Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages
MetadataShow full item record
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.
Cite this version of the work
Janusz Brzozowski, Corwin Sinnamon (2017). Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages. UWSpace. http://hdl.handle.net/10012/13159
Showing items related by title, author, creator and subject.
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 ...
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 ...