Equivalence (formal languages)In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees are reasonably similar in that the same semantic interpretation can be assigned to both. Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages.
Noam ChomskyAvram Noam Chomsky (born December 7, 1928) is an American professor and public intellectual known for his work in linguistics, political activism, and social criticism. Sometimes called "the father of modern linguistics", Chomsky is also a major figure in analytic philosophy and one of the founders of the field of cognitive science. He is a laureate professor of linguistics at the University of Arizona and an institute professor emeritus at the Massachusetts Institute of Technology (MIT).
Automata theoryAutomata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word automata comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM).
Abstract syntax treeIn computer science, an abstract syntax tree (AST), or just syntax tree, is a tree representation of the abstract syntactic structure of text (often source code) written in a formal language. Each node of the tree denotes a construct occurring in the text. The syntax is "abstract" in the sense that it does not represent every detail appearing in the real syntax, but rather just the structural or content-related details. For instance, grouping parentheses are implicit in the tree structure, so these do not have to be represented as separate nodes.
Symbol (formal)A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in the formal languages studied in mathematics and logic, the term "symbol" refers to the idea, and the marks are considered to be a token instance of the symbol.
Formal methodsIn computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
Formal systemA formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought.
ColorColor (American English) or colour (Commonwealth English) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorption, reflection, emission spectra and interference. For most humans, color are perceived in the visible light spectrum with three types of cone cells (trichromacy). Other animals may have a different number of cone cell types or have eyes sensitive to different wavelength, such as bees that can distinguish ultraviolet, and thus have a different color sensitivity range.
Color blindnessColor blindness or color vision deficiency (CVD) is the decreased ability to see color or differences in color. It can impair tasks such as selecting ripe fruit, choosing clothing, and reading traffic lights. Color blindness may make some academic activities more difficult. However, issues are generally minor, and people with colorblindness automatically develop adaptations and coping mechanisms. People with total color blindness (achromatopsia) may also be uncomfortable in bright environments and have decreased visual acuity.
Primary colorA set of primary colors or primary colours (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a broad range of colors in, e.g., electronic displays, color printing, and paintings. Perceptions associated with a given combination of primary colors can be predicted by an appropriate mixing model (e.g., additive, subtractive) that reflects the physics of how light interacts with physical media, and ultimately the retina.
PenA pen is a common writing instrument that applies ink to a surface, usually paper, for writing or drawing. Early pens such as reed pens, quill pens, dip pens and ruling pens held a small amount of ink on a nib or in a small void or cavity which had to be periodically recharged by dipping the tip of the pen into an inkwell. Today, such pens find only a small number of specialized uses, such as in illustration and calligraphy. Reed pens, quill pens and dip pens, which were used for writing, have been replaced by ballpoint pens, rollerball pens, fountain pens and felt or ceramic tip pens.
Violet (color)Violet is the color of light at the short wavelength end of the visible spectrum, between blue and invisible ultraviolet. It is one of the seven colors that Isaac Newton labeled when dividing the spectrum of visible light in 1672. Violet light has a wavelength between approximately 380 and 435 nanometers. The color's name is derived from the violet flower. In the RGB color model used in computer and television screens, violet is produced by mixing red and blue light, with more blue than red.
