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Three Approaches to Data Analysis pp 3–60Cite as

Test Theory: Tools and Applications

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 41))

Abstract

Test Theory (TT) was created by Yablonskii and Chegis in the middle of fifties of the last century as a tool for analysis of problems connected with control and diagnosis of faults in circuits. The first short paper [75] was published in 1955, and the principal paper [10] - in 1958. In 1966 Dmitriev, Zhuravlev and Krendelev [16] adapted test approach to the study of pattern recognition (prediction) problems. Later TT was developed in the two directions related to tools and applications.

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References

  1. Alkhalid, A., Chikalov, I., Hussain, S., Moshkov, M.: Extensions of Dynamic Programming as a New Tool for Decision Tree Optimization. In: Ramanna, S., Howlett, R.J., Jain, L.C. (eds.) Emerging Paradigms in Machine Learning and Applications. SIST, vol. 13, pp. 17–36. Springer, Heidelberg (2012)

    Google Scholar 

  2. Alkhalid, A., Chikalov, I., Moshkov, M.: On Algorithm for Building of Optimal α-Decision Trees. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS, vol. 6086, pp. 438–445. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Amin, T., Chikalov, I., Moshkov, M., Zielosko, B.: Dynamic programming algorithm for optimization of β-decision rules. In: Szczuka, M., Czaja, L., Skowron, A., Kacprzak, M. (eds.) Proc. of Int’l Workshop Concurrency, Specification and Programming, CS&P 2011, Pułtusk, Poland, pp. 10–16. Białystok University of Technology (2011)

    Google Scholar 

  4. Amin, T., Chikalov, I., Moshkov, M., Zielosko, B.: Dynamic programming approach for exact decision rule optimization. In: Skowron, A., Suraj, Z. (eds.) Special Volume Dedicated to the Memory of Professor Zdzislaw Pawlak. ISRL, Springer (to appear, 2012)

    Google Scholar 

  5. Armstrong, D.B.: On finding a nearly minimal set of fault detection tests for combinatorial logic nets. IEEE Trans. Electron. Comput. EC-15, 66–73 (1966)

    Article  Google Scholar 

  6. Baskalova, L.V., Zhuravlev, Y.I.: A model of recognition algorithms with representative samples and systems of supporting sets. USSR Comput. Maths. and Mathematical Phys. 21(5), 189–199 (1981)

    Article  Google Scholar 

  7. Borodina, Y.V.: Synthesis of easily-tested circuits in the case of single-type constant malfunctions at the element outputs. In: Proc. of the Ninth International Seminar on Discrete Mathematics and its Applications, pp. 64–65. MSU Publishers, Moscow (2007) (in Russian)

    Google Scholar 

  8. Borodina, Y.V.: Synthesis of easily-tested circuits in the case of single-type constant malfunctions at the element outputs. Moscow University Computational Mathematics and Cybernetics 32, 42–46 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Borodina, Y.V.: Synthesis of easily-tested circuits in the case of single-type constant malfunctions at the element outputs. Abstract of dissertation for the degree of candidate of physical and mathematical sciences (2008) (in Russian)

    Google Scholar 

  10. Chegis, I.A., Yablonskii, S.V.: Logical methods of control of work of electric schemes. Trudy Mat. Inst. Steklov. 51, 270–360 (1958) (in Russian)

    MathSciNet  MATH  Google Scholar 

  11. Chikalov, I.: Algorithm for constructing of decision trees with minimal average depth. In: Proc. of the Eighth Int’l Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, Spain, vol. 1, pp. 376–379 (2000)

    Google Scholar 

  12. Chikalov, I.V.: On Algorithm for Constructing of Decision Trees with Minimal Number of Nodes. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 139–143. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Chikalov, I.: Average Time Complexity of Decision Trees. ISRL, vol. 21. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  14. Chikalov, I., Hussain, S., Moshkov, M.: Relationships for cost and uncertainty of decision trees. In: Skowron, A., Suraj, Z. (eds.) Special Volume Dedicated to the Memory of Professor Zdzisław Pawlak. ISRL. Springer (to appear, 2012)

