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Similarly, (4,2,4) is lexicographically larger than (2,4,4). The following algorithm can be used to compute whether x is leximin-larger than y: Let x' be a vector containing the same elements of x but in ascending order; Let y' be a vector containing the same elements of y but in ascending order; Return "true" iff x' is lexicographically-larger ...
The words in a lexicon (the set of words used in some language) have a conventional ordering, used in dictionaries and encyclopedias, that depends on the underlying ordering of the alphabet of symbols used to build the words. The lexicographical order is one way of formalizing word order given the order of the underlying symbols.
Lexicography is the study of lexicons and the art of compiling dictionaries. [1] It is divided into two separate academic disciplines: . Practical lexicography is the art or craft of compiling, writing and editing dictionaries.
Lexicographic optimization is sometimes called preemptive optimization, [1] since a small increase in one objective value preempts a much larger increase in less important objective values. As an example, consider a firm which puts safety above all. It wants to maximize the safety of its workers and customers.
In general, a lexmaxmin optimization problem may have more than one optimal solution. If and are two optimal solutions, then their ordered value vector must be the same, that is, [] = [] for all [], [5]: Thm.2 that is, the smallest value is the same, the second-smallest value is the same, and so on.
In economics, lexicographic preferences or lexicographic orderings describe comparative preferences where an agent prefers any amount of one good (X) to any amount of another (Y). Specifically, if offered several bundles of goods, the agent will choose the bundle that offers the most X, no matter how much Y there is.
Diachronic or historical lexicology is devoted to the evolution of words and word-formation over time. It investigates the origins of a word and the ways in which its structure, meaning, and usage have since changed. [9] Synchronic or descriptive lexicology examines the words of a language within a certain time frame. This could be a period ...
However, even here there are many edge cases such as contractions, hyphenated words, emoticons, and larger constructs such as URIs (which for some purposes may count as single tokens). A classic example is "New York-based", which a naive tokenizer may break at the space even though the better break is (arguably) at the hyphen.