… \), these reset thresholds are attained by members of what we will call the Černý family. This
… The Černý family presented in this paper contains for all \(n\le 10\) a binary PFA with n states …

… PFAs (with partial transition function) can have … to binary PFAs. However, asymptotics do
not give conclusions for fixed n . We prove that the maximal reset threshold for binary PFAs is …

… the Cerný family gives reset thresholds of polynomial order. We prove that PFAs in the family
are not extremal … an improvement of Martyugin’s prime number construction of binary PFAs. …

… This ternary PFA can be transformed to a binary PFA by a … Here we extend the analysis
to n = 7, for which Cerný’s DFA … These extreme cases require up to eight symbols, where for …

… Extremal Binary PFAs with Small Number of States”, by Stijn Cambie, Michiel de Bondt, and
Henk Don, considers a family of binary PFAs … states (conjectured by Cerný to be the maximal …

… This ternary PFA can be transformed to a binary PFA by a … Here we extend the analysis
to n = 7, for which Cerný’s DFA … These extreme cases require up to eight symbols, where for …

… Cerný also presented in [40] a family of DFAs having reset … quadratic reset threshold, called
extremal automata, are very … We say that a matrix is binary if it has entries in {0, 1}. We call …

… reset threshold and that do not resemble the Černý family? … Note that we state it for sets
of binary NZ-matrices but it more … , here we found an extremal automaton of quadratic reset …

… in Subsection 3.2: we show that a random binary set of n × n matrices generated by setting
each … our families differ from the Černý automaton and the other known families of extremal …

… Special thanks are also due to our families, particularly to Robert's wife Marie and his
children Maruska and Robik, for their understanding during the writing of this book, which was …