Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages Export

@incollection{delaney:sdooaahosfrl, abstract = {The spider diagram logic forms a fragment of the constraint diagram logic and was designed to be primarily used as a diagrammatic software specification tool. Our interest is in using the logical basis of spider diagrams and the existing known equivalences between certain logics, formal language theory classes and some automata to inform the development of diagrammatic logics. Such developments could have many advantages, one of which would be aiding software engineers who are familiar with formal languages and automata to more intuitively understand diagrammatic logics. In this paper we consider relationships between spider diagrams of order (an extension of spider diagrams) and the star-free subset of regular languages. We extend the concept of the language of a spider diagram to encompass languages over arbitrary alphabets. Furthermore, the product of spider diagrams is introduced. This operator is the diagrammatic analogue of language concatenation. We establish that star-free languages are definable by spider diagrams of order equipped with the product operator and, based on this relationship, spider diagrams of order are as expressive as first order monadic logic of order.}, author = {Delaney, Aidan and Taylor, John and Thompson, Simon}, citeulike-article-id = {3322345}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/978-3-540-87730-1_18}, doi = {10.1007/978-3-540-87730-1_18}, journal = {Diagrammatic Representation and Inference}, keywords = {diagrams, formal-methods, spider-diagrams}, pages = {172--187}, posted-at = {2008-09-23 16:33:14}, priority = {0}, title = {Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages}, url = {http://dx.doi.org/10.1007/978-3-540-87730-1_18}, year = {2008} }

TY - CHAP ID - delaney:sdooaahosfrl L3 - citeulike-article-id:3322345 N2 - The spider diagram logic forms a fragment of the constraint diagram logic and was designed to be primarily used as a diagrammatic software specification tool. Our interest is in using the logical basis of spider diagrams and the existing known equivalences between certain logics, formal language theory classes and some automata to inform the development of diagrammatic logics. Such developments could have many advantages, one of which would be aiding software engineers who are familiar with formal languages and automata to more intuitively understand diagrammatic logics. In this paper we consider relationships between spider diagrams of order (an extension of spider diagrams) and the star-free subset of regular languages. We extend the concept of the language of a spider diagram to encompass languages over arbitrary alphabets. Furthermore, the product of spider diagrams is introduced. This operator is the diagrammatic analogue of language concatenation. We establish that star-free languages are definable by spider diagrams of order equipped with the product operator and, based on this relationship, spider diagrams of order are as expressive as first order monadic logic of order. JF - Diagrammatic Representation and Inference EP - 187 TI - Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages SP - 172 KW - diagrams KW - formal-methods KW - spider-diagrams AU - Delaney, Aidan AU - Taylor, John AU - Thompson, Simon PY - 2008/// UR - http://dx.doi.org/10.1007/978-3-540-87730-1_18 ER -