Duration Calculus
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Duration Calculus
Duration calculus (DC) is an interval logic for real-time systems. It was originally developed by Zhou Chaochen with the help of Anders P. Ravn and C. A. R. Hoare on the European ESPRIT Basic Research Action (BRA) ''ProCoS'' project on ''Provably Correct Systems''. Duration calculus is mainly useful at the requirements level of the software development process for real-time systems. Some tools are available (e.g., DCVALID, IDLVALID,IDLVALID: Model checking dense time Duration Calculus formulae
TIFR, India. etc.). Subsets of duration calculus have been studied (e.g., using rather than
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Discrete Time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities ...
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1991 Introductions
File:1991 Events Collage.png, From left, clockwise: Boris Yeltsin, elected as Russia's first president, waves the new flag of Russia after the 1991 Soviet coup d'état attempt, orchestrated by Soviet hardliners; Mount Pinatubo erupts in the Philippines, making it the second-largest volcanic eruption of the 20th century; MTS Oceanos sinks off the coast of South Africa, but the crew notoriously abandons the vessel before the passengers are rescued; Dissolution of the Soviet Union: The Soviet flag is lowered from the Kremlin for the last time and replaced with the flag of the Russian Federation; The United States and soon-to-be dissolved Soviet Union sign the START I Treaty; A tropical cyclone strikes Bangladesh, killing nearly 140,000 people; Lauda Air Flight 004 crashes after one of its thrust reversers activates during the flight; A United States-led coalition initiates Operation Desert Storm to remove Iraq and Saddam Hussein from Kuwait, 300x300px, thumb rect 0 0 200 200 ...
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Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a '' possible world''. A formula's truth value ...
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Temporal Logic Of Actions
Temporal logic of actions (TLA) is a logic developed by Leslie Lamport, which combines temporal logic with a logic of actions. It is used to describe behaviours of concurrent and distributed systems. It is the logic underlying the specification language TLA+. Details Statements in the temporal logic of actions are of the form t, where ''A'' is an action and ''t'' contains a subset of the variables appearing in ''A''. An action is an expression containing primed and non-primed variables, such as x+x'*y=y'. The meaning of the non-primed variables is ''the variable's value in this state''. The meaning of primed variables is ''the variable's value in the next state''. The above expression means the value of ''x'' ''today'', plus the value of ''x'' ''tomorrow'' times the value of ''y'' ''today'', equals the value of ''y'' ''tomorrow''. The meaning of t is that either ''A'' is valid now, or the variables appearing in ''t'' do not change. This allows for stuttering steps, in which n ...
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Temporal Logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I eat something"). It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians. Temporal logic has found an important application in formal verification, where it is used to state requirements of hardware or software systems. For instance, one may wish to say that ''whenever'' a request is made, access to a resource is ''eventually'' granted, but it is ''never'' granted to two requestors simultaneously. Such a statement can conveniently be expressed in a temporal logic. Motivation Consider the statement "I am hungry". Though it ...
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Mumbai
Mumbai (, ; also known as Bombay — List of renamed Indian cities and states#Maharashtra, the official name until 1995) is the capital city of the Indian States and union territories of India, state of Maharashtra and the ''de facto'' financial centre of India. According to the United Nations, as of 2018, Mumbai is the List of cities in India by population, second-most populous city in India after Delhi and the List of largest cities, eighth-most populous city in the world with a population of roughly 20 million (2 crore). As per the Indian government population census of 2011, Mumbai was the list of cities in India by population, most populous city in India with an estimated city proper population of 12.5 million (1.25 crore) living under the Municipal Corporation of Greater Mumbai, Brihanmumbai Municipal Corporation. Mumbai is the centre of the Mumbai Metropolitan Region, the sixth most populous metropolitan area in the world with a population of over 23 million ...
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Tata Institute Of Fundamental Research
Tata Institute of Fundamental Research (TIFR) is a public deemed research university located in Mumbai, India that is dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the Department of Atomic Energy of the Government of India. It is located at Navy Nagar, Colaba, Mumbai, with a campus in Bangalore, International Centre for Theoretical Sciences (ICTS), and an affiliated campus in Serilingampally near Hyderabad. TIFR conducts research primarily in the natural sciences, mathematics, the biological sciences and theoretical computer science. History In 1944, Homi J. Bhabha, known for his role in the development of the Indian atomic energy programme, wrote to the Sir Dorabji Tata Trust requesting financial assistance to set up a scientific research institute. With support from J.R.D. Tata, then chairman of the Tata Group, TIFR was founded on 1 June 1945, and Homi Bhabha was appointed its first director. Th ...
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Macau
Macau or Macao (; ; ; ), officially the Macao Special Administrative Region of the People's Republic of China (MSAR), is a city and special administrative region of China in the western Pearl River Delta by the South China Sea. With a population of about 680,000 and an area of , it is the most densely populated region in the world. Formerly a Portuguese colony, the territory of Portuguese Macau was first leased to Portugal as a trading post by the Ming dynasty in 1557. Portugal paid an annual rent and administered the territory under Chinese sovereignty until 1887. Portugal later gained perpetual colonial rights in the Sino-Portuguese Treaty of Peking. The colony remained under Portuguese rule until 1999, when it was transferred to China. Macau is a special administrative region of China, which maintains separate governing and economic systems from those of mainland China under the principle of " one country, two systems".. The unique blend of Portuguese and Chinese ...
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UNU-IIST
The United Nations University International Institute for Software Technology (UNU-IIST; ; Portuguese: ''Instituto Internacional para Tecnologia de Programação da Universidade das Nações Unidas'') was a United Nations University Research Training Centre based in Macau, China. History During 1987–1989, United Nations University conducted two studies regarding the need for a research and training centre for computing in the developing nations. The studies led to the decision of the Council of the UNU to establish in Macau the United Nations University International Institute for Software Technology (UNU-IIST), which was founded on 12 March 1991 and opened its door in July 1992.https://staff.fnwi.uva.nl/c.a.middelburg/unu-iist.pdf The Macao authorities also supply the institute with its office premises, located in a heritage building Casa Silva Mendes, and subsidize fellow accommodation. As part of the United Nations, the institute was to address the pressing global problem ...
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Continuous Time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities ...
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