Is grammar Markovian?

Abstract
One of the cardinal assumptions about the nature of grammar is that it is a formal system, meaning that the operations and symbols in the grammar should have a precise meaning, so that one can tell precisely how it functions, and whether a given structure is in fact created by the grammar. The issue of how much information is available to the grammar, viewed as a computational device that computes structures, is called the issue of computational complexity. The computational powers of various grammars, and the capacity of recognition devices to characterize as licit or not the structures that they generate, has been the province of mathematical linguistics, but has also occasionally been felt to have implications for empirical syntactic theory. One central question that has raised its head over the years is the question of whether or not grammar ( which is now referred to as CHL, for Computation of Human Language (Chomsky (1995)) is Markovian, an issue first raised in Chomsky (1957). For a computational device to be Markovian, it can only make reference to the current state that the device is in, when deciding what the next state of the device can be; it cannot, for example, make reference to alternative states, earlier states, future states, or , as a consequence of its being a formal system, factors outside of the computational device.
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