This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Counting Two-State Transition-Tour Sequences
November 1996 (vol. 45 no. 11)
pp. 1337-1342

Abstract—This paper develops a closed-form formula, f(k), to count the number of transition-tour sequences of length k for bistable machines. It is shown that the function f(k) is related to Fibonacci numbers. Some applications of the results in this paper are in the areas of testable sequential machine designs, random testing of register data paths, and qualification tests for random pattern generators.

[1] H. Ural, “Formal Methods for Test Sequence Generation,” Computer Comm., vol. 15, no. 5, pp. 311-325, June 1992.
[2] A.V. Aho, A.T. Dahbura, D. Lee, and M.U. Uyar, “An Optimization Technique for Protocol Conformance Test Sequence Generation Based on UIO Sequences and Rural Chinese Postman Tours,” IEEE Trans. Comm., vol. 39, pp. 1604-1615, 1991.
[3] S. Boyd, "The Synchronization Problem in Protocol testing and its Complexity," Information Processing Letters, vol. 48, no. 3, pp. 131-136, Nov. 1991.
[4] M.D. Smith, M.A. Horowitz, and M.S. Lam, "Efficient Superscalar Performance Through Boosting," Proc. Fifth Int'l Conf. Architectural Support for Programming Languages and Operating Systems, pp. 248-259,Boston, Oct. 1992.
[5] S. Naito and M. Tsunoyama, "Fault Detection for Sequential Machine by Transition-Tours," Proc. FTCS-11, pp. 238-243, June 1981.
[6] N.R. Saxena, R. Tangirala, and A. Srivastava, "Algorithmic Synthesis of High Level Tests for Data Path Designs," Proc. 23rd Int'l Symp. Fault-Tolerant Computing, pp. 360-369,Toulouse, France, June 1993.
[7] Zvi Kohavi, Switching and Finite Automata Theory, second edition. New Delhi: Tata McGraw-Hill Publishing Co., 1978.
[8] E.J. McCluskey, Logic Design Principles with Emphasis on Testable Semicustom Circuits, Prentice Hall, Englewood Cliffs, N.J., 1986.
[9] S.R. Makar and E.J. McCluskey, "Checking Experiments to Test Latches," Proc. 13th IEEE VLSI Test Symp., pp. 196-201, Apr. 1995.
[10] R.L. Graham, D.E. Knuth, and O. Patashnik, Concrete Mathematics- A Foundation for Computer Science. Addison-Wesley, 1989.
[11] M. Karnaugh, "The Map Method for Synthesis of Combinational Logic Circuits," Trans. AIEE. pt. I, vol. 72, no. 9, pp. 593-599, 1953.
[12] S.W. Golomb, Shift Register Sequences. Aegean Park Press, 1982.
[13] D.E. Knuth, Seminumerical Algorithms.Reading, Mass.: Addison-Wesley Publishing Company, Inc., 1969.

Index Terms:
Transition-tours, sequential machine testing, Fibonacci numbers, checking experiments, testable synthesis.
Citation:
Nirmal R. Saxena, Edward J. McCluskey, "Counting Two-State Transition-Tour Sequences," IEEE Transactions on Computers, vol. 45, no. 11, pp. 1337-1342, Nov. 1996, doi:10.1109/12.544493
Usage of this product signifies your acceptance of the Terms of Use.