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.
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.
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.
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 .
Paxos (computer science)Paxos is a family of protocols for solving consensus in a network of unreliable or fallible processors. Consensus is the process of agreeing on one result among a group of participants. This problem becomes difficult when the participants or their communications may experience failures. Consensus protocols are the basis for the state machine replication approach to distributed computing, as suggested by Leslie Lamport and surveyed by Fred Schneider.
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.
Randomized algorithmA randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables.
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
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.
Bitcoin networkThe Bitcoin network is a peer-to-peer network of nodes which implement the Bitcoin protocol. The protocol itself implements a highly available, public, and decentralized ledger. The nodes verify that each update to the ledger follows the rules of the Bitcoin protocol. Users broadcast cryptographically signed messages to the network using Bitcoin cryptocurrency wallet software. These messages are proposed transactions, changes to be made in the ledger. Each node has a copy of the ledger's entire transaction history.
Worst-case complexityIn computer science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as n in asymptotic notation). It gives an upper bound on the resources required by the algorithm. In the case of running time, the worst-case time complexity indicates the longest running time performed by an algorithm given any input of size n, and thus guarantees that the algorithm will finish in the indicated period of time.
Unbounded nondeterminismIn computer science, unbounded nondeterminism or unbounded indeterminacy is a property of concurrency by which the amount of delay in servicing a request can become unbounded as a result of arbitration of contention for shared resources while still guaranteeing that the request will eventually be serviced. Unbounded nondeterminism became an important issue in the development of the denotational semantics of concurrency, and later became part of research into the theoretical concept of hypercomputation.
BitcoinBitcoin (abbreviation: BTC or XBT; sign: ₿) is a decentralized digital currency. Bitcoin transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. The cryptocurrency was invented in 2008 by an unknown person or group of people using the name Satoshi Nakamoto. The currency began use in 2009, when its implementation was released as open-source software. The word "bitcoin" was defined in a white paper published on October 31, 2008.
Smart contractA smart contract is a computer program or a transaction protocol that is intended to automatically execute, control or document events and actions according to the terms of a contract or an agreement. The objectives of smart contracts are the reduction of need for trusted intermediators, arbitration costs, and fraud losses, as well as the reduction of malicious and accidental exceptions. Smart contracts are commonly associated with cryptocurrencies, and the smart contracts introduced by Ethereum are generally considered a fundamental building block for decentralized finance (DeFi) and NFT applications.
Actor modelThe actor model in computer science is a mathematical model of concurrent computation that treats an actor as the basic building block of concurrent computation. In response to a message it receives, an actor can: make local decisions, create more actors, send more messages, and determine how to respond to the next message received. Actors may modify their own private state, but can only affect each other indirectly through messaging (removing the need for lock-based synchronization). The actor model originated in 1973.
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.
Proof of workProof of work (PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their part. The concept was invented by Moni Naor and Cynthia Dwork in 1993 as a way to deter denial-of-service attacks and other service abuses such as spam on a network by requiring some work from a service requester, usually meaning processing time by a computer.
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.
Best, worst and average caseIn computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n.
Quadratic residueIn number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.
