Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages
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A language L over an alphabet Σ is suffix-convex if, for any words x,y,z∈Σ∗, whenever z and xyz are in L, then so is yz. Suffix-convex languages include three special cases: left-ideal, suffix-closed, and suffix-free languages. We examine complexity properties of these three special classes of suffix-convex regular languages. In particular, we study the quotient/state complexity of boolean operations, product (concatenation), star, and reversal on these languages, as well as the size of their syntactic semigroups, and the quotient complexity of their atoms.
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Janusz Brzozowski, Corwin Sinnamon (2017). Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages. UWSpace. http://hdl.handle.net/10012/13159
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Brzozowski, Janusz; Szykuła, Marek; Ye, Yuli (Springer, 2017-08-04)The state complexity of a regular language is the number of states in a minimal deterministic finite automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic ...
Brzozowski, Janusz; Szykuła, Marek (Elsevier, 2017-11-01)We study various complexity properties of suffix-free regular languages. A sequence (Lk,Lk+1,…) of regular languages in some class, where n is the quotient complexity of Ln, is most complex if its languages Ln meet the ...
Brzozowski, Janusz; Szykuła, Marek (Elsevier, 2017-09-05)We solve an open problem concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a suffix-free language with n left quotients (that is, with state complexity n) is at most (n−1)n−2+n−2 ...