The DFAs of Finitely Different Languages
Andrew Badr, Ian Shipman
TL;DR
This paper explores the structure of DFAs for finitely different regular languages, characterizes the non-uniqueness of minimal such automata, and proposes a method to find these f-minimal DFAs.
Contribution
It introduces the concept of f-minimal DFAs for finitely different languages and provides a solution to their minimization problem.
Findings
Structural similarities among DFAs of finitely different languages
Characterization of non-uniqueness of f-minimal DFAs
A proposed method to find f-minimal DFAs
Abstract
Two languages are "finitely different" if their symmetric difference is finite. We consider the DFAs of finitely different regular languages and find major structural similarities. We proceed to consider the smallest DFAs that recognize a language finitely different from some given DFA. Such "f-minimal" DFAs are not unique, and this non-uniqueness is characterized. Finally, we offer a solution to the minimization problem of finding such f-minimal DFAs.
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Taxonomy
Topicssemigroups and automata theory · Natural Language Processing Techniques · Advanced Algebra and Logic