Formal methodsIn computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
Model checkingIn computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language.
Formal verificationIn the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code.
Runtime verificationRuntime verification is a computing system analysis and execution approach based on extracting information from a running system and using it to detect and possibly react to observed behaviors satisfying or violating certain properties. Some very particular properties, such as datarace and deadlock freedom, are typically desired to be satisfied by all systems and may be best implemented algorithmically. Other properties can be more conveniently captured as formal specifications.
Kripke structure (model checking)This article describes Kripke structures as used in model checking. For a more general description, see Kripke semantics. A Kripke structure is a variation of the transition system, originally proposed by Saul Kripke, used in model checking to represent the behavior of a system. It consists of a graph whose nodes represent the reachable states of the system and whose edges represent state transitions, together with a labelling function which maps each node to a set of properties that hold in the corresponding state.
Formal languageIn logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas.
Bounded setIn mathematical analysis and related areas of mathematics, a set is called bounded if it is, in a certain sense, of finite measure. Conversely, a set which is not bounded is called unbounded. The word "bounded" makes no sense in a general topological space without a corresponding metric. Boundary is a distinct concept: for example, a circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary. A bounded set is not necessarily a closed set and vice versa.
Bounded functionIn mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number M such that for all x in X. A function that is not bounded is said to be unbounded. If f is real-valued and f(x) ≤ A for all x in X, then the function is said to be bounded (from) above by A. If f(x) ≥ B for all x in X, then the function is said to be bounded (from) below by B. A real-valued function is bounded if and only if it is bounded from above and below.
Real-time operating systemA real-time operating system (RTOS) is an operating system (OS) for real-time computing applications that processes data and events that have critically defined time constraints. An RTOS is distinct from a time-sharing operating system, such as Unix, which manages the sharing of system resources with a scheduler, data buffers, or fixed task prioritization in a multitasking or multiprogramming environment. Processing time requirements need to be fully understood and bound rather than just kept as a minimum.
Critical race theoryCritical race theory (CRT) is an interdisciplinary academic field devoted to analysing how laws, social and political movements, and media shape, and are shaped by, social conceptions of race and ethnicity. CRT also considers racism to be systemic in various laws and rules, and not only based on individuals' prejudices. The word critical in the name is an academic reference to critical thinking, critical theory, and scholarly criticism, rather than criticizing or blaming individuals.
Bounded operatorIn functional analysis and operator theory, a bounded linear operator is a linear transformation between topological vector spaces (TVSs) and that maps bounded subsets of to bounded subsets of If and are normed vector spaces (a special type of TVS), then is bounded if and only if there exists some such that for all The smallest such is called the operator norm of and denoted by A bounded operator between normed spaces is continuous and vice versa. The concept of a bounded linear operator has been extended from normed spaces to all topological vector spaces.
Totally bounded spaceIn topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered by finitely many subsets of every fixed “size” (where the meaning of “size” depends on the structure of the ambient space). The term precompact (or pre-compact) is sometimes used with the same meaning, but precompact is also used to mean relatively compact. These definitions coincide for subsets of a complete metric space, but not in general.
Bounded set (topological vector space)In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.
Race conditionA race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of the possible behaviors is undesirable. The term race condition was already in use by 1954, for example in David A. Huffman's doctoral thesis "The synthesis of sequential switching circuits". Race conditions can occur especially in logic circuits, multithreaded, or distributed software programs.
Thread (computing)In computer science, a thread of execution is the smallest sequence of programmed instructions that can be managed independently by a scheduler, which is typically a part of the operating system. The implementation of threads and processes differs between operating systems. In Modern Operating Systems, Tanenbaum shows that many distinct models of process organization are possible. In many cases, a thread is a component of a process.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.
Race (human categorization)Race is a categorization of humans based on shared physical or social qualities into groups generally viewed as distinct within a given society. The term came into common usage during the 16th century, when it was used to refer to groups of various kinds, including those characterized by close kinship relations. By the 17th century, the term began to refer to physical (phenotypical) traits, and then later to national affiliations. Modern science regards race as a social construct, an identity which is assigned based on rules made by society.
Whiteness studiesWhiteness studies is the study of the structures that produce white privilege, the examination of what whiteness is when analyzed as a race, a culture, and a source of systemic racism, and the exploration of other social phenomena generated by the societal compositions, perceptions and group behaviors of white people. It is an interdisciplinary arena of inquiry that has developed beginning in the United States from white trash studies and critical race studies, particularly since the late 20th century.
OpenMPOpenMP (Open Multi-Processing) is an application programming interface (API) that supports multi-platform shared-memory multiprocessing programming in C, C++, and Fortran, on many platforms, instruction-set architectures and operating systems, including Solaris, AIX, FreeBSD, HP-UX, Linux, macOS, and Windows. It consists of a set of compiler directives, library routines, and environment variables that influence run-time behavior.
Ada (programming language)Ada is a structured, statically typed, imperative, and object-oriented high-level programming language, inspired by Pascal and other languages. It has built-in language support for design by contract (DbC), extremely strong typing, explicit concurrency, tasks, synchronous message passing, protected objects, and non-determinism. Ada improves code safety and maintainability by using the compiler to find errors in favor of runtime errors.
