Some results on the generalized star-height problem
Information and Computation
Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Handbook of formal languages, vol. 1
Logic and Visual Information
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
VL '99 Proceedings of the IEEE Symposium on Visual Languages
The Expressiveness of Spider Diagrams
Journal of Logic and Computation
Fragments of spider diagrams of order and their relative expressiveness
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Creating a second order diagrammatic logic
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
On the expressiveness of spider diagrams and commutative star-free regular languages
Journal of Visual Languages and Computing
On the expressiveness of second-order spider diagrams
Journal of Visual Languages and Computing
Twelve years of diagrams research
Journal of Visual Languages and Computing
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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.