The state complexity of star-complement-star
Galina Jiraskova, Jeffrey Shallit
TL;DR
This paper establishes tight asymptotic bounds on the state complexity of the operation transforming a language L into (c(L*))*, resolving an open question in automata theory.
Contribution
It provides the first precise asymptotic bounds for the state complexity of the star-complement-star operation, advancing understanding of automata transformations.
Findings
Matching asymptotic upper and lower bounds are derived.
The bounds resolve an open problem in the field.
The results clarify the complexity of nested star and complement operations.
Abstract
We resolve an open question by determining matching (asymptotic) upper and lower bounds on the state complexity of the operation that sends a language L to (c(L*))*, where c() denotes complement.
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Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Advanced Algebra and Logic