In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user. For example, a stack has push/pop operations that follow a Last-In-First-Out rule, and can be concretely implemented using either a list or an array. Another example is a set which stores values, without any particular order, and no repeated values. Values themselves are not retrieved from sets; rather, one tests a value for membership to obtain a Boolean "in" or "not in".
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "... is a man" and "... is mortal" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
In computer science, denotational semantics is an approach of formalizing the meanings of programming languages by constructing mathematical objects that describe the meanings of expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics and operational semantics.
The Vienna Development Method (VDM) is one of the longest-established formal methods for the development of computer-based systems. Originating in work done at the IBM Laboratory Vienna in the 1970s, it has grown to include a group of techniques and tools based on a formal specification language—the VDM Specification Language (VDM-SL). It has an extended form, VDM++, which supports the modeling of object-oriented and concurrent systems. Support for VDM includes commercial and academic tools for analyzing models, including support for testing and proving properties of models and generating program code from validated VDM models. There is a history of industrial usage of VDM and its tools and a growing body of research in the formalism has led to notable contributions to the engineering of critical systems, compilers, concurrent systems and in logic for computer science.
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values.
A Petri net, also known as a place/transition net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that has two types of elements: places and transitions. Place elements are depicted as white circles and transition elements are depicted as rectangles. A place can contain any number of tokens, depicted as black circles. A transition is enabled if all places connected to it as inputs contain at least one token. Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes.
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification is a key incentive for formal specification of systems, and is at the core of formal methods. It represents an important dimension of analysis and verification in electronic design automation and is one approach to software verification. The use of formal verification enables the highest Evaluation Assurance Level (EAL7) in the framework of common criteria for computer security certification.
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs.
Concurrency refers to the ability of a system to execute multiple tasks through simultaneous execution or time-sharing, sharing resources and managing interactions. Concurrency improves responsiveness, throughput, and scalability in modern computing, including:
The CO-OPN specification language is based on both algebraic specifications and algebraic Petri nets formalisms. The former formalism represent the data structures aspects, while the latter stands for the behavioral and concurrent aspects of systems. In order to deal with large specifications some structuring capabilities have been introduced. The object-oriented paradigm has been adopted, which means that a CO-OPN specification is a collection of objects which interact concurrently. Cooperation between the objects is achieved by means of a synchronization mechanism, i.e., each object event may request to be synchronized with some methods of one or a group of partners by means of a synchronization expression.
Coloured Petri nets are a backward compatible extension of the mathematical concept of Petri nets.
In computer science, the Actor model, first published in 1973, is a mathematical model of concurrent computation.
Algebraic specification is a software engineering technique for formally specifying system behavior. It was a very active subject of computer science research around 1980.
YAWL is a workflow language based on workflow patterns. It is supported by a software system that includes an execution engine, a graphical editor and a worklist handler. It is available as open-source software under the LGPL license.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
In computer science, algebraic semantics is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program specifications in a formal manner.
Nets within Nets is a modelling method belonging to the family of Petri nets. This method is distinguished from other sorts of Petri nets by the possibility to provide their tokens with a proper structure, which is based on Petri net modelling again. Hence, a net can contain further net items, being able to move around and fire themselves.
Hartmut Ehrig was a German computer scientist and professor of theoretical computer science and formal specification. He was a pioneer in algebraic specification of abstract data types, and in graph grammars.
Signal Transition Graphs (STGs) are typically used in electronic engineering and computer engineering to describe dynamic behaviour of asynchronous circuits, for the purposes of their analysis or synthesis.
