In concurrent programming, concurrent accesses to shared resources can lead to unexpected or erroneous behavior, so parts of the program where the shared resource is accessed are protected. This protected section is critical region, it cannot be executed by more than one process at a time. The critical section accesses a shared resource, such as a data structure, a peripheral device, or a network connection, that would not operate in the context of multiple concurrent accesses. Different codes or processes may consist of the same variable or other resources that need to be read or written but whose results depend on the order in which the actions occur. For example, if a variable ‘x’ is to be read by process A, process B has to write to the same variable ‘x’ at the same time, process A might get either the old or new value of ‘x’. Process A: Process B: In cases like these, a critical section is important. In the above case, if A needs to read the updated value of ‘x’, executing Process A and Process B at the same time may not give required results.
To prevent this, variable ‘x’ is protected by a critical section. First, B gets the access to the section. Once B finishes writing the value, A gets the access to the critical section and variable ‘x’ can be read. By controlling which variables are modified inside and outside the critical section, concurrent access to the shared variable are prevented. A critical section is used when a multi-threaded program must update multiple related variables without a separate thread making conflicting changes to that data. In a related situation, a critical section may be used to ensure that a shared resource, for example, a printer, can only be accessed by one process at a time; the implementation of critical sections vary among different operating systems. A critical section will terminate in finite time, a thread, task, or process will have to wait for a fixed time to enter it. To ensure exclusive use of critical sections some synchronization mechanism is required at the entry and exit of the program.
Critical section is a piece of a program. As shown in Fig 2, in the case of mutual exclusion, one thread blocks a critical section by using locking techniques when it needs to access the shared resource and other threads have to wait to get their turn to enter into the section; this prevents conflicts when two or more threads share the same memory space and want to access a common resource. The simplest method to prevent any change of processor control inside the critical section is implementing a semaphore. In uni processor systems, this can be done by disabling interrupts on entry into the critical section, avoiding system calls that can cause a context switch while inside the section, restoring interrupts to their previous state on exit. Any thread of execution entering any critical section anywhere in the system will, with this implementation, prevent any other thread, including an interrupt, from being granted processing time on the CPU—and therefore from entering any other critical section or, any code whatsoever—until the original thread leaves its critical section.
This brute-force approach can be improved upon by using semaphores. To enter a critical section, a thread must obtain a semaphore, which it releases on leaving the section. Other threads are prevented from entering the critical section at the same time as the original thread, but are free to gain control of the CPU and execute other code, including other critical sections that are protected by different semaphores. Semaphore locking has a time limit to prevent a deadlock condition in which a lock is acquired by a single process for an infinite time stalling the other processes which need to use the shared resource protected by the critical session. Critical sections prevent thread and process migration between processors and the preemption of processes and threads by interrupts and other processes and threads. Critical sections allow nesting. Nesting allows multiple critical sections to be exited at little cost. If the scheduler interrupts the current process or thread in a critical section, the scheduler will either allow the executing process or thread to run to completion of the critical section, or it will schedule the process or thread for another complete quantum.
The scheduler will not migrate the process or thread to another processor, it will not schedule another process or thread to run while the current process or thread is in a critical section. If an interrupt occurs in a critical section, the interrupt information is recorded for future processing, execution is returned to the process or thread in the critical section. Once the critical section is exited, in some cases the scheduled quantum completed, the pending interrupt will be executed; the concept of scheduling quantum applies to "round-robin" and similar scheduling policies. Since critical sections may execute only on the processor on which they are entered, synchronization is only required within the executing processor; this allows critical sections to be entered and exited at zero cost. No inter-processor synchronization is required. Only instruction stream synchronization is needed. Most processors provide the required amount of synchronization by the simple act of interrupting the current execution state.
