Synchronizing Automata and the Cerny Conjecture

We survey several results and open problems related to synchronizing automata. In particular, we discuss some recent advances towards a solution of the Cerný conjecture.

[1]  Seymour Ginsburg,et al.  On the Length of the Smallest Uniform Experiment which Distinguishes the Terminal States of a Machine , 1958, JACM.

[2]  Masahiro Fujita,et al.  Model Checking Based on Sequential ATPG , 1999, CAV.

[3]  A. N. Trahtman.  The Černý Conjecture for Aperiodic Automata , 2005 .

[4]  Frederick C. Hennie,et al.  Finite-state Models for Logical Machines , 1968 .

[5]  Zvi Kohavi,et al.  Establishing Certain Bounds Concerning Finite Automata , 1973, J. Comput. Syst. Sci..

[6]  Seh-Woong Jeong,et al.  Synchronizing sequences and symbolic traversal techniques in test generation , 1993, J. Electron. Test..

[7]  Jarkko Kari,et al.  A Counter Example to a Conjecture Concerning Synchronizing Words in Finite Automata , 2001, Bull. EATCS.

[8]  Edward F. Moore,et al.  Gedanken-Experiments on Sequential Machines , 1956 .

[9]  Z. Kohavi,et al.  BOUNDS ON THE LENGTH OF SYNCHRONIZING SEQUENCES AND THE ORDER OF INFORMATION LOSSLESSNESS , 1971 .

[10]  Mikhail V. Volkov.  Synchronizing automata preserving a chain of partial orders , 2009, Theor. Comput. Sci..

[11]  Doug Ierardi,et al.  The complexity of oblivious plans for orienting and distinguishing polygonal parts , 2005, Algorithmica.

[12]  Borivoj Melichar,et al.  Finding Common Motifs with Gaps Using Finite Automata , 2006, CIAA.

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

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

[15]  Mikhail V. Volkov,et al.  SOME RESULTS ON ČERNÝ TYPE PROBLEMS FOR TRANSFORMATION SEMIGROUPS , 2004 .

[16]  F. C. Hennie.  Fault detecting experiments for sequential circuits , 1964, SWCT.

[17]  Beulah Rudner,et al.  STUDY OF THE APPLICATION OF CODING THEORY. , 1962 .

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

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

[20]  Rastislav Královič,et al.  Mathematical Foundations of Computer Science 2006, 31st International Symposium, MFCS 2006, Stará Lesná, Slovakia, August 28-September 1, 2006, Proceedings , 2006, MFCS.

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

[22]  Peter M. Higgins,et al.  The range order of a product of i transformations from a finite full transformation semigroup , 1988 .

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

[24]  Seh-Woong Jeong,et al.  Exact calculation of synchronization sequences based on binary decision diagrams , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[25]  A. N. Trahtman,et al.  The road coloring problem , 2007, 0709.0099.

[26]  Taylor L. Booth,et al.  Sequential machines and automata theory , 1967 .

[27]  I. K. Rystsov,et al.  In extremal combinatorial problem associated with the bound on the length of a synchronizing word in an automaton , 1987 .

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

[29]  S. Yang,et al.  Logic Synthesis and Optimization Benchmarks User Guide Version 3.0 , 1991 .

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

[31]  J. Taylor,et al.  Switching and finite automata theory, 2nd ed. , 1980, Proceedings of the IEEE.

[32]  Martin A. Fischler,et al.  Synchronizing and Representation Problems for Sequential Machines with Masked Outputs , 1970, SWAT.

[33]  Manfred Broy,et al.  Model-Based Testing of Reactive Systems, Advanced Lectures [The volume is the outcome of a research seminar that was held in Schloss Dagstuhl in January 2004] , 2005, Model-Based Testing of Reactive Systems.

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

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

[36]  Arthur Gill,et al.  Sate-Identification Experiments in Finite Automata , 1961, Inf. Control..

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

[38]  Ján Cerný,et al.  On directable automata , 1971, Kybernetika (Praha).

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

[40]  Peter H. Starke.  Eine Bemerkung über homogene Experimente , 1966, J. Inf. Process. Cybern..

[41]  Grzegorz Rozenberg,et al.  Developments in Language Theory II , 2002 .

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

[43]  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.

[44]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[45]  Carl Pixley,et al.  Minimum Length Synchronizing Sequences of Finite State Machine , 1993, 30th ACM/IEEE Design Automation Conference.

[46]  Mikhail V. Volkov,et al.  Synchronizing Automata with a Letter of Deficiency 2 , 2006, Developments in Language Theory.

[47]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[48]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

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

[50]  A. N. Trahtman,et al.  An efficient algorithm finds noticeable trends and examples concerning the Černy conjecture , 2006, 0709.1197.

[51]  Jorge Almeida,et al.  Representation theory of finite semigroups, semigroup radicals and formal language theory , 2008 .

[52]  Viktor Mikhaĭlovich Glushkov,et al.  An Introduction to Cybernetics , 1957, The Mathematical Gazette.

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

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