A model of computation may be defined in terms of an abstract computer, e. g., Turing machine, and / or by postulating that certain operations are executed in unit time.

In it he stated another notion of " effective computability " with the introduction of his a-machines ( now known as the Turing machine abstract computational model ).

It is conceived as an abstract machine that can be in one of a finite number of states.

Considered as an abstract model of computation, the finite state machine is weak ; it has less computational power than some other models of computation such as the Turing machine.

In the 18th century, many deists viewed God merely as an abstract and impersonal creator of the universe, which they likened to a giant machine.

In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.

More generally, a programming language may describe computation on some, possibly abstract, machine.

3GLs are more abstract and are " portable ", or at least implemented similarly on computers that do not support the same native machine code.

The Standard Pascal Model Implementation was also based on this compiler, having been adapted, by Welsh and Hay at Manchester University in 1984, to check rigorously for conformity to the BSI 6192 / ISO 7185 Standard and to generate code for a portable abstract machine.

* Abstract interpretation models the effect that every statement has on the state of an abstract machine ( i. e., it ' executes ' the software based on the mathematical properties of each statement and declaration ).

This abstract machine over-approximates the behaviours of the system: the abstract system is thus made simpler to analyze, at the expense of incompleteness ( not every property true of the original system is true of the abstract system ).

The SECD machine is a highly influential virtual machine and abstract machine intended as a target for functional programming language compilers.

In computability theory, several closely related terms are used to describe the computational power of a computational system ( such as an abstract machine or programming language ):

; Machine independent vs machine dependent: Many optimizations that operate on abstract programming concepts ( loops, objects, structures ) are independent of the machine targeted by the compiler, but many of the most effective optimizations are those that best exploit special features of the target platform.

The SSP implements the Basic Call State Machine ( BCSM ) which is a Finite state machine that represents an abstract view of a call from beginning to end ( off hook, dialing, answer, no answer, busy, hang up, etc .).

Like any other Java program, they must be executed within a Java virtual machine ( JVM ) that integrates with the server's host operating system to provide an abstract platform-neutral environment.

Turing tarpits are characterized by having a simple abstract machine which requires the user to deal with many details in the solution of a problem.

An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.

DanceWriting uses figurative and abstract symbols on a five-line staff ( the Western music notation staff ).

All tensors are written in abstract index notation.

In his above-mentioned account, he introduced the bra-ket notation, together with an abstract formulation in terms of the Hilbert space used in functional analysis ; he showed that Schrödinger's and Heisenberg's approaches were two different representations of the same theory, and found a third, most general one, which represented the dynamics of the system.

When Polish notation is used as a syntax for mathematical expressions by interpreters of programming languages, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same.

This is an abuse of notation, since element of matrices being multiplied must allow multiplication and addition, but is suggestive notion for the ( formally correct ) abstract group ( the wreath product of the group G by the symmetric group ).

It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another ( in the style of a higher-order function in computer science ).

His experiences with object technology through the Simula language, as well as early work on abstract data types and formal specification ( including the Z notation ), provided some of the background for the development of Eiffel.

Though often atonal, highly abstract, and dissonant in sound, the " New Complexity " is most readily characterized by the use of techniques which require complex musical notation.

Treatise is a graphic musical score comprising 193 pages of lines, symbols, and various geometric or abstract shapes that eschew conventional musical notation.

Making use of abstract symbols Action Stroke Dance Notation is visually similar to Motif notation, a subset of Labannotation that is also designed for speed of writing.

Unlike the Z notation, the Larch family has one language for algebraic specification of abstract data types ( LSL, the Larch Shared Language ), and a separate interface language tailored to each language in which programs are to be written ( Modula-3, C, Smalltalk, etc .).

It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another ( in the style of a higher-order function in computer science ).

The actual symmetry group is specified by the point or axis of symmetry, together with the n. For each point or axis of symmetry the abstract group type is cyclic group Z < sub > n </ sub > of order n. Although for the latter also the notation C < sub > n </ sub > is used, the geometric and abstract C < sub > n </ sub > should be distinguished: there are other symmetry groups of the same abstract group type which are geometrically different, see cyclic symmetry groups in 3D.

Using the abstract index notation, let a, b, c, ... refer to and μ, ν, ... refer to the tangent bundle.

Here, d is the exterior derivative of the a < sup > th </ sup > component of x, which is a scalar field ( so this isn't a pure abstract index notation ).

This Alphabet of Movements of the Human Body is a notation that encodes dance movements with musical notes and not with pictographs or newly invented abstract symbols.

In particular, in abstract index notation, the set of Maxwell's equations ( in the Lorenz gauge ) may be written ( in Gaussian units ) as follows:

can be represented in this abstract notation by

2n-fold rotoreflection ( angle of 180 °/ n ) with symmetry group S2n of order 2n ( not to be confused with symmetric groups, for which the same notation is used ; abstract group C2n ); a special case is n = 1, inversion, because it does not depend on the axis and the plane, it is characterized by just the point of inversion.

The notation was introduced by Roger Penrose as a way to use the formal aspects of the Einstein summation convention in order to compensate for the difficulty in describing contractions and covariant differentiation in modern abstract tensor notation, while preserving the explicit covariance of the expressions involved.

The test of form is fidelity to the experience, a gauge also accepted by the abstract expressionist painters.

In the first instance, `` mimesis '' is here used to mean the recalling of experience in terms of vivid images rather than in terms of abstract ideas or conventional designations.

What I have observed time and time again is a process of integration, integration that begins as abstract design and gradually takes on recognizable form ; ;

for this division is but an abstract representation of the social struggle between mysticism and science.

An operational approach to sociology can never expect abstract certainty, since it is certainty which every new discovery in science either replaces or reshapes.

Its abstract decor is by John Hultberg.

In law, an abstract is a brief statement that contains the most important points of a long legal document or of several related legal papers.

The Abstract of Title, used in real estate transactions, is the more common form of abstract.

After this is accomplished, no abstract of title is necessary.

The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny quantities has been around for millennia, but these ideas were founded in abstract, philosophical reasoning rather than experimentation and empirical observation.

The most general setting in which these words have meaning is an abstract branch of mathematics called category theory.

This is a very abstract definition since, in category theory, morphisms aren't necessarily functions and objects aren't necessarily sets.

In the context of abstract algebra, for example, a mathematical object is an algebraic structure such as a group, ring, or vector space.

Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.

Walter Burkert notes that " Ares is apparently an ancient abstract noun meaning throng of battle, war.

He is also noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.

The term is also used, especially in the description of algorithms, to mean associative array or " abstract array ", a theoretical computer science model ( an abstract data type or ADT ) intended to capture the essential properties of arrays.

In abstract algebra, a field extension L / K is called algebraic if every element of L is algebraic over K, i. e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions that are not algebraic, i. e. which contain transcendental elements, are called transcendental.

(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Another line of defense is to maintain that abstract objects are relevant to mathematical reasoning in a way that is non causal, and not analogous to perception.