# Enumeration Conservation Law and Natural Parallelism of the *D*-algorithms for Test Generation and Modeling in Engineering Diagnostics

- 22 Downloads

## Abstract

In Part I, typical and minimum diagnostic labyrinths that graphically model generation and modeling of tests were introduced using the *D*-algorithms. Notions of the value of diagnostic enumeration and the minimum value Pr_{min} of this enumeration were introduced. A diagnostic unit was introduced for measuring this enumeration. A counterpart of the well-known “physical” Noether theorem was proved relying on the symmetry of the minimum diagnostic labyrinths. The theorem gives rise to the enumeration conservation law Pr_{min} = 2*N* – *n* – *m* = const for sequential *D*-algorithms, where *N* is the number of arcs in the logical network of a combinational device, and *n* and *m* are, respectively, the numbers of its external inputs and outputs. Efficiency of the *D*-algorithm was defined, and a formula to calculate it was presented. For the ideal test generator which is a theoretical prototype of the physical generators with scaled, potentially unlimited, throughput, the mechanism of natural parallelism was substantiated. In Part II, described was a mechanism of natural (hypermass) parallelism of the ideal test generator, which uses new parallel-sequential *D*-algorithms to design discrete devices and, thus, appreciably enhance test generation and diagnostic modeling. The mechanism was shown to overcome the lower constraint on the time of solution of the direct and inverse problems which is imposed by the enumeration conservation law for the sequential *D*-algorithms. The spectrum of the parallel-sequential *D*-algorithms was described in general terms. A diagnostic counterpart of the Noether theorem was proved, and the corresponding numerical forms of the enumeration conservation law were deduced for them, as well as for the sequential algorithms. Conclusions substantiated a new direction of the research program for the diagnostic theory of tolerance and similitude—the possibility of using the mechanism of natural parallelism to solve systems of logical, algebraic, and differential equations.

## Keywords

Inverse Problem Test Generation External Input Physical Generator Logical Network## Preview

Unable to display preview. Download preview PDF.

