The Vector Space Model (VSM) represents words as vectors in a multidimensional space, where the dimensions correspond to the words' co-occurrence frequencies with other words in a large text corpus.

A grammar in the context of mathematical models of language defines the rules that govern the structure of sentences in a language, specifying how words can be combined to form grammatically correct sentences.

The Bayesian Network Model (BNM) represents words as nodes in a network, where the connections between nodes represent the probabilistic relationships between words.

A lexicon in the context of mathematical models of language specifies the meaning of words in a language, typically represented as vectors of semantic features or as distributional vectors.

The Syntactic Tree Model (STM) represents sentences as trees, where the nodes represent words and the branches represent grammatical relationships between words.

A parser in the context of mathematical models of language generates new sentences in a language by applying a set of rules to a given grammar.

The Hidden Markov Model (HMM) represents sentences as sequences of hidden states, where each state corresponds to a particular word or phrase.

A generator in the context of mathematical models of language translates sentences from one language to another by applying a set of rules to a given grammar.

The Vector Space Model (VSM) represents words as points in a multidimensional space, where the dimensions correspond to the words' semantic features.

A discriminator in the context of mathematical models of language specifies the meaning of words in a language by assigning them to semantic categories.

The Hidden Markov Model (HMM) represents sentences as sequences of symbols, where each symbol represents a word or phrase.

A transducer in the context of mathematical models of language translates sentences from one language to another by applying a set of rules to a given grammar.

The Bayesian Network Model (BNM) represents words as nodes in a network, where the connections between nodes represent the semantic relationships between words.

A decoder in the context of mathematical models of language translates sentences from one language to another by applying a set of rules to a given grammar.

The Vector Space Model (VSM) represents sentences as sequences of words, where each word is represented by a vector of numbers.