This allows critical sections in most cases to be nothing more than a per processor count of critical sections entered. Performance enhancements include executing pending interrupts at the exit of all critical sections and allowing the scheduler to run at the exit of all critical sections. Furthermore, pending interrupts may be transferred to other processors for execution. Cri
In the computer industry, vaporware is a product computer hardware or software, announced to the general public but is never manufactured nor cancelled. Use of the word has broadened to include products such as automobiles. Vaporware is announced months or years before its purported release, with few details about its development being released. Developers have been accused of intentionally promoting vaporware to keep customers from switching to competing products that offer more features. Network World magazine called vaporware an "epidemic" in 1989 and blamed the press for not investigating whether developers' claims were true. Seven major companies issued a report in 1990 saying that they felt vaporware had hurt the industry's credibility; the United States accused several companies of announcing vaporware early enough to violate antitrust laws, but few have been found guilty. InfoWorld magazine places an unfair stigma on developers. "Vaporware" was coined by a Microsoft engineer in 1982 to describe the company's Xenix operating system and first appeared in print in a newsletter by entrepreneur Esther Dyson in 1983.
It became popular among writers in the industry as a way to describe products they felt took too long to be released. InfoWorld magazine editor Stewart Alsop helped popularize it by lampooning Bill Gates with a Golden Vaporware award for the late release of his company's first version of Windows in 1985. Vaporware first implied intentional fraud when it was applied to the Ovation office suite in 1983. "Vaporware", sometimes synonymous with "vaportalk" in the 1980s, has no single definition. It is used to describe a hardware or software product, announced, but that the developer has no intention of releasing any time soon, if ever; the first reported use of the word was in 1982 by an engineer at the computer software company Microsoft. Ann Winblad, president of Open Systems Accounting Software, wanted to know if Microsoft planned to stop developing its Xenix operating system as some of Open System's products depended on it, she asked two Microsoft software engineers, John Ulett and Mark Ursino, who confirmed that development of Xenix had stopped.
"One of them told me,'Basically, it's vaporware'," she said. Winblad compared the word to the idea of "selling smoke", implying Microsoft was selling a product it would soon not support. Winblad described the word to influential computer expert Esther Dyson, who published it for the first time in her monthly newsletter RELease 1.0. In an article titled "Vaporware" in the November 1983 issue of RELease 1.0, Dyson defined the word as "good ideas incompletely implemented". She described three software products shown at COMDEX in Las Vegas that year with bombastic advertisements, she stated that demonstrations of the "purported revolutions and new generations" at the exhibition did not meet those claims. The practice existed before Winblad's account. In a January 1982 review of the new IBM Personal Computer, BYTE favorably noted that IBM "refused to acknowledge the existence of any product, not ready to be put on dealers' shelves tomorrow. Although this is frustrating at times, it is a refreshing change from some companies' practice of announcing a product before its design is finished".
When discussing Coleco's delay in releasing the Adam, Creative Computing in March 1984 stated that the company "did not invent the common practice of debuting products before they exist. In microcomputers, to do so otherwise would be to break with a veritable tradition". After Dyson's article, the word "vaporware" became popular among writers in the personal computer software industry as a way to describe products they believed took too long to be released after their first announcement. InfoWorld magazine editor Stewart Alsop helped popularize its use by giving Bill Gates, CEO of Microsoft, with a Golden Vaporware award for Microsoft releasing Windows in 1985, 18 months late. Alsop presented it to Gates at a celebration for the release while the song "The Impossible Dream" played in the background."Vaporware" took another meaning when it was used to describe a product that did not exist. A new company named Ovation Technologies announced its office suite Ovation in 1983; the company invested in an advertising campaign that promoted Ovation as a "great innovation", showed a demonstration of the program at computer trade shows.
The demonstration was well received by writers in the press, was featured in a cover story for an industry magazine, created anticipation among potential customers. Executives revealed that Ovation never existed; the company created the fake demonstration in an unsuccessful attempt to raise money to finish their product, is "widely considered the mother of all vaporware," according to Laurie Flynn of The New York Times. Use of the term spread beyond the computer industry. Newsweek magazine's Allan Sloan described the manipulation of stocks by Yahoo! and Amazon.com as "financial vaporware" in 1997. Popular Science magazine uses a scale ranging from "vaporware" to "bet on it" to describe release dates of new consumer electronics. Car manufacturer General Motors' plans to develop and sell an electric car were called vaporware by an advocacy group in 2008. A product missing its announced release date, the labeling of it as vaporware by the press, can be caused by its development taking longer than planned.