## REFERENCES

- 1.Pravil'shchikov, P.A., Elements of the Diagnostic Theory of Tolerance and Similarity,
*Avtom. Telemekh.*, 1992, no. 10, pp. 141–160.Google Scholar - 2.Karibskii, V.V., Parkhomenko, P.P., Sogomonyan, E.S., and Khalchev, V.F.,
*Osnovy tekhnicheskoi diagnostiki*(Fundamentals of Engineering Diagnostics), Moscow: Energiya, 1976.Google Scholar - 3.Chang, H.Y., Manning, E., and Metze, G.,
*Fault Diagnosis of Digital Systems*, New York: Wiley, 1970. Translated under the title*Diagnostika neispravnostei TsVM*, Moscow: Mir, 1972.Google Scholar - 4.Roth, J.P., Diagnosis of Automata Failures: A Calculus and a Method,
*IBM J. Res. Dev.*, 1966, no. 7, pp. 18–32.Google Scholar - 5.Roth, J.P., Bouricius, W.G., and Schneider P.R., Programmed Algorithm to Compute and Distinguish Between Failures in Logic Circuits,
*IEEE Trans. Electron. Comput.*, 1967, vol. EC-16, no. 5, pp. 567–580.Google Scholar - 6.Armstrong, B., A Deductive Method for Simulating Faults in Logic Circuits,
*IEEE Trans. Comput.*, 1971, vol. C-20, no. 5, pp. 321–336.Google Scholar - 7.Putzolu, G.R. and Roth, J.P., A Heuristic Algorithm for the Testing of Asynchronous Circuit,
*IEEE Trans. Comput.*, 1971, vol. C-20, no. 6, pp. 639–647.Google Scholar - 8.Goel, P., An Implicit Enumeration Algorithm to Generate Tests for Combinational Logic Circuits,
*IEEE Trans. Comput.*, 1981, vol. C-30, no. 3, pp. 215–222.Google Scholar - 9.Strassberg, S.W., ASIC Test: It's a New Ball Game,
*EDN*, 1994, pp. 168–173.Google Scholar - 10.Deep-submicron Test (A Design & Test Roundtable),
*IEEE Design Test Comput.*, 1994, vol. 11, no. 1, pp. 102–110.Google Scholar - 11.Zorian, Y., Error-free Product,
*IEEE Design Test Comput.*, 2001, vol. 18, no. 4, p. 1.Google Scholar - 12.Agraval, P., Agraval, V., Cheng, K.T., and Tutundjian, R., Fault Simulation in Pipeline Multiprocessor System,
*Proc. 20-th ITS*, 1989, pp. 727–734.Google Scholar - 13.Sergeev, B.G., Hardware Acceleration of CLSI Circuit Modeling,
*Miroelektronika*, 1989, vol. 18, no. 4, pp. 554–560.Google Scholar - 14.Kravitz, S.A., Brayant, R.E., and Rutenbar, R.A., Massively Parallel Switch-Level Simulation: A Feasibility Study,
*IEEE Trans. Computer-Aided Design*, 1991, vol. 10, no. 7, pp. 871–874.CrossRefGoogle Scholar - 15.Pravil'shchikov, P.A., “Diogen,” the First Diagnostic Coprocessor for Personal Computers IBM PC-386 and IBM PC-486, in
*Produktsiya NPO “Orion” dlya grazhdanskogo priborostroeniya i narodnogo khozyaistva*(Products of the “Orion” Scientific-Industrial Association for Civil Instrumentation and National Economy), Moscow: Research Center “INFORMTEKhNIKA”, 1993, pp. 50–55.Google Scholar - 16.Pravil'shchikov, P.A., Parallel-sequential
*D*-algorithms of the First Type and the Enumeration Conservation Law for Them,*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2000, no. 3, pp. 13–33.Google Scholar - 17.Pravil'shchikov, P.A., Parallel-sequential
*D*-algorithms of the Second Type and the Enumeration Conservation Law for Them,*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2000, no. 3, pp. 33–53.Google Scholar - 18.Pravil'shchikov, P.A., Parallel-sequential
*D*-algorithms of the Third Type and the Enumeration Conservation Law for Them,*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2000, no. 4, pp. 93–102.Google Scholar - 19.Pravil'shchikov, P.A., Parallel
*D*-algorithms and the Enumeration Conservation Law for Them,*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2000, no. 4, pp. 103–116.Google Scholar - 20.Pravil'shchikov, P.A., Problem of VLSI Circuit Verification and Its Solution by “Computing Sieve” Using the Enumeration Conservation Law,
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2001, no. 4, pp. 45–61.Google Scholar - 21.Schneider, P.R., On the Necessity to Examine
*D*-chains in Diagnostic Test Generation-An Example,*IBM J. Res. Dev.*, 1967, no. 1, pp. 34–37.Google Scholar - 22.Harary, F.,
*Graph Theory*, Reading: Addison-Wesley, 1969. Translated under the title*Teoriya grafov*, Moscow: Mir, 1973.Google Scholar - 23.Gannon, C., Error Detection Using Path Testing and Static Analysis,
