Synchronizing automata preserving a chain of partial orders

We present a new class of automata which strictly contains the class of aperiodic automata and shares with the latter certain synchronization properties. In particular, every strongly connected automaton in this new class is synchronizing and has a reset word of length ⌊n(n+1)/6⌋ where n is the number of states of the automaton.

[1]  Václav Koubek,et al.  Rank Problems for Composite Transformations , 1995, Int. J. Algebra Comput..

[2]  T. Kanade.  Model-Based Testing of Reactive Systems , 2005 .

[3]  Mikhail V. Volkov,et al.  Synchronizing Automata and the Cerny Conjecture , 2008, LATA.

[4]  Robert McNaughton,et al.  Counter-Free Automata (M.I.T. research monograph no. 65) , 1971 .

[5]  Avraham Trakhtman,et al.  The Černý Conjecture for Aperiodic Automata , 2021, Discret. Math. Theor. Comput. Sci..

[6]  L. Dubuc,et al.  Sur Les Automates Circulaires et la Conjecture de Cerný , 1998, RAIRO Theor. Informatics Appl..

[7]  I. K. Rystsov,et al.  Reset Words for Commutative and Solvable Automata , 1997, Theor. Comput. Sci..

[8]  Jarkko Kari,et al.  Synchronizing Finite Automata on Eulerian Digraphs , 2003, MFCS.

[9]  Mikhail V. Volkov,et al.  Synchronizing generalized monotonic automata , 2005, Theor. Comput. Sci..

[10]  R. McNaughton,et al.  Counter-Free Automata , 1971 .

[11]  Sven Sandberg,et al.  Homing and Synchronizing Sequences , 2004, Model-Based Testing of Reactive Systems.

[12]  J. Pin.  On two Combinatorial Problems Arising from Automata Theory , 1983 .

[13]  Dmitry S. Ananichev.  The Mortality Threshold for Partially Monotonic Automata , 2005, Developments in Language Theory.

[14]  Kenneth Y. Goldberg,et al.  Orienting polygonal parts without sensors , 1993, Algorithmica.

[15]  Arto Salomaa,et al.  Many-Valued Truth Functions, Cerny's Conjecture and Road Coloring , 1999, Bull. EATCS.

[16]  Arto Salomaa,et al.  Composition sequences for functions over a finite domain , 2003, Theor. Comput. Sci..

[17]  David Eppstein,et al.  Reset Sequences for Monotonic Automata , 1990, SIAM J. Comput..

[18]  P. FRANKL,et al.  An Extremal Problem for two Families of Sets , 1982, Eur. J. Comb..