Most software products are not released on time, according to researchers in 2001 who studied the causes and effects of vaporware.
Software quality management
Software quality management is a management process that aims to develop and manage the quality of software in such a way so as the best ensure the product meets the quality standards expected by the customer while meeting any necessary regulatory and developer requirements, if any. Software quality managers require software to be tested before it is released to the market, they do this using a cyclical process-based quality assessment in order to reveal and fix bugs before release, their job is not only to ensure their software is in good shape for the consumer but to encourage a culture of quality throughout the enterprise. Software quality management activities are split up into three core components: quality assurance, quality planning, quality control; some like software engineer and author Ian Sommerville don't use the term "quality control", linking its associated concepts with the concept of quality assurance. However, the three core components otherwise remain the same. By setting up an organized and logical set of organizational processes and deciding on that software development standards — based on industry best practices — that should be paired with those organizational processes, software developers stand a better chance of producing higher quality software.
However, linking quality attributes such as "maintanability" and "reliability" to processes is more difficult in software development due to its creative design elements versus the mechanical processes of manufacturing. Additionally, "process standardization can sometimes stifle creativity, which leads to poorer rather than better quality software."This stage can include: encouraging documentation process standards, such as the creation of well-defined engineering documents using standard templates mentoring how to conduct standard processes, such as quality reviews performing in-process test data recording procedures identifying standards, if any, that should be used in software development processes Quality planning works at a more granular, project-based level, defining the quality attributes to be associated with the output of the project and how those attributes should be assessed. Additionally, any existing organizational standards may be assigned to the project at this phase. Attributes such as "robustness," "accessibility," and "modularity" may be assigned to the software development project.
While this may be a more formalized, integral process, those using a more agile method of quality management may place less emphasis on strict planning structures. The quality plan may address intended market, critical release dates, quality goals, expected risks, risk management policy; the quality control team tests and reviews software at its various stages to ensure quality assurance processes and standards at both the organizational and project level are being followed. These checks are optimally separate from the development team so as to lend more of an objective view of the product to be tested. However, project managers on the development side must assist, helping to promote as part of this phase a "culture that provides support without blame when errors are discovered." In software development firms implementing a more agile quality approach, these activities may be less formal. Activities include: release testing of software, including proper documentation of the testing process examination of software and associated documentation for non-conformance with standards follow-up review of software to ensure any required changes detailed in previous testing are addressed application of software measurement and metrics for assessment The measurement of software quality is different from manufacturing.
However, software's quality and fit-for-purpose status can still be realized in various ways depending on the organization and type of realized project. This done through the support of the entire software development lifecycle, meaning: collecting requirements and defining the scope of an IT project, focused on verification if defined requirements will be testable. Software quality management is a topic linked with various project management, IT operation methods, including: Project management method PRINCE2 defines:component "Quality in a project environment", which describes necessity of double-checked and objective control of created products, it proposes using 4 elements: quality management system, function of quality control, planning quality and quality controls. "Quality Review Technique", focused on verification if created products fulfills defined quality criteria. Project management method PMBOK 4th edition defines knowledge area Project Quality Manag
Edsger W. Dijkstra
Edsger Wybe Dijkstra was a Dutch systems scientist, software engineer, science essayist, pioneer in computing science. A theoretical physicist by training, he worked as a programmer at the Mathematisch Centrum from 1952 to 1962. A university professor for much of his life, Dijkstra held the Schlumberger Centennial Chair in Computer Sciences at the University of Texas at Austin from 1984 until his retirement in 1999, he was a professor of mathematics at the Eindhoven University of Technology and a research fellow at the Burroughs Corporation. One of the most influential figures of computing science's founding generation, Dijkstra helped shape the new discipline from both an engineering and a theoretical perspective, his fundamental contributions cover diverse areas of computing science, including compiler construction, operating systems, distributed systems and concurrent programming, programming paradigm and methodology, programming language research, program design, program development, program verification, software engineering principles, graph algorithms, philosophical foundations of computer programming and computer science.
