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The latter corresponds to a hierarchical structure ("syntax tree") which is unique for the given expression. The compiler generates machine code from the tree in such a way that operations originating at the lowest hierarchy level are executed first. Examples: !A + !B is interpreted as (!A) + (!B) ++A + !B is interpreted as (++A) + (!B)
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set , though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets .
An illustration of how the levels of the hierarchy interact and where some basic set categories lie within it. In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on the complexity of formulas that define them.
In a branching hierarchy, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). [2] For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. [2] Branching hierarchies are present within numerous systems, including organizations and classification schemes. The broad ...