Dimensional Confluence Algebra of Information Space Modulo Quotient Abstraction Relations in Automated Problem Solving Paradigm

Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics defined by alphabetically abstracting net block homomorphism. We obtain minimum prerequisites for the comprehensive connector pairs in a multitude dimensional rewriting closure generating confluence in Participatory algebra for different horizontal and vertical level projections modulo abstraction relations constituting formal semantics for confluence in information space. Participatory algebra with formal automata syntax in its entirety representing automated problem solving paradigm generates rich variety of multitude confluence harmonizers under each fundamental abstraction relation set, horizontal structure mapping and vertical process iteration cardinality.Comment: The current work is an application as a continuation for my previous works in arXiv:1305.5637 and arXiv:1308.5321 using the key definitions of them sustaining consistency, consequently references being minimized. Readers are strongly advised to resort to the mentioned previous works for preliminaries. arXiv admin note: text overlap with arXiv:1408.137

The congruence theory of closure properties of regular tree languages

AbstractBoolean operations, tree homomorphisms and their converses, and forest product, in special cases σ-catenation, x-product, x-quotient and x-iteration, preserve the regularity of forests. These closure properties are proved algebraically by using congruences of term algebras which saturate the forests operated on and constructing, by means of them, a congruence which saturates the product forest. The index of the constructed congruence is finite, if the congruences saturating the forests to operate are of finite indexes. The cardinalities of ranked and frontier alphabets are arbitrary. The preservation of recognizability is a straightforward consequence of those congruence constructions and the Nerode type of congruence characterization for recognizable forests. Furthermore, the constructed congruences can also be applied directly to construct explictly tree automatas to recognize the product forests

The Mathematical Abstraction Theory, The Fundamentals for Knowledge Representation and Self-Evolving Autonomous Problem Solving Systems

The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with gluing forms connecting in- and out-edges to nodes. Nets are caused to undergo transformations in conceptual level by type wise differentiated intervening net rewriting systems dispersing problems to abstract parts, matching being determined by substitution relations. Achieved sets of conceptual nets constitute congruent classes. New results are obtained within construction of problem solving systems where solution algorithms are derived parallel with other candidates applied to the same net classes. By applying parallel transducer paths consisting of net rewriting systems to net classes congruent quotient algebras are established and the manifested class rewriting comprises all solution candidates whenever produced nets are in anticipated languages liable to acceptance of net automata. Furthermore new solutions will be added to the set of already known ones thus expanding the solving power in the forthcoming. Moreover special attention is set on universal abstraction, thereof generation by net block homomorphism, consequently multiple order solving systems and the overall decidability of the set of the solutions. By overlapping presentation of nets new abstraction relation among nets is formulated alongside with consequent alphabetical net block renetting system proportional to normal forms of renetting systems regarding the operational power. A new structure in self-evolving problem solving is established via saturation by groups of equivalence relations and iterative closures of generated quotient transducer algebras over the whole evolution.Comment: This article is a part of my thesis giving the unity for both knowledge presentation and self-evolution in autonomous problem solving mathematical systems and for that reason draws heavily from my previous work arxiv:1305.563

Rengastusvuosi 2021

Non peer reviewe

Patent nr. FI63702

<p>Method and Apparatus in order to transfer liquid with help of atmospheric pressure</p

US Patent US20070050318 A1

<p>Graph Rewriting based Parallel System for Automated Problem Solving</p

Mathematical Entanglement Theory of Parallel Realities

<p>ABSTRACT</p> <p>The current study with proceedings totally of mathematical nature regards our reality as embodied by problem solving paradigm on quotient algebras over crusts of different gravity. Because each entity perception can be presented by realizations of a net in the appropriate algebra, concept and processes thereof on those entities are dealt with subject to iteratively derived multiple order and dimension abstract algebra quotient operations. Crust elements are multiple order and dimension partially quotient algebra nets classified by possessed gravity, Cartesian element the saturating sets constituted by multidimensional abstraction relations classes. Entangled crust operations share common causality with respect to the quotient transducers they generate. Conceptual realities are set as abstract partial algebra comprising crust elements and of the next order quotient transducers over them. Perceptual multiverse manifested as realizations of conceptual realities over set of algebras will be shown to be generated by realizations of ITG-type entangled parallel realities and by satisfying commutative property establishes a closure system.</p

Conceptualizing Conditions for Transducer Induced Algebraic Lattice of Successively Embedded Subalgebras of Multilevel Quotient Abstraction Algebra in Renetting Based Transducer Information Field

<p>ABSTRACT </p> <p> </p> <p>The work at hand concentrates in achieving via conceptualizing condition characterization transducer induced multi-order algebraic lattice of successively embedded algebras. Carrier nets of transducers satisfying specific out-arity requirements enable to be smoothed for related multi-level partitions, because nets are possible to inward-arity supplement if and only if they are reducible to operational letters by singularifying<i> </i>renetting systems, i.e. conceptualizing conditions are fulfilled. Consequently multi-order successively embedded subalgebra lattice family in Generalized Participatory family algebra is generated via iterative quotient induced conceptualizing conditions satisfied transducer carrier nets induced multi-order embedded multidimensional abstraction relation classes. </p