Non-deterministic pushdown automata are another formalism equivalent to context-free grammars.

Noam Chomsky, teaching linguistics to students of information theory at MIT, combined linguistics and mathematics, by taking what is essentially Thue's formalism as the basis for the description of the syntax of natural language ; he also introduced a clear distinction between generative rules ( those of context-free grammars ) and transformation rules ( 1956 ).

Non-deterministic pushdown automata are another formalism equivalent to context-free grammars.

* not only the context-free part, but the full language syntax and semantics were defined formally, in terms of Van Wijngaarden grammar, a formalism designed specifically for this purpose.

In linguistics, the affix grammars over a finite lattice ( AGFL ) formalism is a notation for context-free grammars with finite set-valued features, acceptable to linguists of many different schools.

This research has been implemented in fluid construction grammar ( FCG ), a formalism for construction grammars that has been specially designed for the origins and evolution of language.

It is also possible to build LL parsers and LR parsers from parsing expression grammars, with better worst-case performance than a recursive descent parser, but the unlimited lookahead capability of the grammar formalism is then lost.

FCG is a fully operational and computationally implemented formalism for construction grammars and proposes a uniform mechanism for parsing and production.

Ibn Yasin certainly had the ardor of a puritan zealot, his creed was mainly characterized by a rigid formalism and a strict adherence to the dictates of the Qur ' an, and the Orthodox tradition.

He tried to free the methods of scholarship from the rigidity and formalism of medieval traditions, but he was not satisfied with this.

They then concluded that quantum mechanics was incomplete since, in its formalism, there was no space for such hidden parameters.

Einstein later expressed to Erwin Schrödinger that, " it did not come out as well as I had originally wanted ; rather, the essential thing was, so to speak, smothered by the formalism.

Stueckelberg was motivated by the need for a manifestly covariant formalism for quantum field theory, but did not provide as automated a way to handle symmetry factors and loops, although he was first to find the correct physical interpretation in terms of forward and backward in time particle paths, all without the path-integral.

During the late 1920s, ' 30s, and ' 40s, Bertrand Russell and Ludwig Wittgenstein's formalism was developed by a group of philosophers in Vienna and Berlin, who formed the Vienna Circle and Berlin Circle into a doctrine known as logical positivism ( or logical empiricism ).

Mansfield was credited with introducing the mathematical formalism and developing techniques for efficient gradient utilization and fast imaging.

This limitation was first elucidated by Heisenberg through a thought experiment, and is represented mathematically in the new formalism by the non-commutativity of quantum observables.

The most sophisticated version of this formalism was the so-called Sommerfeld – Wilson – Ishiwara quantization.

Schrödinger's formalism was considered easier to understand, visualize and calculate with as it led to differential equations, which physicists were already familiar with solving.

A practical method for investigating neutrino oscillations was first suggested by Bruno Pontecorvo in 1957 using an analogy with kaon oscillations ; over the subsequent 10 years he developed the mathematical formalism and the modern formulation of vacuum oscillations.

Deeper theorems from real analysis were not included, but by the end of the third volume it was clear to experts that a large amount of known mathematics could in principle be developed in the adopted formalism.

The need for formalism in arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction.

The Ratio was indeed imbued with a sense of the divine, of the incarnate logos, that is of rhetoric as an eloquent and humane means to reach further devotion and further action in the Christian city, which was absent from Ramist formalism.

Before the Twelve Tables ( 754 – 449 BC ), private law comprised the Roman civil law ( ius civile Quiritium ) that applied only to Roman citizens, and was bonded to religion ; undeveloped, with attributes of strict formalism, symbolism, and conservatism, e. g. the ritual practice of mancipatio ( a form of sale ).

In 1948 Prokofiev was criticized for " anti-democratic formalism ", and with his income severely curtailed was forced to compose Stalinist works such as On Guard for Peace.

Prokofiev's music was now seen as a grave example of formalism, and was branded as " anti-democratic ".

" We were actually trying to build something complicated and discovered, serendipitously, that we had accidentally designed something that met all our goals but was much simpler than we had intended .... we realized that the lambda calculus — a small, simple formalism — could serve as the core of a powerful and expressive programming language.

The Soviet film industry was solving the sound-film issue without him and his films, techniques, and theories were becoming increasingly attacked as ' ideological failures ' and prime examples of formalism.

We will now make the above discussion concrete, using the formalism developed in the article on the mathematical formulation of quantum mechanics.

The following subsections are for those with a good working knowledge of the formal, mathematical description of quantum mechanics, including familiarity with the formalism and theoretical framework developed in the articles: bra-ket notation and mathematical formulation of quantum mechanics.

Originally developed in order to quantize vacuum general relativity in 3 + 1 dimensions, the formalism can accommodate arbitrary spacetime dimensionalities, fermions, an arbitrary gauge group ( or even quantum group ), and supersymmetry, and results in a quantization of the kinematics of the corresponding diffeomorphism-invariant gauge theory.

Hence there is good reason for viewing gauge theory as it developed from Weyl's ideas as a formalism of physical measurement and not a theory of anything physical, i. e. as scientific formalism.

Epstein developed such a formalism in the subsequent sections of his 1911 paper.

The concept of three-dimensional photonic crystals was then discussed by Ohtaka in 1979, who also developed a formalism for the calculation of the photonic band structure.

Researchers working at NECSI have developed a mathematical formalism for simultaneously describing systems on multiple scales.

In theoretical physics, the Batalin – Vilkovisky ( BV ) formalism ( named for Igor Batalin and Grigori Vilkovisky ) was developed as a method for determining the ghost structure for Lagrangian gauge theories, such as gravity and supergravity, whose corresponding Hamiltonian formulation has constraints not related to a Lie algebra ( i. e., the role of Lie algebra structure constants are played by more general structure functions ).

The AIC penalizes the number of parameters less strongly than does the Bayesian information criterion ( BIC ), which was independently developed by Akaike and by Schwarz in 1978, using Bayesian formalism.

The name derives from physicists Eugene Wigner and Carl Eckart who developed the formalism as a link between the symmetry transformation groups of space ( applied to the Schrödinger equations ) and the laws of conservation of energy, momentum, and angular momentum.

Minkowski's space-time formalism was quickly accepted and further developed.

* The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model.

* ADM formalism, a formulation of general relativity in physics developed by Arnowitt, Deser and Misner

The EAG compiler developed there will generate either a recogniser, a transducer, a translator, or a syntax directed editor for a language described in the EAG formalism.

Two schools of formalist literary criticism developed, Russian formalism, and soon after Anglo-American New Criticism.

In fact, Akaike was so impressed with Schwarz's Bayesian formalism that he developed his own Bayesian formalism, now often referred to as the ABIC for " a Bayesian Information Criterion " or more casually " Akaike's Bayesian Information Criterion ".

The density matrix formalism was developed to extend the tools of classical statistical mechanics to the quantum domain.

The vertebrate model of CPG has been also developed with both Hodgkin-Huxley formalism, its variants and control system approaches.