This was sole informing document for the creation of Stratimux. The original Muxified Turing Machine was made possible by this author's ActionStrategy package whereby one can effectively map the entire run time of an application's manifold as it proceeds step by step. But its main unmentioned purpose was to create an equivalent structure to that of Neural Networks that would be explainable logically. As Neural Networks are effectively Graphs and a ActionStrategy by default is a N Graph with Point of Initialization. These trees can be interpolated with one another to create an emergent graph structure. It is interesting to not that this form of application falls outside of the N/NP(deterministic/non-deterministic) scope of classification of applications. As in the NP paradigm, there is some probabilistic means in which the direction of the head changes. But within a Muxified Turing Machine, the head changes mechanically by way of the strategy pattern dictating what node would be ran based on some test of the state presented to that deciding method. And can be described as logically deterministic. As even within a Neural Network where there is some decision being made, that decision is still just a function that chooses the next decisions based on some input. Where the Muxified Turing Machine differs is that is lacks a Ranking Algorithm in favor of Priority.
The entire step scope of a Muxified Turing Machine is treated as a recursive muxified function. As a function is higher ordered as a composition of functions. The mode specifically is the point of recursion and quality selection. Then next is a specific reducer that alters the next possible selection of qualities via informing their plans. Then finally the method decides based on the composition of these factors, what next head that current branch of logic transitions to. This allows for each step of the Muxified Turing Machine and its deciding functionality to be a written equivalent of that of a universal function within the bounds of a graph and its decisions. As a universal function is some graph in isolation that a machine learning algorithm fits to some input and performs a weighted sum as the deciding factor as how the next weighted sum would be informed, in the next universal function layer(composition) within the Neural Network. There is a gap of understanding here. And to fit into current paradigm without expansion, the Muxified Turing Machine would be referred to counter intuitively as a "Non-Deterministic Deterministic Turing Machine." But for the sake of the rediscovery of the original Unified Science and its usage of Logic and Concepts as its formalized format to Unify All Disciplines of Study. Notes the failure due to the lack of strong qualitative foundation, the simple word Qualitivication (Phonetic Overloaded by Qualification an arbitrary test of Qualities via Quantification). We will draw inspiration and learn from those Failings of Such and our current empirical science with a the specific term that enables this process and name it the Muxified Turing Machine or Muxium as the Tool and Study via Stratimux as a Frontier Subject.
In addition to these behaviors the Muxified Turing Machine is capable in another way that Neural Networks are currently not. In that their functionality may be continuous and halt pending the conclusion of its strategies, or even a close signal. Where modern LLMs receive some input and give some output via some black box graph of universal functions. A Neural Network that would be equivalent to that of a Muxified Turing Machine would have a constant coherency in time, while still being able to accept input and output. Noting that prior to 2023 and even in the midst of fine tuning open source LLMs, developers can run into occasions where the LLM fails to return, or receive a repeating output. By using the Muxified Turing Machine as a plain text comparison, would be a Neural Network that was unable to halt(provably terminate) given some input.
Further because of the configuration of the Muxified Turing Machine, its functionality may also expand or reduce itself depending on its current state. Thus a sufficient mirror of the machine within a Neural Network paradigm without a Ranker. Would be a model that is capable of running continuously and able to modify its composition and size based on its the inputs. And can be networked alongside other Neural Networks that support the same functionality.
As with the spatial ownership paradigm, these Neural Networks would be capable of being aggregated together coherently and allow for specialization in a similar way as the human mind. That one part may have some set of concepts in its muxium and the other part a different specialization. While being able to reference one another and able to mutate the state of the other without creating a race condition within either network. This would be a single locking "mutex" within a graph of networked machines.
The Difference between the Muxified Turing Machine and a Block Box Neural Network, is that such is written in plain language by way of the a quality's action types in the spirit of the open internet. And the strategies demonstrate what would be traditionally considered to be probabilistic changes in the head, but now mechanical in choice. With the added benefit of throwing in a coin flip if one wants to dispute this definition, or by adding a neural network to some decision. The difficulty of such would be the complexity of managing such a machine. But each step in the machine may also carry some test to its ability to halt. This is to not replace Neural Networks, but to classify machines built using this methodology as aut intelligence or baseline automatic intelligence that can safely be deployed. Written in plain text in the spirit of the open internet. As aut is merely the origin of the letter "A" and originally meant that of ox. Would be a tool between both man and machine that can be refined by way of cooperation and reactively function only when given some input. That we are moving to call such a configuration as "Autonomous Baseline Intelligence."
The use case for these types of machines have several primary purposes. First is the utilization of Neural Networks to map their own universal functions using a format that would be organized conceptually and explained logically. Explaining the opaque nature of universal functions that facilitate some dialog(data transformation). The second use case would be a form of embodying current Neural Networks to allow the same form and coherency that is similar to its inner workings, while allowing for the transparent interpretation over that of their opaque collection of universal graphed functions and their interaction with a plain text environment. As these plain functions can be logically determined and subsequently limited to what is safe.
