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Language Learning and Nonlinear Dynamical Systems
, 2003
"... stems can be mapped directly to any member of a large class of lowdimensional chaotic dynamical systems. The importance of this is that for a given chaotic dynamical system to be a model of a given language, we may set up a target probability distribution over its statespace, such that if it visit ..."
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stems can be mapped directly to any member of a large class of lowdimensional chaotic dynamical systems. The importance of this is that for a given chaotic dynamical system to be a model of a given language, we may set up a target probability distribution over its statespace, such that if it visits its statespace according to this distribution it will generate the language that is desired. A specific dynamical system is chosen as a model for learning. This is known as the 2d tentmap. We derive a learning algorithm for this particular dynamical system. This algorithm is based on a matrix approximation of the FrobeniusPerron operator. Examples of learning regular, contextfree and contextsensitive languages are provided. BIOGRAPHICAL SKETCH Mark Andrews was born in Ireland in 1973. In 1995, he graduated with a BA from the National University of Ireland. The same year, he began graduate study in Cornell Univeristy in Ithaca, New York. In 1998, he received a M.Sc from Cornell. In
Stochastic ContextFree Grammars
, 2004
"... Introduction: Strings, Grammars & Formal Languages Stochastic contextfree grammars, or SCFGs, are generative systems of stochastic languages. In other words, a SCFG specifies a probability distribution over the set of all possible strings that are concatenated from a finite alphabet . Defin ..."
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Introduction: Strings, Grammars & Formal Languages Stochastic contextfree grammars, or SCFGs, are generative systems of stochastic languages. In other words, a SCFG specifies a probability distribution over the set of all possible strings that are concatenated from a finite alphabet . Definition 1 An alphabet is a finite set of symbols. It denoted here by }. Definition 2 The kth power of an alphabet , denoted , is the set of strings of length k made from the elements of . Example 1 For the alphabet 1}, where V = 2. will be set of strings, made from the elements of , that are of length 1, or 1}. Likewise, 01, 10, 11}, {000, 001, 010, 011, 100, 101, 110, 111}, etc. Definition 3 # , or Kleene closure of , is the union of all powers of the alphabet, or # = . . . . Definition 4 A formal language L is defined as L # . In other words, L is a (possibly infinite) set of strings, each formed by concatenation from a finite set of