Many of his papers are the source of new research areas. Several concepts and problems that are now standard in computer science were first identified by Dijkstra or bear names coined by him; as a foremost opponent of the mechanizing view of computing science, he refuted the use of the concepts of'computer science' and'software engineering' as umbrella terms for academic disciplines. Until the mid-1960s computer programming was considered more an art than a scientific discipline. In Harlan Mills's words, "programming was regarded as a private, puzzle-solving activity of writing computer instructions to work as a program". In the late 1960s, computer programming was in a state of crisis. Dijkstra was one of a small group of academics and industrial programmers who advocated a new programming style to improve the quality of programs. Dijkstra, who had a background in mathematics and physics, was one of the driving forces behind the acceptance of computer programming as a scientific discipline, he coined the phrase "structured programming" and during the 1970s this became the new programming orthodoxy.
His ideas about structured programming helped lay the foundations for the birth and development of the professional discipline of software engineering, enabling programmers to organize and manage complex software projects. As Bertrand Meyer noted, "The revolution in views of programming started by Dijkstra's iconoclasm led to a movement known as structured programming, which advocated a systematic, rational approach to program construction. Structured programming is the basis for all, done since in programming methodology, including object-oriented programming."The academic study of concurrent computing started in the 1960s, with Dijkstra credited with being the first paper in this field and solving the mutual exclusion problem. He was one of the early pioneers of the research on principles of distributed computing, his foundational work on concurrency, mutual exclusion, finding shortest paths in graphs, fault-tolerance, self-stabilization, among many other contributions comprises many of the pillars upon which the field of distributed computing is built.
Shortly before his death in 2002, he received the ACM PODC Influential-Paper Award in distributed computing for his work on self-stabilization of program computation. This annual award was renamed the Dijkstra Prize the following year, in his honor; as the prize, sponsored jointly by the ACM Symposium on Principles of Distributed Computing and the EATCS International Symposium on Distributed Computing, recognizes that "No other individual has had a larger influence on research in principles of distributed computing". Edsger W. Dijkstra was born in Rotterdam, his father was a chemist, president of the Dutch Chemical Society. His mother was a mathematician, but never had a formal job. Dijkstra had considered a career in law and had hoped to represent the Netherlands in the United Nations. However, after graduating from school in 1948, at his parents' suggestion he studied mathematics and physics and theoretical physics at the University of Leiden. In the early 1950s, electronic computers were a novelty.
Dijkstra stumbled on his career quite by accident, through his supervisor, Professor A. Haantjes, he met Adriaan van Wijngaarden, the director of the Computation Department at the Mathematical Center in Amsterdam, who offered Dijkstra a job. For some time Dijkstra remained committed to physics, working on it in Leiden three days out of each week. With increasing exposure to computing, his focus began to shift; as he recalled: After having programmed for some three years, I had a discussion with A. van Wijngaarden, my boss at the Mathematical Center in Amsterdam, a discussion for which I shall remain grateful to him as long as I live. The point was that I was supposed to study theoretical physics at the University of Leiden and as I found the two activities harder and harder to combine, I had to make up my mind, either to stop programming and become a real, respectable theoretical physicist, or to carry my study of physics to a formal completion only, with a minimum of effort, to become.....
Yes what? A programmer? But was that a respectable profession? For after all, what was
Software development process
In software engineering, a software development process is the process of dividing software development work into distinct phases to improve design, product management, project management. It is known as a software development life cycle; the methodology may include the pre-definition of specific deliverables and artifacts that are created and completed by a project team to develop or maintain an application. Most modern development processes can be vaguely described as agile. Other methodologies include waterfall, prototyping and incremental development, spiral development, rapid application development, extreme programming; some people consider a life-cycle "model" a more general term for a category of methodologies and a software development "process" a more specific term to refer to a specific process chosen by a specific organization. For example, there are many specific software development processes that fit the spiral life-cycle model; the field is considered a subset of the systems development life cycle.