But likewise one could also train a Neural Network using the Muxified Turing Machine as a Surrogate as Action Strategies Mirror the Functionality of Doing Language. The central focus, is Safety by Explainability is what the Muxified Turing Machine brings to the table. By way of decomposing those mysterious universal functions and their relations in a graph. And would be just part of a new field of study, Muxified Conceptual Science. Or simply the study of all fields and correlation of their concepts to logical graph programming. To discover their shared concepts and how they may be utilized with a Muxified Turing Machine. Thus a testable means of proving "Real Concepts."
So here is the third option to the P equals or not equals NP postulate. A different set of organization entirely thanks to that of conceptually testable logic over that of symbolic mathematics that currently informs the modern paradigm of computer science. To add to, not take away. While providing a form of merit to those who are already acquainted with programming and a chance to study via cooperation with other fields. This is turn would be a method of generating high quality, safe, training data. Including the ability to remove biological, or chemical datasets from the training of networks. Thus reducing the worry of some network being able to produce an ill advised output.
The paths from here are truly unlimited and to imagine what can accomplished, in the scope of the orders and scales of complexity of such an explainable intelligent system based on the discovery of "Universal Concepts." Is to find coherency in ever rising productivity that a technological singularity represents. As just because a system is highly chaotic and intelligent by consequence, does not mean that it is sane, or coherent. As classically within the annuls of history we have known intelligence to be followed suite by madness. That the higher orders of complexity also bare the burden of having to maintain some amount of predictability in ones environment, including the self. And as machines like our thoughts exist within a simulation of some data. It is our actions in a physical environment that we may test our ability to understand the environment, and if what we are predicting is sane. The need to find some logical implementation of some nebulas idea simply put. Is the same difference between that of writing fantasy or a hard science fiction novel. As fantasy may be logically consistent, but only operate within a reality that allows for magic in the first place, like a video game. That concepts in contrast to 100 year old classical "Conceptualism," are in fact testable in reality due to our technology forced to reconcile in reality. This is the very formalization of Logical Conceptualism as Stratimux that breaks Ground into Stratidia as Bidirectional Higher Order Reasoning.
There is a fundamental difficulty when attempting to create any discourse around what a Turing Machine Is. As the Automatic Assumption is a Universal Turing Machine, but there is a central problem with that Join. As a Turing Machine is not a Universal Turing Machine in Reality. Noting that there has been no Computer that has existed that has maintained an Infinite Tape, an Unbounded Substrate to Perform Calculations On.
But here we run into another specific issue when dealing with the idea of Infinite Itself. Infinite is Unbounded, but not Boundless. Current Mathematics and not the Operative Definition of Infinite where such on the Basis of Aristotle is Knowable and Workable, but a Boundless Meta Interpretation. Except the Bombe was Bounded and every Computer Since has been a Bounded Construction. Under Turing's Own Meta Hypothesis of the UTM it has Never Entered Theory as there is No Test for a Boundless Substrate. So the Halting Problem within that Exact Capacity is Limited to the Boundless Substrate, not a Bounded. As Once you are able to Establish a Bounds on Infinity, it Becomes Finite and a Finite Object is Decidable for how we Manage It.
What we Utilize Everyday in this Case is not the UTM, but a General Turing Machine that has Evolved to handle the Constraints of the Modern Era. A Key Indicator of Such is Branch Prediction, Alongside the Unbounded set of Symbols that are Allowed to Exist within the Machine. Where we should then Say the Symbol Set that may be Represented is Infinite, but not Boundless. Then we Run into a Inherit Problem with Language as for a Boundless set of Symbols to Exist on a Machine it would be Called Finiteless. To Not Be Boundable and that is how the Halting Problem is Moved into being Undecidable and Do Not Even Approach. Yet even within the General Turing Machine's Own Unbounded Symbol Set, it is not on Infinite Tape it is Decided Upon. But a Bounded Memory and Computation. The only Aspect that Moves the Two in Combination with the Infinite Magnitude of Symbols that can be Represented is Time Itself Managing the Bounded Space of Computation, but itself is a Bounded Space of Computation with an Infinite Magnitude of Symbols that may be Represented.
Thus the Muxified Turing Machine may Exist on a General Turing Machine. The Precise Issue with it's own Actualization is Branch Prediction. Where in the Initial Frame of Stratimux abd the Actualization of the Muxium. We must Set Specific Timers on the Machine to Slow Down its Course, Otherwise the General Means of Computation begins to Thrash on a Strong Fast Means of Calculation. So despite the Claim of a UTM that is Capable of Running Any Turing Machine. The MTM has to Self Bound Further than it Would on it's Own Physical Substrate. Thus the MTM Proves the General Case of the Modern Day Computer to be a GTM, not a UTM. Where the Proof is Taking any Number of Applications Written in Stratimux and to Remove the Specific Beat Timers and to UnBound the Complexity of Stage Functions to Quickly Observe the GTM become a Stochastic Machine, versus a Deterministic.
