Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages
نویسندگان
چکیده
The spider diagram logic forms a fragment of constraint diagram logic and is 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 logic. 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.
منابع مشابه
Defining star-free regular languages using diagrammatic logic
Spider diagrams are a recently developed visual logic that make statements about relationships between sets, their members and their cardinalities. By contrast, the study of regular languages is one of the oldest active branches of computer science research. The work in this thesis examines the previously unstudied relationship between spider diagrams and regular languages. In this thesis, the ...
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