The efficient market hypothesis, that prices reflect all available information, imputes a meaning to market moving information, a view of information foreign to standard information theory. Here, after reviewing properties that make a proposed formula for ``pragmatic information" a plausible measure of meaning, we consider the role that the receiver's position in the machine hierarchy corresponding to the Chomsky hierarchy play in extracting this meaning. We show that a receiver at a given level in the hierarchy may be unable to extract pragmatic information from a message because it appears random, yet a receiver at a higher level in the hierarchy finds the message perfectly intelligible. Also, the maximum processing rates for messages of different levels of hierarchy serve as a kind of channel capacity, leading to a tradeoff between the amount of pragmatic information extracted and the extraction time. All of the above suggests a recasting of market efficiency in terms of ``computational efficiency'', i.e. the question of whether a market appears efficient to a participant with a given computational endowment. Successful trading strategies implementable as finite state machines, the lowest level in the hierarchy, imply departures from ``finite state efficiency''. We show, via a stylized example, how pragmatic information can characterize the ensuing approach to finite state efficiency. We also show that actual market dynamics can be more computationally intractable than any finite state machine can process by proving the PSPACE-completeness of the processing of the smart order routing systems of major brokerage firms. We conclude that computational efficiency is the norm and pragmatic information can characterize any departure from it.

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