    Google Scholar 

  15. Chikalov, I.V., Moshkov, M.J., Zelentsova, M.S.: On Optimization of Decision Trees. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 18–36. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Dmitriyev, A.N., Zhuravlev, Y.I., Krendelev, F.P.: On mathematical principles for classification of objects and phenomena. Diskret. Analiz 7, 3–15 (1966) (in Russian)

    Google Scholar 

  17. Dmitriyev, A.N., Zhuravlev, Y.I., Krendelev, F.P.: On a principle of classification and prediction of geological objects and phenomena. Geol. Geofiz. 5, 50–64 (1968) (in Russian)

    Google Scholar 

  18. Dudina, J.V., Knyazev, A.N.: On complexity of recognition of words from languages generated by context-free grammars with one nonterminal symbol. In: Vestnik of Lobachevsky State University of Nizhny Novgorod. Mathematical Simulation and Optimal Control, vol. 2, pp. 214–223 (1998) (in Russian)

    Google Scholar 

  19. Dyukova, E.V., Zhuravlev, Y.I.: Discrete analysis of feature descriptions in recognition problems of high dimensionality. Computational Mathematics and Mathematical Physics 40, 1214–1227 (2000)

    MathSciNet  MATH  Google Scholar 

  20. Eldred, R.D.: Test routines based on symbolic logic statements. J. ACM 6(1), 33–36 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  21. Feige, U.: A threshold of ln n for approximating set cover (preliminary version). In: Proc. of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 314–318. ACM, New York (1996)

    Chapter  Google Scholar 

  22. Goldman, R.S., Chipulis, V.P.: Diagnosis of iteration-free combinatorial circuits. Diskret. Analiz 14, 3–15 (1969) (in Russian)

    Google Scholar 

  23. Goldman, S.A., Kearns, M.J.: On the complexity of teaching. In: Warmuth, M.K., Valiant, L.G. (eds.) Proc. of the Fourth Annual Workshop on Computational Learning Theory, COLT 1991, Santa Cruz, California, USA, pp. 303–314. Morgan Kaufmann (1991)

    Google Scholar 

  24. Hegedüs, T.: Generalized teaching dimensions and the query complexity of learning. In: Maass, W. (ed.) Proc. of the Eigth Annual Conference on Computational Learning Theory, COLT 1995, Santa Cruz, California, USA, pp. 108–117. ACM, New York (1995)

    Chapter  Google Scholar 

  25. Hellerstein, L., Pillaipakkamnatt, K., Raghavan, V., Wilkins, D.: How many queries are needed to learn. J. ACM 43, 840–862 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  26. Johnson, D.S.: Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9, 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  27. Karavai, M.F.: Diagnosis of tree-like circuits in arbitrary basis. Automation and Telemechanics 1, 173–181 (1973) (in Russian)

    Google Scholar 

  28. Knyazev, A.: On Recognition of Words from Languages Generated by Linear Grammars with one Nonterminal Symbol. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 111–114. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  29. Knyazev, A.: On recognition of words from languages generated by context-free grammars with one nonterminal symbol. In: Proc. of the Eighth Int’l Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, Spain, vol. 1, pp. 1945–1948 (2000)

    Google Scholar 

  30. Konstantinov, R.M., Koroleva, Z.E., Kudryavtsev, V.B.: Combinatory logic approach to problems of predicting ore yields. Problemy Kibernet. 31, 25–41 (1976) (in Russian)

    Google Scholar 

  31. Korshunov, A.D.: The length of minimum tests for rectangular tables. I. Cybernetics and Systems Analysis 6, 723–733 (1970)

    Google Scholar 

  32. Kospanov, E.S.: An algorithm for the construction of sufficiently simple tests. Diskret. Analiz 1, 43–47 (1966)

    MathSciNet  Google Scholar 

  33. Kudryavtsev, V.B., Andreev, A.E.: Test recognition. Journal of Mathematical Sciences 169(4), 457–480 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  34. Laskowski, M.C.: Vapnik-Chervonenkis classes of definable sets. J. London Math. Society 45, 377–384 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  35. Madatyan, K.A.: On complete tests for contact circuits without repetitions. Problemy Kibernet. 23, 103–118 (1970) (in Russian)

