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D. Lee, M. Yannakakis, "Testing FiniteState Machines: State Identification and Verification," IEEE Transactions on Computers, vol. 43, no. 3, pp. 306320, March, 1994.  
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@article{ 10.1109/12.272431, author = {D. Lee and M. Yannakakis}, title = {Testing FiniteState Machines: State Identification and Verification}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {3}, issn = {00189340}, year = {1994}, pages = {306320}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.272431}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Testing FiniteState Machines: State Identification and Verification IS  3 SN  00189340 SP306 EP320 EPD  306320 A1  D. Lee, A1  M. Yannakakis, PY  1994 KW  finite state machines; computational complexity; protocols; conformance testing; finitestate machines; state identification; state verification; complexity; testing; PSPACEcomplete; polynomial time algorithm; adaptive distinguishing sequence; unique input output sequences; protocol testing. VL  43 JA  IEEE Transactions on Computers ER   
We study the complexity of two fundamental problems in the testing of finitestate machines. 1) Distinguishing sequences (state identification). We show that it is PSPACEcomplete to determine whether a finitestate machine has a preset distinguishing sequence. There are machines that have distinguishing sequences, but only of exponential length. We give a polynomial time algorithm that determines whether a finitestate machine has an adaptive distinguishing sequence. (The previous classical algorithms take exponential time.) Furthermore, if there is an adaptive distinguishing sequence, then we give an efficient algorithm that constructs such a sequence of length at most n(n/spl minus/1)/2 (which is the best possible), where n is the number of states. 2) Unique input output sequences (state verification). It is PSPACEcomplete to determine whether a state of a machine has a unique input output sequence. There are machines whose states have unique input output sequences but only of exponential length.
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