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R.c. Holt - One of the best experts on this subject based on the ideXlab platform.

  • Structural manipulations of software architecture using Tarski Relational algebra
    Reverse Engineering, 1998. Proceedings. Fifth Working Conference on, 1998
    Co-Authors: R.c. Holt
    Abstract:

    A software architecture is typically drawn as a nested set of box and arrow diagrams. The boxes represent components of the software system and the edges represent interactions These diagrams correspond to typed graphs, in which there are a number of “types” or “colors” of edges, and in which there is a distinguished “contain” relation that represents the system hierarchy (the nesting of boxes). During reverse engineering, one often transforms such diagrams in various ways to make them easier to understand. These transformations include edge aggregation, box abstraction (closing a box to hide its contents), and box separation (separating a box from its surrounding system). Such transformations are essential in helping make software architecture diagrams useful in practice. Paper shows how structural manipulations such as these can be specified and automatically carried out in a notation based on Tarski's Relational algebra. The operators in this algebra include Relational Composition, union, subtraction, etc. These operators are supported in a language called Grok. Grok scripts have been used in manipulating the graphs for large scale software systems, such as Linux, to help in program visualization and understanding

Ivo Düntsch - One of the best experts on this subject based on the ideXlab platform.

  • Relation algebras and their application in temporal and spatial reasoning
    2020
    Co-Authors: Ivo Düntsch
    Abstract:

    Abstract Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by Relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations must exist, given several basic operations, such as Boolean operations on relations, Relational Composition and converse. Each equation in the calculus corresponds to a theorem, and, for a situation where there are only nitely many relations, one can construct a Composition table which can serve as a look up table for the relations involved. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. In this sense, Relational calculus is pointless. Relation algebras were introduced into temporal reasoning by Allen [1] and into spatial reasoning by Egenhofer and Sharm

Hitoshi Furusawa - One of the best experts on this subject based on the ideXlab platform.

  • Relational representation theorem for powerset quantales
    RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science, 2012
    Co-Authors: Koki Nishizawa, Hitoshi Furusawa
    Abstract:

    The paper gives a sufficient condition for a quantale to be isomorphic to a sub-quantale of the quantale whose elements are binary relations on a set and whose order and monoid structure are respectively given by inclusion and Relational Composition and the identity relation. A quantale has such a Relational representation, if its underlying lattice is a powerset of some set. We also show some other equivalent conditions of the sufficient condition.

Jas Semrl - One of the best experts on this subject based on the ideXlab platform.

  • finite representability of semigroups with demonic refinement
    Algebra Universalis, 2021
    Co-Authors: Robin Hirsch, Jas Semrl
    Abstract:

    The motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled Relationally. Relational Composition (; ) models sequential runs of two programs and demonic refinement ( $$\sqsubseteq $$ ) arises from the partial order given by modeling demonic choice ( $$\sqcup $$ ) of programs (see below for the formal Relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ of abstract $$(\le , \circ )$$ structures isomorphic to a set of binary relations ordered by demonic refinement with Composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ . We prove that a finite representable $$(\le , \circ )$$ structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with Composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

Koki Nishizawa - One of the best experts on this subject based on the ideXlab platform.

  • Relational representation theorem for powerset quantales
    RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science, 2012
    Co-Authors: Koki Nishizawa, Hitoshi Furusawa
    Abstract:

    The paper gives a sufficient condition for a quantale to be isomorphic to a sub-quantale of the quantale whose elements are binary relations on a set and whose order and monoid structure are respectively given by inclusion and Relational Composition and the identity relation. A quantale has such a Relational representation, if its underlying lattice is a powerset of some set. We also show some other equivalent conditions of the sufficient condition.