Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Formal languages: an introduction and a synopsis
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
Automata, Languages, and Machines
Automata, Languages, and Machines
VL '99 Proceedings of the IEEE Symposium on Visual Languages
An n log n algorithm for minimizing states in a finite automaton
An n log n algorithm for minimizing states in a finite automaton
The Expressiveness of Spider Diagrams
Journal of Logic and Computation
A Decidable Constraint Diagram Reasoning System
Journal of Logic and Computation
Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Finite automata and their decision problems
IBM Journal of Research and Development
Introducing Second-Order Spider Diagrams for Defining Regular Languages
VLHCC '10 Proceedings of the 2010 IEEE Symposium on Visual Languages and Human-Centric Computing
Heterogeneous proofs: spider diagrams meet higher-order provers
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
On the expressiveness of second-order spider diagrams
Journal of Visual Languages and Computing
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Spider diagrams provide a visual logic to express relations between sets and their elements, extending the expressiveness of Venn diagrams. Sound and complete inference systems for spider diagrams have been developed and it is known that they are equivalent in expressive power to monadic first-order logic with equality, MFOL[=]. In this paper, we further characterize their expressiveness by articulating a link between them and formal languages. First, we establish that spider diagrams define precisely the languages that are finite unions of languages of the form K@C^@?, where K is a finite commutative language and @C is a finite set of letters. We note that it was previously established that spider diagrams define commutative star-free languages. As a corollary, all languages of the form K@C^@? are commutative star-free languages. We further demonstrate that every commutative star-free language is also such a finite union. In summary, we establish that spider diagrams define precisely: (a) languages definable in MFOL[=], (b) the commutative star-free regular languages, and (c) finite unions of the form K@C^@?, as just described.