Describing Homing and Distinguishing Sequences for Nondeterministic Finite State Machines via Synchronizing Automata

There is a long standing problem of the study of homing and distinguishing sequences for deterministic and nondeterministic Finite State Machines (FSMs) which are widely used in many applications. A homing sequence allows establishing the state of the given FSM after applying the sequence while a distinguishing sequence allows learning the state of the given FSM before the sequence is applied. On the other hand, other sequences, namely, synchronizing sequences, have been thoroughly studied for finite automata. For a synchronizing automaton, there is a state such that a synchronizing sequence takes the automaton from any state to this state. There are many papers reported on such automata as well as on the complexity of synchronizing sequences. In this paper, given a complete nondeterministic FSM, we propose a method for deriving a corresponding finite automaton such that the set of all homing (or distinguishing) sequences coincides with the set of all synchronizing sequences of the derived automaton.

[1]  N. Yevtushenko,et al.  Studying the separability relation between finite state machines , 2007 .

[2]  Nina Yevtushenko,et al.  Adaptive Testing of Deterministic Implementations Specified by Nondeterministic FSMs , 2011, ICTSS.

[3]  Canan Güniçen,et al.  The relation between preset distinguishing sequences and synchronizing sequences , 2014, Formal Aspects of Computing.

[4]  Grzegorz Rozenberg,et al.  Theory Is Forever , 2004, Lecture Notes in Computer Science.

[5]  Victor V. Kulyamin,et al.  On the complexity of existence of homing sequences for nondeterministic finite state machines , 2014, Programming and Computer Software.

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

[7]  Nina Yevtushenko,et al.  Adaptive Homing and Distinguishing Experiments for Nondeterministic Finite State Machines , 2013, ICTSS.

[8]  David Lee,et al.  Testing Finite-State Machines: State Identification and Verification , 1994, IEEE Trans. Computers.

[9]  耕二 麓,et al.  Self－rewetting溶液を用いた自励振動型ヒートパイプの性能向上に関する研究(ブタノールとペンタノールの場合) , 2011 .

[10]  Masami Ito,et al.  Some Results on Directable Automata , 2004, Theory Is Forever.

[11]  Fan Zhang,et al.  Optimal Transfer Trees and Distinguishing Trees for Testing Observable Nondeterministic Finite-State Machines , 2003, IEEE Trans. Software Eng..

[12]  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.

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

[14]  Robert M. Hierons,et al.  Using adaptive distinguishing sequences in checking sequence constructions , 2008, SAC '08.

[15]  Ana R. Cavalli,et al.  On adaptive experiments for nondeterministic finite state machines , 2014, International Journal on Software Tools for Technology Transfer.

[16]  Rajeev Alur,et al.  Distinguishing tests for nondeterministic and probabilistic machines , 1995, STOC '95.

[17]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[18]  Boris A. Trakhtenbrot,et al.  Finite automata : behavior and synthesis , 1973 .

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

[20]  Nina Yevtushenko,et al.  On the Length of Homing Sequences for Nondeterministic Finite State Machines , 2013, CIAA.