Consensus (computer science)A fundamental problem in distributed computing and multi-agent systems is to achieve overall system reliability in the presence of a number of faulty processes. This often requires coordinating processes to reach consensus, or agree on some data value that is needed during computation. Example applications of consensus include agreeing on what transactions to commit to a database in which order, state machine replication, and atomic broadcasts.
Byzantine faultA Byzantine fault (also Byzantine generals problem, interactive consistency, source congruency, error avalanche, Byzantine agreement problem, and Byzantine failure) is a condition of a computer system, particularly distributed computing systems, where components may fail and there is imperfect information on whether a component has failed. The term takes its name from an allegory, the "Byzantine generals problem", developed to describe a situation in which, to avoid catastrophic failure of the system, the system's actors must agree on a concerted strategy, but some of these actors are unreliable.
Proof of stakeProof-of-stake (PoS) protocols are a class of consensus mechanisms for blockchains that work by selecting validators in proportion to their quantity of holdings in the associated cryptocurrency. This is done to avoid the computational cost of proof-of-work (POW) schemes. The first functioning use of PoS for cryptocurrency was Peercoin in 2012, although the scheme, on the surface, still resembled a POW. For a blockchain transaction to be recognized, it must be appended to the blockchain.
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
Problem solvingProblem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.
Byzantine Empire under the Komnenos dynastyThe Byzantine Empire was ruled by emperors of the Komnenos dynasty for a period of 104 years, from 1081 to about 1185. The Komnenian (also spelled Comnenian) period comprises the reigns of five emperors, Alexios I, John II, Manuel I, Alexios II and Andronikos I. It was a period of sustained, though ultimately incomplete, restoration of the military, territorial, economic and political position of the Byzantine Empire.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.
Communication complexityIn theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. The problem is usually stated as follows: two parties (traditionally called Alice and Bob) each receive a (potentially different) -bit string and .
Byzantine EmpireThe Byzantine Empire, also referred to as the Eastern Roman Empire, was the continuation of the Roman Empire primarily in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople. It survived the fall of the Western Roman Empire in the 5th century AD and continued to exist until the fall of Constantinople to the Ottoman Empire in 1453. During most of its existence, the empire remained the most powerful economic, cultural, and military force in the Mediterranean world.
LawLaw is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior, with its precise definition a matter of longstanding debate. It has been variously described as a science and as the art of justice. State-enforced laws can be made by a group legislature or by a single legislator, resulting in statutes; by the executive through decrees and regulations; or established by judges through precedent, usually in common law jurisdictions.
Rashidun CaliphateThe Rashidun Caliphate (al-Khilāfah ar-Rāšidah; 632 661) was the first caliphate to succeed the Islamic prophet Muhammad. It was ruled by the first four successive caliphs of Muhammad after his death in 632 CE (11 AH). During its existence, the empire was the most powerful economic, cultural, and military force in West Asia. The caliphate arose following Muhammad’s passing in June 632 and the subsequent debate over the succession to his leadership.
ConstitutionA constitution is the aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organisation or other type of entity, and commonly determines how that entity is to be governed. When these principles are written down into a single document or set of legal documents, those documents may be said to embody a written constitution; if they are encompassed in a single comprehensive document, it is said to embody a codified constitution.
NP (complexity)In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine.
Knapsack problemThe knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
Common lawIn law, common law (also known as judicial precedent, judge-made law, or case law) is the body of law created by judges and similar quasi-judicial tribunals by virtue of being stated in written opinions. The defining characteristic of common law is that it arises as precedent. Common law courts look to the past decisions of courts to synthesize the legal principles of past cases. Stare decisis, the principle that cases should be decided according to consistent principled rules so that similar facts will yield similar results, lies at the heart of all common law systems.
Temple MountThe Temple Mount (הַר הַבַּיִת) is a hill in the Old City of Jerusalem that has been venerated as a holy site in Judaism, Christianity, and Islam for thousands of years. As the site of a large mosque compound, it is also known as Al-Aqsa or al-Aqsa mosque compound (المسجد الأقصى, al-Masjid al-Aqṣā, lit. 'The Furthest Mosque'), known honorifically as al-Ḥaram al-Sharīf (Arabic: الحرم الشريف, lit. 'The Noble Sanctuary'), and sometimes as Jerusalem's sacred (or holy) esplanade.
CommunicationCommunication is usually defined as the transmission of information. The term can also refer to the message itself, or the field of inquiry studying these transmissions, also known as communication studies. The precise definition of communication is disputed. Controversial issues are whether unintentional or failed transmissions are included and whether communication does not just transmit meaning but also create it. Models of communication aim to provide a simplified overview of its main components and their interaction.
Broadcast syndicationBroadcast syndication is the practice of leasing the right to broadcasting television shows and radio programs to multiple television stations and radio stations, without going through a broadcast network. It is common in the United States where broadcast programming is scheduled by television networks with local independent affiliates. Syndication is less widespread in the rest of the world, as most countries have centralized networks or television stations without local affiliates.
Decision problemIn computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.
