New Algorithms for Finding Short Reset Sequences in Synchronizing Automata

Finding synchronizing sequences for the finite automata is a very important problem in many practical applications (part orienters in industry, reset problem in biocomputing theory, network issues etc). Problem of finding the shortest synchronizing sequence is NP-hard, so polynomial algorithms probably can work only as heuristic ones. In this paper we propose two versions of polynomial algorithms which work better than well-known Eppstein's Greedy and Cycle algorithms. Keywords—Synchronizing words, reset sequences, Cerný Conjecture.

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

[2]  Balas K. Natarajan.  An algorithmic approach to the automated design of parts orienters , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[3]  Ehud Shapiro,et al.  DNA molecule provides a computing machine with both data and fuel , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Arto Salomaa,et al.  Compositions over a Finite Domain: From Completeness to Synchronizable Automata , 2001, A Half-Century of Automata Theory.

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

[6]  E. Shapiro,et al.  Programmable and autonomous computing machine made of biomolecules , 2001, Nature.

[7]  Mikhail V. Volkov,et al.  Synchronizing monotonic automata , 2003, Theor. Comput. Sci..

[8]  Balas K. Natarajan,et al.  Some Paradigms for the Automated Design of Parts Feeders , 1989, Int. J. Robotics Res..