized. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checkers, which determine if a given artifact possesses safety or liveness properties. For example, CTL can specify that when some initial condition is satisfied (e.g., all program variables are positive or no cars on a highway straddle two lanes), then all possible executions of a program avoid some undesirable condition (e.g., dividing a number by zero or two cars colliding on a highway). In this example, the safety property could be verified by a model checker that explores all possible transitions out of program states satisfying the initial condition and ensures that all such executions satisfy the property. Computation tree logic belongs to a class of temporal logics that includes linear temporal logic (LTL). Although there are properties expressible only in CTL and properties expressible only in LTL, all properties expressible in either logic can also be expressed in CTL*. CTL was first proposed by Edmund M. Clarke and E. Allen Emerson in 1981, who used it to synthesize so-called synchronisation skeletons, i.e abstractions of concurrent programs. (Wikipedia).

Video thumbnail

An Introduction to Propositional Logic

An introduction to propositions, truth tables, and logical equivalence, and logical operators — including negation, conjunction, disjunction, and implication. *** Spanning Tree is a collection of educational videos covering topics related to computer science and mathematics. https://span

From playlist Spanning Tree's Most Recent

Video thumbnail

Introduction to tree algorithms | Graph Theory

An introduction to tree algorithms. This video covers how trees are stored and represented on a computer. Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube: https://www.udemy.com/course/graph-t

From playlist Tree Algorithms

Video thumbnail

Tree Data & Computation

Trees are fundamental data structures in mathematics and science, with standard examples including XML trees, file systems and Wolfram Language expressions. We present symbolic Tree objects, added in Version 12.3 of the Wolfram Language, which are used to represent rooted, ordered, labeled

From playlist Wolfram Technology Conference 2021

Video thumbnail

TRUTH TREES for QUANTIFIERS in Predicate Logic - Logic

In this video on Logic, we start truth trees. We learn how to do negated universal decomposition, negated existential decomposition, universal elimination, and existential elimination. We then do three practice truth trees. 0:00 - [Negated Decompositions] 2:22 - [Universal Elimination] 4:

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Logic: The Structure of Reason

As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be

From playlist Logic & Philosophy of Mathematics

Video thumbnail

Understanding Computation

Hands on learning of computational theory for software developers from all walks of life. Using semantics and the barebones of the Ruby programming language, learn the meaning of programs and why specific algorithms do their job.

From playlist Programming Podcast

Video thumbnail

TRUTH TREES with Negation, Conditional, and Biconditional - Logic

In this video on #Logic / #PhilosphicalLogic I introduce rules for the conditional and biconditional for truth trees. We talk about conditional decomposition, biconditional decomposition, negated conditional decomposition, and negated biconditional decomposition. Then, we do an example of

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions

What are trees in graph theory? Tree graphs are connected graphs with no cycles. We'll introduce them and some equivalent definitions, with of course examples of tree graphs in today's graph theory video lesson! Some equivalent definitions of tree graphs are as follows. A graph is a tree

From playlist Graph Theory

Video thumbnail

Diego Figueira: Semistructured data, Logic, and Automata – lecture 2

Semistructured data is an umbrella term encompassing data models which are not logically organized in tables (i.e., the relational data model) but rather in hierarchical structures using markers such as tags to separate semantic elements and data fields in a ‘self-describing’ way. In this

From playlist Logic and Foundations

Video thumbnail

Citus Architecture Extending Postgres to Build

Citus is a distributed database that scales out Postgres. By using the extension APIs, Citus distributes your tables across a cluster of machines and parallelizes SQL queires. This talk describes the Citus architecture by focusing on our learnings in distributed systems. http://www.pgconf

From playlist 2016

Video thumbnail

Proof synthesis and differential linear logic

Linear logic is a refinement of intuitionistic logic which, viewed as a functional programming language in the sense of the Curry-Howard correspondence, has an explicit mechanism for copying and discarding information. It turns out that, due to these mechanisms, linear logic is naturally r

From playlist Talks

Video thumbnail

Diego Figueira: Semistructured data, Logic, and Automata – lecture 1

Semistructured data is an umbrella term encompassing data models which are not logically organized in tables (i.e., the relational data model) but rather in hierarchical structures using markers such as tags to separate semantic elements and data fields in a ‘self-describing’ way. In this

From playlist Logic and Foundations

Video thumbnail

Thomas Colcombet : Algebra vs Logic over (generalised) words

CONFERENCE Recording during the thematic meeting : « Discrete mathematics and logic: between mathematics and the computer science » the January 17, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks give

From playlist Logic and Foundations

Video thumbnail

8.2.3 Carry-lookahead Adders

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 8.2.3 Carry-lookahead Adders License: Creative Commons BY-NC-SA More in

From playlist MIT 6.004 Computation Structures, Spring 2017

Video thumbnail

Computer Science and Homotopy Theory - Vladimir Voevodsky

Vladimir Voevodsky Professor, School of Mathematics April 27, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Data structures: Introduction to Trees

See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have described tree data structure as a logical model in computer science. We have briefly discussed tree as a non-linear hierarchical data structure, i

From playlist Data structures

Video thumbnail

The Master Algorithm | Pedro Domingos | Talks at Google

Machine learning is the automation of discovery, and it is responsible for making our smartphones work, helping Netflix suggest movies for us to watch, and getting presidents elected. But there is a push to use machine learning to do even more—to cure cancer and AIDS and possibly solve ev

From playlist AI talks

Video thumbnail

Exercises in COMPLEX TRUTH TREES - Logic

In this video in #Logic / #PhilosophicalLogic we do two examples of complex truth trees and then I give general strategies for doing these. The trees here use rules for negation, conjunction, disjunction, the conditional, and the biconditional. 0:00 [Example #1] 4:53 [Example #2] 9:29 [St

From playlist Logic in Philosophy and Mathematics

Video thumbnail

(ML 2.3) Growing a regression tree (CART)

How to build a decision tree for regression using the CART approach. A playlist of these Machine Learning videos is available here: http://www.youtube.com/my_playlists?p=D0F06AA0D2E8FFBA

From playlist Machine Learning

Related pages

Graph (discrete mathematics) | Monadic second-order logic | Undecidable problem | Fair computational tree logic | Alternating-time temporal logic | Context-free grammar | False (logic) | Time | Formal verification | Well-formed formula | Atomic formula | Tree (graph theory) | CTL* | Temporal logic | De Morgan's laws | Transition system | PSPACE-complete | Model checking | Mathematical logic | Linear temporal logic | Logical connective | Probabilistic CTL | First-order logic