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Signal Automaton
In automata theory, a field of computer science, a signal automaton is a finite automaton extended with a finite set of real-valued clocks. During a run of a signal automaton, clock values increase all with the same speed. Along the transitions of the automaton, clock values can be compared to integers. These comparisons form guards that may enable or disable transitions and by doing so constrain the possible behaviors of the automaton. Further, clocks can be reset. Example Before formally defining what a signal automaton is, an example will be given. Let one consider the language \mathcal L of signals, over a binary alphabet \, which contains signals \gamma such that: * A appears in singular intervals. That is, the set of times \ is discrete, and * A appears at least once during each interval of length one. This language can be accepted by the automaton pictured nearby. As for finite automaton, incoming arrows represents initial locations and double circle represents acceptin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees a symbol of input, it makes a transition (or jump) to another state, according to its transition function, which takes the previous state and current input symbol as its arguments. Automata the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Automaton
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Automaton Ensuring A Holds Discretly And At Least Once By Time Unit
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing'' includes audio, video, speech, image, sonar, and radar as examples of signal. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information. In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling. Signaling theory, in evolutionary biology, proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clock (model Checking)
In model checking, a subfield of computer science, a clock is a mathematical object used to model time. More precisely, a clock measures how much time passed since a particular event occurs, in this sense, a clock is more precisely an abstraction of a stopwatch. In a model of some particular program, the value of the clock may either be the time since the program was started, or the time since a particular event occurred in the program. Those clocks are used in the definition of timed automaton, signal automaton, timed propositional temporal logic and clock temporal logic. They are also used in programs such as UPPAAL which implement timed automata. Generally, the model of a system uses many clocks. Those multiple clocks are required in order to track a bounded number of events. All of those clocks are synchronized. That means that the difference in value between two fixed clocks is constant until one of them is restarted. In the language of electronics, it means that clock's jitter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Set
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, :\ is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the '' cardinality (or the cardinal number)'' of the set. A set that is not a finite set is called an '' infinite set''. For example, the set of all positive integers is infinite: :\. Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. Definition and terminology Formally, a set is called finite if there exists a bijection :f\colon S\to\ for some natural number . The number is the set's cardinality, denoted as . The empty s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clock (model Checking)
In model checking, a subfield of computer science, a clock is a mathematical object used to model time. More precisely, a clock measures how much time passed since a particular event occurs, in this sense, a clock is more precisely an abstraction of a stopwatch. In a model of some particular program, the value of the clock may either be the time since the program was started, or the time since a particular event occurred in the program. Those clocks are used in the definition of timed automaton, signal automaton, timed propositional temporal logic and clock temporal logic. They are also used in programs such as UPPAAL which implement timed automata. Generally, the model of a system uses many clocks. Those multiple clocks are required in order to track a bounded number of events. All of those clocks are synchronized. That means that the difference in value between two fixed clocks is constant until one of them is restarted. In the language of electronics, it means that clock's jitter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Powerset
In mathematics, the power set (or powerset) of a set is the set of all subsets of , including the empty set and itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of is variously denoted as , , , \mathbb(S), or . The notation , meaning the set of all functions from S to a given set of two elements (e.g., ), is used because the powerset of can be identified with, equivalent to, or bijective to the set of all the functions from to the given two elements set. Any subset of is called a ''family of sets'' over . Example If is the set , then all the subsets of are * (also denoted \varnothing or \empty, the empty set or the null set) * * * * * * * and hence the power set of is . Properties If is a finite set with the cardinality (i.e., the number of all elements in the set is ), then the number of all the subsets of is . This fact as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Automata
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal (model Checking)
In model checking, a subfield of computer science, a signal or timed state sequence is an extension of the notion of words in a formal language, in which letters are continuously emitted. While a word is traditionally defined as a function from a set of non-negative integers to letters, a signal is a function from a set of real numbers to letters. This allow the use of formalisms similar to the ones of automata theory to deal with continuous signals. Example Consider an elevator. What is formally called a letter could be in fact information such as "someone is pressing the button on the 2nd floor", or "the doors are currently open on the third floor". In this case, a signal indicates, at each time, which is the current state of the elevator and its buttons. The signal can then be analyzed using formal methods to check whether a property such that "each time the elevator is called, it arrives in less than three minutes, assuming that no one held the door for more than fifteen seco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Büchi Automata
Buchi can mean: __NOTOC__ Items *Bachi, special Japanese drumsticks *Butsi, the Hispanised term for jin deui (pastry made from glutinous rice) in the Philippines *Büchi automaton, finite state automata extended to infinite inputs * Büchi arithmetic, a mathematical logical fragment People Given names * Buchi Atuonwu, Nigerian reggae gospel artist *Buchi (comedian), stage name of Onyebuchi Ojieh, Nigerian comedian * Buchi Emecheta, (d. 2017) Nigerian British writer Family names *George Büchi (1921–1998), an organic chemist *Julius Richard Büchi (1924–1984), developer of the Büchi automaton *Hernán Büchi (born 1949), Finance Minister of Chile (1985–1989) * Albert Büchi (1907–1988), a Swiss professional road bicycle racer Nicknames *Yutaka Izubuchi, anime designer and director *Nigerian Igbo first names such as Onyebuchi, Nnabuchi, Maduabuchi, a suffix that translates as "...is God." Fictional characters *Buchi in ''One Piece ''One Piece'' (stylized i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zone (convex Polytope)
In model checking, a field of computer science, a difference bound matrix (DBM) is a data structure used to represent some convex polytopes called zones. This structure can be used to efficiently implement some geometrical operations over zones, such as testing emptyness, inclusion, equality, and computing the intersection and the sum of two zones. It is, for example, used in the Uppaal model checker; where it is also distributed as an independent library. More precisely, there is a notion of canonical DBM; there is a one-to-one relation between canonical DBMs and zones and from each DBM a canonical equivalent DBM can be efficiently computed. Thus, equality of zone can be tested by checking for equality of canonical DBMs. Zone A difference bound matrix is used to represents some kind of convex polytopes. Those polytopes are called zone. They are now defined. Formally, a zone is defined by equations of the form x\le c, x\ge c, x_1\le x_2+c and x_1\ge x_2+c, with x_1 and x_2 some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
