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

Extending a multi-set relational algebra to a parallel environment

Parallel database systems will very probably be the future for high-performance data-intensive applications. In the past decade, many parallel database systems have been developed, together with many languages and approaches to specify operations in these systems. A common background is still missing, however. This paper proposes an extended relational algebra for this purpose, based on the well-known standard relational algebra. The extended algebra provides both complete database manipulation language features, and data distribution and process allocation primitives to describe parallelism. It is defined in terms of multi-sets of tuples to allow handling of duplicates and to obtain a close connection to the world of high-performance data processing. Due to its algebraic nature, the language is well suited for optimization and parallelization through expression rewriting. The proposed language can be used as a database manipulation language on its own, as has been done in the PRISMA parallel database project, or as a formal basis for other languages, like SQL

A multi-set extended relational algebra: a formal approach to a practical issue

The relational data model is based on sets of tuples, i.e. it does not allow duplicate tuples an a relation. Many database languages and systems do require multi-set semantics though, either because of functional requirements or because of the high costs of duplicate removal in database operations. Several proposals have been presented that discuss multi-set semantics. As these proposals tend to be either rather practical, lacking the formal background, or rather formal, lacking the connection to database practice, the gap between theory and practice has not been spanned yet. This paper proposes a complete extended relational algebra with multi-set semantics, having a clear formal background and a close connection to the standard relational algebra. It includes constructs that extend the algebra to a complete sequential database manipulation language that can either be used as a formal background to other multi-set languages like SQL, or as a database manipulation language on its own. The practical usability of the latter option has been demonstrated in the PRISMA/DB database project, where a variant of the language has been used as the primary database languag

Integrability and Fusion Algebra for Quantum Mappings

We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As an important class of examples, we present the Yang-Baxter structure of the Gel'fand-Dikii mapping hierarchy, that we have introduced in previous papers, together with the corresponding explicit commuting family of quantum invariants.Comment: 26 page