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Program Verification
In 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. The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite-state machines, labelled transition systems, Petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software System
A software system is a system of intercommunicating components based on software forming part of a computer system (a combination of hardware and software). It "consists of a number of separate programs, configuration files, which are used to set up these programs, system documentation, which describes the structure of the system, and user documentation, which explains how to use the system". The term "software system" should be distinguished from the terms "computer program" and "software". The term computer program generally refers to a set of instructions ( source, or object code) that perform a specific task. However, a software system generally refers to a more encompassing concept with many more components such as specification, test results, end-user documentation, maintenance records, etc.' The use of the term software system is at times related to the application of systems theory approaches in the context of software engineering. A software system consists of seve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timed Automaton
In automata theory, a timed automaton is a finite automaton extended with a finite set of real-valued clocks. During a run of a timed 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. Timed automata are a sub-class of a type hybrid automata. Timed automata can be used to model and analyse the timing behavior of computer systems, e.g., real-time systems or networks. Methods for checking both safety and liveness properties have been developed and intensively studied over the last 20 years. It has been shown that the state reachability problem for timed automata is decidable,Rajeev Alur, David L. Dill. 199A Theory of Timed Automata In Theoretical Computer Science, vol. 126, 183–235, pp. 194–1955 which makes this an interesting su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Temporal Logic
In logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc. It is a fragment of the more complex CTL*, which additionally allows branching time and quantifiers. Subsequently, LTL is sometimes called ''propositional temporal logic'', abbreviated ''PTL''. In terms of expressive power, linear temporal logic (LTL) is a fragment of first-order logic. LTL was first proposed for the formal verification of computer programs by Amir Pnueli in 1977. Syntax LTL is built up from a finite set of propositional variables ''AP'', the logical operators ¬ and ∨, and the temporal modal operators X (some literature uses O or N) and U. Formally, the set of LTL formulas over ''AP'' is inductively defined as follows: * if p ∈ ''AP'' then p is an LTL formula; * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbolic Simulation
In computer science, a simulation is a computation of the execution of some appropriately modelled state-transition system. Typically this process models the complete state of the system at individual points in a discrete linear time frame, computing each state sequentially from its predecessor. Models for computer programs or VLSI logic designs can be very easily simulated, as they often have an operational semantics which can be used directly for simulation. Symbolic simulation is a form of simulation where many possible executions of a system are considered simultaneously. This is typically achieved by augmenting the domain over which the simulation takes place. A symbolic variable can be used in the simulation state representation in order to index multiple executions of the system. For each possible valuation of these variables, there is a concrete system state that is being indirectly simulated. Because symbolic simulation can cover many system executions in a single sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Interpretation
In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains information about its semantics (e.g., control-flow, data-flow) without performing all the calculations. Its main concrete application is formal static analysis, the automatic extraction of information about the possible executions of computer programs; such analyses have two main usages: * inside compilers, to analyse programs to decide whether certain optimizations or transformations are applicable; * for debugging or even the certification of programs against classes of bugs. Abstract interpretation was formalized by the French computer scientist working couple Patrick Cousot and Radhia Cousot in the late 1970s. Intuition This section illustrates abstract interpretation by means of real-world, non-computin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Space Enumeration
In 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 Applied science, practical discipli ..., state space enumeration are methods that consider each reachable program state to determine whether a program satisfies a given property. As programs increase in size and complexity, the state space grows exponentially. The state space used by these methods can be reduced by maintaining only the parts of the state space that are relevant to the analysis. However, the use of state and memory reduction techniques makes runtime a major limiting factor."Proceedings of the conference on Application and theory of petri nets: formal methods in software engineering and defence systems - Volume 12", ACM International Conference Proceeding Series, Vol. 145, by Marko Mäkelä, Laboratory for Theoretical Computer Science, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Model Theory
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe. Since many central theorems of model theory do not hold when restricted to finite structures, finite model theory is quite different from model theory in its methods of proof. Central results of classical model theory that fail for finite structures under finite model theory include the compactness theorem, Gödel's completeness theorem, and the method of ultraproducts for first-order logic (FO). While model theory has many applications to mathematical algebra, finite model theory became an "unusually effective" instrument in computer science. In other words: "In the history of mathematical logic most interest has concentrated on infinite structures. ..Yet, the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Checking
In 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. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoare Logic
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare, and subsequently refined by Hoare and other researchers. The original ideas were seeded by the work of Robert W. Floyd, who had published a similar system for flowcharts. Hoare triple The central feature of Hoare logic is the Hoare triple. A triple describes how the execution of a piece of code changes the state of the computation. A Hoare triple is of the form : \ C \ where P and Q are '' assertions'' and C is a ''command''.Hoare originally wrote "P\Q" rather than "\C\". P is named the '' precondition'' and Q the '' postcondition'': when the precondition is met, executing the command establishes the postcondition. Assertions are formulae in predicate logic. Hoare logic provides axioms and inference rules for all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiomatic Semantics
Axiomatic semantics is an approach based on mathematical logic for proving the correctness of computer programs. It is closely related to Hoare logic Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and l .... Axiomatic semantics define the meaning of a command in a program by describing its effect on assertions about the program state. The assertions are logical statements—predicates with variables, where the variables define the state of the program. See also * Algebraic semantics (computer science) — in terms of algebras * Denotational semantics — by translation of the program into another language * Operational semantics — in terms of the state of the computation * Formal semantics of programming languages — overview * Predicate transformer semantics — describes the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denotational Semantics
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called ''denotations'') that describe the meanings of expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics and operational semantics. Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do. For example, programs (or program phrases) might be represented by partial functionsDana S. ScottOutline of a mathematical theory of computation Technical Monograph PRG-2, Oxford University Computing Laboratory, Oxford, England, November 1970. Dana Scott and Christopher Strachey. ''Toward a mathematical semantics for computer languages'' Oxford Programming Research Group Technical Monograph. PRG-6. 1971. or by ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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