On Completeness of Cost Metrics and Meta-Search Algorithms in \$-Calculus

In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. We started the population process of these new classes. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation -- the \$-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in \$-calculus

Cloud Computing and Cloud Automata as A New Paradigm for Computation

Cloud computing addresses how to make right resources available to right computation to improve scaling, resiliency and efficiency of the computation. We argue that cloud computing indeed, is a new paradigm for computation with a higher order of artificial intelligence (AI), and put forward cloud automata as a new model for computation. A high-level AI requires infusing features that mimic human functioning into AI systems. One of the central features is that humans learn all the time and the learning is incremental. Consequently, for AI, we need to use computational models, which reflect incremental learning without stopping (sentience). These features are inherent in reflexive, inductive and limit Turing machines. To construct cloud automata, we use the mathematical theory of Oracles, which include Oracles of Turing machines as its special case. We develop a hierarchical approach based on Oracles with different ranks that includes Oracle AI as a special case. Discussing a named-set approach, we describe an implementation of a high-performance edge cloud using hierarchical name-oriented networking and Oracle AI-based orchestration. We demonstrate how cloud automata with a control overlay allows microservice network provisioning, monitoring and reconfiguration to address non-deterministic fluctuations affecting their behavior without interrupting the overall evolution of computation

State of the Art of Information Technology Computing Models for Autonomic Cloud Computing

In the paper we present several models of computation for autonomic cloud computing. In particular, we justify that for autonomic cloud computing if we require perfect self-reflection, we need models of computation going beyond Turing machines. To approximate self-reflection, models below Turing machines are sufficient. The above claims are illustrated using as an example the DIME Network Architecture

Undecidability and Complexity for Super-Turing Models of Computation

It seems that intelligent complex systems will require formalisms having richer behavior than Turing machines. Very little is known about the relations (e.g., the expressiveness and/or effectiveness) between new super-Turing models of computation. The objective of this paper is an attempt to establish a hierarchy of expressiveness of super-Turing models. Truly, a new theory of undecidability and complexity for super-Turing models has to be developed. Some preliminary steps have been done in this paper by introducing a-decidable and i-decidable algorithms and U-complete, D-complete, and H-complete complexity classes that were inspired by NP-complete and PSPACE-complete classes for intractable problems. This paper should be understood as a preliminary step leading to feasible approximate solutions of Turing machine undecidable problems, in a similar way as approximate, randomized, and parallel algorithms allow for feasible solutions for intractable problems

Application of Information Theory Entropy as a Cost Measure in the Automatic Problem Solving

We study the relation between Information Theory and Automatic Problem Solving to demonstrate that the Entropy measure can be used as a special case of $-Calculus Cost Functions measure. We hypothesize that Kolmogorov Complexity (Algorithmic Entropy) can be useful to standardize$-Calculus Search (Algorithm) Cost Function