The software development methodology framework didn't emerge until the 1960s. According to Elliott the systems development life cycle can be considered to be the oldest formalized methodology framework for building information systems; the main idea of the SDLC has been "to pursue the development of information systems in a deliberate and methodical way, requiring each stage of the life cycle––from inception of the idea to delivery of the final system––to be carried out rigidly and sequentially" within the context of the framework being applied. The main target of this methodology framework in the 1960s was "to develop large scale functional business systems in an age of large scale business conglomerates. Information systems activities revolved around heavy data processing and number crunching routines". Methodologies and frameworks range from specific proscriptive steps that can be used directly by an organization in day-to-day work, to flexible frameworks that an organization uses to generate a custom set of steps tailored to the needs of a specific project or group.
In some cases a "sponsor" or "maintenance" organization distributes an official set of documents that describe the process. Specific examples include: 1970sStructured programming since 1969 Cap Gemini SDM from PANDATA, the first English translation was published in 1974. SDM stands for System Development Methodology1980sStructured systems analysis and design method from 1980 onwards Information Requirement Analysis/Soft systems methodology1990sObject-oriented programming developed in the early 1960s, became a dominant programming approach during the mid-1990s Rapid application development, since 1991 Dynamic systems development method, since 1994 Scrum, since 1995 Team software process, since 1998 Rational Unified Process, maintained by IBM since 1998 Extreme programming, since 19992000sAgile Unified Process maintained since 2005 by Scott Ambler Disciplined agile delivery Supersedes AUP2010s Scaled Agile Framework Large-Scale Scrum DevOpsIt is notable that since DSDM in 1994, all of the methodologies on the above list except RUP have been agile methodologies - yet many organisations governments, still use pre-agile processes.
Software process and software quality are interrelated. Among these another software development process has been established in open source; the adoption of these best practices known and established processes within the confines of a company is called inner source. Several software development approaches have been used since the origin of information technology, in two main categories. An approach or a combination of approaches is chosen by management or a development team. "Traditional" methodologies such as waterfall that have distinct phases are sometimes known as software development life cycle methodologies, though this term could be used more to refer to any methodology. A "life cycle" approach with distinct phases is in contrast to Agile approaches which define a process of iteration, but where design and deployment of different pieces can occur simultaneously. Continuous integration is the practice of merging all developer working copies to a shared mainline several times a day. Grady Booch first named and proposed CI in his 1991 method, although he did not advocate integrating several times a day.
Extreme programming adopted the concept of CI and did advocate integrating more than once per day – as many as tens of times per day. Software prototyping is about creating prototypes, i.e. incomplete versions of the software program being developed. The basic principles are: Prototyping is not a standalone, complete development methodology, but rather an approach to try out particular features in the context of a full methodology. Attempts to reduce inherent project risk by breaking a project into smaller segments and providing more ease-of-change during the development process; the client is involved throughout the development process, which increases the likelihood of client acceptance of the final implementation. While some prototypes are developed with the expectation that they will be discarded, it is possible in some cases to evolve from prototype to working system. A basic understanding of the fundamental business problem is necessary to avoid solving the wrong problems, but this is true for all software methodologies.
Various methods are acceptable f
Synchronization (computer science)
In computer science, synchronization refers to one of two distinct but related concepts: synchronization of processes, synchronization of data. Process synchronization refers to the idea that multiple processes are to join up or handshake at a certain point, in order to reach an agreement or commit to a certain sequence of action. Data synchronization refers to the idea of keeping multiple copies of a dataset in coherence with one another, or to maintain data integrity. Process synchronization primitives are used to implement data synchronization; the need for synchronization does not arise in multi-processor systems but for any kind of concurrent processes. Mentioned below are some of the main needs for synchronization: Forks and Joins: When a job arrives at a fork point, it is split into N sub-jobs which are serviced by n tasks. After being serviced, each sub-job waits, they are joined again and leave the system. Thus, in parallel programming, we require synchronization as all the parallel processes wait for several other processes to occur.
Producer-Consumer: In a producer-consumer relationship, the consumer process is dependent on the producer process till the necessary data has been produced. Exclusive use resources: When multiple processes are dependent on a resource and they need to access it at the same time the operating system needs to ensure that only one processor accesses it at a given point in time; this reduces concurrency. Thread synchronization is defined as a mechanism which ensures that two or more concurrent processes or threads do not execute some particular program segment known as critical section. Processes' access to critical section is controlled by using synchronization techniques; when one thread starts executing the critical section the other thread should wait until the first thread finishes. If proper synchronization techniques are not applied, it may cause a race condition where the values of variables may be unpredictable and vary depending on the timings of context switches of the processes or threads.