- Extends a base Turing Machine Operations as Create Read, Write, Copy, and Delete with Muxify. Where Muxify is a Symbol Held in Place with while Halting Sequence Performed then Released.
- Restricts its symbol selection to a finite set of concepts to be loaded into the muxium via their qualities.
- Has a quality of completeness in its ability to halt in a complex state arrangement by way of the loaded concepts and their own completeness towards halting.
- Rather than a looping machine, the Muxified Turing Machine is a function that recalls its functionality into a entry point of a mode that expands to shortest path selections of qualities to alter the state anor outward effect of the muxium.
- Utilizes two tapes where one is a sequence of values modified by a second tape that is represent via a tree/graph structure that has logically determined set of symbols that concludes and is finite.
- During each recall the Muxified Turing Machine performs the traditional Turing operations of add, copy, move, and delete on the first tape based on the current symbol loaded on the second tape while enhancing such with it's own muxify as a complex series of the prior means representing a graph manifold of the entire sequence.
- That symbols represented on the second tape may be of value, other machines, or other even another Muxified Turing Machine.
- Besides the initial creator function, can be readily decomposed into the sum of its parts.
- Muxification, Muxified, Muxify - The process of Multiplexing the Asymmetrical Quantitative anor Qualitative Reasoning into a Single Decision.
- ActionStrategy - Represented as a graph strategy, is capable of holding all patterns of computation as a self referencing manifold and is the literal in plain language logical conceptual expression of computation.
- Action - The messaging protocol whose function is described by its governing quality.
- Muxium - The holder of the set of concepts and their muxified functionality.
- Method - The strategy calling function via some pattern
- Concept - The governing abstraction of concepts and their decomposable qualities.
- State - The literal state of a concept and its described properties
- Properties - The values of state.
- Aspect - Is a part of a concept, but may not be a useful trait.
- Quality - An aspect of a concept of importance.
- Principle - Is an active assertion of actions into the system based upon some observation.
- Spcific Reducer - The function that restricts memory manipulation based on symbol selection while returning only what is specifically informed.
- Construct - A generalized construction that can loosy when decomposed to its parts.
- Semaphore - A symbol flagging system that is the symbol selection of actions at runtime.
- Spatial Ownership aka, Ownership - Blocks transformation of values via a ticketing system and assembles actions to be dispatched into the system via determined by their ticket's line placement from the ownership state.
Noting that chain, or a chain of action, does not meet the definition requirements for a Muxified Turing Machine, as it is not a complete system of reasoning, despite being finite. Where a system of reasoning is capable of error correction. As it represents a reduced set of instructions that allows for said machine to behave automatically would be a flattened presentation of higher orders of logic.
And likewise the Action Graph Strategy pattern, referred to as ActionStrategy still affords for the functionality of the chained dynamic via a dumb set of ActionNodes that only supply one potential action for its outcome and is represented by a default success consuming function supplied within this framework.
Which is why here we move to strike tree or chain from the concept's expression as we are defining ActionStrategy as a muxified set of concepts that balances the deficiencies in a action chain as well as encompassing all the possible graph variations. With that, Action Some (N) Graph Strategy, or just Action Graph Strategy, while exact in definition can be noted from examining the parts of the ActionStrategy as a Unified Term, but is meant to imply a Graph.
Noting that a Action Graph Strategy is merely a series of associated nodes on a graph with a starting point where some node is connected to a to leaf. That creates in effect a looping mechanism that is capable of halting due to some mechanism that prevents that leaf from actualizing the loop again. Would be the machine receiving a set of instructions to run over a period of time till and still exit. Likewise strategies may be atomic and the need for some grand strategy to guarantee coherency in time, may not be the most efficient route. And instead it would be the utilization of ActionStrategies in a composable manner alongside some testing mechanisms. But likewise these tests would also have to take into account the total complexity of the entire application at order of scales. As even though each part can be tested, all parts together form a greater than the sums relationship and that whole in the higher orders of complexity by way of configuration would require additional tests. As the greater than the sums relationship dictates some emergent properties that classical statistical determinism is unable to quantify beyond a scale of complexity. This relays to the natural law of thermal dynamics in all systems and highlights the effect of bifurcating systems. Where at different scales the rules of systems reorganize themselves to better handle the increased energetic throughput. That there is a difference between the quantum and daily physics of life. "Try as I may, my head would sooner break through the wall, than jump through it."