|
Probabilistic CTL
Probabilistic Computation Tree Logic (PCTL) is an extension of computation tree logic (CTL) that allows for probabilistic quantification of described properties. It has been defined in the paper by Hansson and Jonsson.Hansson, Hans, and Bengt Jonsson. "A logic for reasoning about time and reliability." Formal aspects of computing 6.5 (1994): 512-535. PCTL is a useful logic for stating soft deadline properties, e.g. "after a request for a service, there is at least a 98% probability that the service will be carried out within 2 seconds". Akin CTL suitability for model-checking PCTL extension is widely used as a property specification language for probabilistic model checkers. PCTL syntax A possible syntax of PCTL can be defined as follows: \phi ::= p \mid \neg \phi \mid \phi \lor \phi \mid \phi \land \phi \mid \mathcal_(\phi \mathcal \phi) \mid \mathcal_(\square\phi) Therein, \sim \in \ is a comparison operator and \lambda is a probability threshold. Formulas of PCTL are int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computation Tree Logic
Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one of which might be an actual path that is realized. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checkers, which determine if a given artifact possesses safety or liveness properties. For example, CTL can specify that when some initial condition is satisfied (e.g., all program variables are positive or no cars on a highway straddle two lanes), then all possible executions of a program avoid some undesirable condition (e.g., dividing a number by zero or two cars colliding on a highway). In this example, the safety property could be verified by a model checker that explores all possible transitions out of program states satisfying the initial condition and ensures that all such executions satisfy the property. Compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantification (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order logic, first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope (logic), scope is called a quantified formula. A quantified formula must contain a Free variables and bound variables, bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as Dual (mathematics), duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...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 des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chains
A Markov chain or Markov process is a stochastic process, stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control, cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computation Tree Logic
Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one of which might be an actual path that is realized. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checkers, which determine if a given artifact possesses safety or liveness properties. For example, CTL can specify that when some initial condition is satisfied (e.g., all program variables are positive or no cars on a highway straddle two lanes), then all possible executions of a program avoid some undesirable condition (e.g., dividing a number by zero or two cars colliding on a highway). In this example, the safety property could be verified by a model checker that explores all possible transitions out of program states satisfying the initial condition and ensures that all such executions satisfy the property. Compu ... [...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 its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Probabilistic")
.jpg "Click for more on -> Model-checking")