*Computer*, 1979, vol. 12, no. 8, pp. 26–31.Google Scholar - 24.Pravil'shchikov, P.A., Symmetry of the Diagnostic Labyrinth and the Enumeration Conservation Law,
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 1996, no. 3, pp. 52–68.Google Scholar - 25.Pravil'shchikov, P.A., The Enumeration Conservation Law for the Test Design Algorithms Based on Calculation of Cubic Complexes and Featuring Necessary Determinacy,
*Oboronnyi kompleks-nauchnotekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2000, no. 1, pp. 11–42.Google Scholar - 26.Pravil'shchikov, P.A., An Algorithm to Generate a Sequence Distinguishing Two Failures in the Sequential Device,
*Avtom. Telemekh.*, 1974, no. 1, pp. 156–173.Google Scholar - 27.Noether, E., Invariante Variationsproblem,
*Gott. Nachr., Math. Phys. Klasse*, 1918, vol. 2, pp. 235.Google Scholar - 28.
*Variatsionnye printsipy mekhaniki, ikh razvitie i primenenie v fizike*, (Variational Principles of Mechanics, Their Development, and Use in Physics ), Polak, L.S., Ed., Moscow: Fizmatgiz, 1960.Google Scholar - 29.Medvedev, B.V.,
*Nachala teoreticheskoi fiziki*(Principles of Theoretical Physics), Moscow: Energiya, 1977.Google Scholar - 30.Bogolyubov, N.N. and Shirkov, D.V.,
*Vvedenie v teoriyu kvantovykh polei*(Quantum Field Theory: An Introduction), Moscow: Nauka, 1984.Google Scholar - 31.Feinmann, R.,
*The Character of Physical Law (A Series of Lectures Recorded by the BBC at Cornell University USA)*, London: Cox and Wyman, 1965. Translated under the title*Kharakter fizicheskikh zakonov*, Moscow: Nauka, 1987.Google Scholar - 32.Frid E.,
*Abstract Algebra-Elimination*, Budapest: Muszaki Konyvkiado, 1972. Translated under the title*Elementarnoe vvedenie v abstraktnuyu algebru*, Moscow: Mir, 1979.Google Scholar - 33.Sholomov, L.A.,
*Logicheskie metody issledovaniya diskretnykh modelei vybora*(Logic Methods to Study the Discrete Models of Choice), Moscow: Nauka, 1989.Google Scholar - 34.Pravil'shchikov, P.A., Individualizing the Structural Law of Test Choice for the Test Design Algorithms Using Calculation of the Cubic Complexes,
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 1996, no. 3.Google Scholar - 35.Val'kovskii, V.A.,
*Rasparallelivanie algoritmov i programm (strukturnyi podkhod)*(Deserialization of Algorithms and Programs (A Structural Approach), Moscow: Radio i Svyaz', 1989.Google Scholar - 36.Pravil'shchikov, P.A., Verification of the Sensitive Paths and Serialization of
*D*-algorithms in the Diagnostic Coprocessor “DIOGEN” for Personal Computers,*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 1996, no. 4, pp. 27–35.Google Scholar - 37.Pravil'shchikov, P.A., Mechanism of Natural Parallelism of the Ideal Test Generator,
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2000, no. 2, pp. 27–35.Google Scholar - 38.Pravil'shchikov, P.A., On Conceptual-Theoretical Substantiation of the Universal Diagnostic Processors,
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 1996, no. 1, pp. 24–32.Google Scholar - 39.Pravil'shchikov, P.A., On Experimental-and-Practical Substantiation of the Universal Diagnostic Processors,
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 1996, no. 1, pp. 33–43.Google Scholar - 40.Pravil'shchikov, P.A., Research Program of the Diagnostic Theory of Tolerance and Similitude
*Oboronnyi kompleks-nauchno-tekhnicheskomu progressu Rossii*(Defense Complex to Scientific and Technical Progress of Russia), 2001, no. 1, pp. 58–80.Google Scholar - 41.Newell, A. and Simon, G., GPS-A Program Modeling Human Thought, in
*Computer and Thought (A Collection of Articles)*, Feigenbaum, E.A. and Feldman, J., Eds., New York: McGraw-Hill, 1963. Translated under the title*Vychislitel'nye mashiny i myshlenie*, Moscow: Mir, 1967.Google Scholar - 42.Podol'skii, S.Ya. and Pravil'shchikov, P.A., Modeling and Diagnosis of Analog LSI Circuits,
*VOT*, 1990, no. 4(68), pp. 20–25.Google Scholar - 43.Pravil'shchikov, P.A., Test Generation for Programs,
*Avtom. Telemekh.*, 1977, no. 5, pp. 147–160.Google Scholar