Harkening back to my prior discussion of minimizing cyclic NOR logic as an approach to algorithmic information's reformulation, hence the "is" half of AIXI's unification of "is" (AIT) with "ought" (Sequential Decision Theory):
Lossless compression is time-reversed decompression, so minimal reversible sequential logic (MRSL?) would seem interesting. I've brought this up before, particularly with regard to the "bit bucket" connections of the reversible logic gates, raising the issue of how one correctly penalizes (measures the "loss") of such models of the data. I suppose one can imagine a restriction on the topology such that no dangling connections are allowed except at the 2 ends, so as to collapse that measure into the already-required measure of the state initialization. But this seems rather an unprincipled kludge. While it is true that, occasionally, a bit string will have a minimum NOR circuit -- or reversible gate circuit -- such that nothing happens on any input (it's all implied by the initialization state and connectivity), usually, it will be lower complexity to have a clocked input on the compressed end, with a "tape" of sorts containing the residual entropy, since encoding that tape as a generating circuit would require more bits to describe the total system. So that residual entropy must correspond in a nontrivial way to one part of the so-called "two part message" (assuming we restrict ourselves to UTM languages): The message as opposed to the model part. If we allow reversible gates, and don't simply kludge our way out of the question of how to measure the "bit bucket" connections by requiring all but one of them to be closed within the circuit, is there any way of thinking about this kind of MRSL that sheds light on the nature of the minimal NOR network outputting the same target bit stream? ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Tff4216f5c5e90891-M6eb1cf14ce8003830fde2469 Delivery options: https://agi.topicbox.com/groups/agi/subscription
