Derivatives of Regular Expressions
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Decidable Hierarchies of Starfree Languages
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Level 5/2 of the Straubing-Thérien Hierarchy for Two-Letter Alphabets
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Languages polylog-time reducible to dot-depth 1/2
Journal of Computer and System Sciences
Classifying regular languages by a split game
Theoretical Computer Science
Descriptional and Computational Complexity of Finite Automata
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Descriptional and computational complexity of finite automata---A survey
Information and Computation
Classifying regular languages via cascade products of automata
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Languages vs. ω-languages in regular infinite games
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Machines that can output empty words
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Polylog-time reductions decrease dot-depth
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Perfect correspondences between dot-depth and polynomial-time hierarchy
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
On the expressiveness of second-order spider diagrams
Journal of Visual Languages and Computing
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A regular event is star-free if it can be denoted by a regular expression involvingonly Boolean operations and concatenation (dot). The family of star-free events can be constructed by alternately applying Boolean operations and concatenation. This approach leads to a hierarchy of star-free events, and to the definition of ''dot-depth'' of a star-free event which appears to be useful as a measure of the complexity of the event. Properties of dot-depth are examined; for example, it is shown that the dot-depthof a star-free event cannot be increased by the quotient operation with respect to any language, nor can it be increased by multiplying the event by a finite language. The use of two-sided quotients adds insight to the theory of star-free events and permits the derivation of some new properties of these events; in particular, every star-free event has at least one quotient which is either empty or full. The family of star-free events has been shown to be equivalent to the family ofregular noncounting events, and also corresponds to the family of finite automata whose semigroups have no nontrivial subgroups (group-fee automata). In the final section an algorithm is developed for constructing a star-free expression for the event accepted by a group-free finite automaton. An upper bound for the dot-depth of the event is found. We conjecture that for each n=0, there exist star-free events of dot depth n. We have been able to show this only for n@?2; the general problem remains open.