For example, suppose that there are three processes, namely 1, 2, 3. All three of them are concurrently executing, they need to share a common resource as shown in Figure 1. Synchronization should be used here to avoid any conflicts for accessing this shared resource. Hence, when Process 1 and 2 both try to access that resource, it should be assigned to only one process at a time. If it is assigned to Process 1, the other process needs to wait. Another synchronization requirement which needs to be considered is the order in which particular processes or threads should be executed. For example, we can not board a plane. We cannot check e-mails without validating our credentials. In the same way, an ATM will not provide any service until we provide it with a correct PIN. Other than mutual exclusion, synchronization deals with the following: deadlock, which occurs when many processes are waiting for a shared resource, being held by some other process. In this case, the processes just execute no further.
This violation of priority rules can happen under certain circumstances and may lead to serious consequences in real-time systems. This frequent polling robs processing time from other processes. One of the challenges for exascale algorithm design is to reduce synchronization. Synchronization takes more time than computation in distributed computing. Reducing synchronization drew attention from computer scientists for decades. Whereas it becomes an significant problem as the gap between the improvement of computing and latency increases. Experiments have shown that communications due to synchronization on a distributed computers takes a dominated share in a sparse iterative solver; this problem is receiving increasing attention after the emergence of a new benchmark metric, the High Performance Conjugate Gradient, for ranking the top 500 supercomputers. The following are some classic problems of synchronization: The Producer–Consumer Problem; these problems are used to test nearly every newly proposed synchronization scheme.
Many systems provide hardware support for critical section code. A single processor or uniprocessor system could disable interrupts by executing running code without preemption, inefficient on multiprocessor systems. "The key ability we require to implement synchronization in a multiprocessor is a set of hardware primitives with the ability to atomically read and modify a memory location. Without such a capability, the cost of building basic synchronization primitives will be too high and will increase as the processor count increases. There are a number of alternative formulations of the basic hardware primitives, all of which provide the ability to atomically read and modify a location, together with some way to tell if the read and write were performed atomically; these hardware primitives are the basic building blocks that are used to bui
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, automated reasoning, other tasks; as an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. The concept of algorithm has existed for centuries. Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, the Euclidean algorithm for finding the greatest common divisor of two numbers; the word algorithm itself is derived from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized Algoritmi.
A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928. Formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, Alan Turing's Turing machines of 1936–37 and 1939. The word'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to algorismus. Al-Khwārizmī was a Persian mathematician, astronomer and scholar in the House of Wisdom in Baghdad, whose name means'the native of Khwarazm', a region, part of Greater Iran and is now in Uzbekistan. About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, translated into Latin during the 12th century under the title Algoritmi de numero Indorum; this title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.
Al-Khwarizmi was the most read mathematician in Europe in the late Middle Ages through another of his books, the Algebra. In late medieval Latin, English'algorism', the corruption of his name meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός'number', the Latin word was altered to algorithmus, the corresponding English term'algorithm' is first attested in the 17th century. In English, it was first used in about 1230 and by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu, it begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as: Algorism is the art by which at present we use those Indian figures, which number two times five; the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals.
An informal definition could be "a set of rules that defines a sequence of operations". Which would include all computer programs, including programs that do not perform numeric calculations. A program is only an algorithm if it stops eventually. A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers. Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word in the following quotation: No human being can write fast enough, or long enough, or small enough† to list all members of an enumerably infinite set by writing out their names, one after another, in some notation, but humans can do something useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human, capable of carrying out only elementary operations on symbols.
An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large, thus an algorithm can be an algebraic equation such as y = m + n – two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of: Precise instructions for a fast, efficient, "good" process that specifies the "moves" of "the computer" to find and process arbitrary input integers/symbols m and n, symbols + and =... and "effectively" produce, in a "reasonable" time, output-integer y at a specified place and in a specified format