    Google Scholar 

  36. Madatyan, K.A.: Construction of single test for contact circuits. In: Collection of Works on Mathematical Cybernetics, pp. 77–86. Computer Centre of USSR Academy of Sciences, Moscow (1981) (in Russian)

    Google Scholar 

  37. Moore, E.F.: Gedanken-experiments on sequential machines. In: Automata Studies. Annals of Mathematical Studies, vol. 34, pp. 129–153. Princeton University Press, Princeton (1956)

    Google Scholar 

  38. Moshkov, M.J.: Conditional tests. Problemy Kibernet. 40, 131–170 (1983) (in Russian)

    MathSciNet  Google Scholar 

  39. Moshkov, M.J.: Decision trees with quasilinear checks. Trudy IM SO RAN 27, 108–141 (1994) (in Russian)

    MathSciNet  Google Scholar 

  40. Moshkov, M.J.: Complexity of deterministic and nondeterministic decision trees for regular language word recognition. In: Bozapalidis, S. (ed.) Proc. of the 3rd International Conference Developments in Language Theory, DLT 1997, Thessaloniki, Greece, pp. 343–349. Aristotle University of Thessaloniki (1997)

    Google Scholar 

  41. Moshkov, M.J.: Diagnosis of constant faults in circuits. In: Mathematical Problems of Cybernetics, vol. 9, pp. 79–100. Nauka Publishers, Moscow (2000) (in Russian)

    Google Scholar 

  42. Moshkov, M.J.: Time Complexity of Decision Trees. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 244–459. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  43. Moshkov, M.J., Chikalov, I.: On algorithm for constructing of decision trees with minimal depth. Fundam. Inform. 41(3), 295–299 (2000)

    MathSciNet  MATH  Google Scholar 

  44. Moshkov, M.J., Piliszczuk, M., Zielosko, B.: Partial Covers, Reducts and Decision Rules in Rough Sets – Theory and Applications. SCI, vol. 145. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  45. Moshkov, M.J., Zielosko, B.: Combinatorial Machine Learning – A Rough Set Approach. SCI, vol. 360. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  46. Moshkova, A.: On Diagnosis of Retaining Faults in Circuits. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 513–516. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  47. Moshkova, A.: On time complexity of retaining fault diagnosis in circuits. In: Proc. of the Eighth Int’l Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, Spain, vol. 1, pp. 372–375 (2000)

    Google Scholar 

  48. Nigmatullin, R.G.: The fastest descent method for covering problems. In: Proc. Questions of Precision and Efficiency of Computer Algorithms, Kiev, USSR, vol. 5, pp. 116–126 (1969) (in Russian)

    Google Scholar 

  49. Noskov, V.: On dead-end and minimal tests for a certain class of tables. Diskret. Analiz 12, 27–49 (1968) (in Russian)

    MathSciNet  MATH  Google Scholar 

  50. Noskov, V.N.: Diagnostic tests for logic diagram inputs. Diskret. Analiz 26, 72–83 (1974) (in Russian)

    MathSciNet  MATH  Google Scholar 

  51. Noskov, V.N.: Complexity of tests checking the operation of logic diagram inputs. Diskret. Analiz 27, 23–51 (1975) (in Russian)

    MathSciNet  MATH  Google Scholar 

  52. Noskov, V.N.: On length of minimal single diagnostic tests checking the operation of logic diagram inputs. Metody Diskret. Analiz. 32, 40–51 (1978) (in Russian)

    MathSciNet  MATH  Google Scholar 

  53. Noskov, V.N., Slepyan, V.A.: Number of dead-end tests for a certain class of tables. Cybernetics and Systems Analysis 8, 64–71 (1972)

    Google Scholar 

  54. Preparata, F.P.: An estimate of the length of diagnostics tests. IEEE Transactions on Reliability R-18(3), 131–136 (1969)

    Article  Google Scholar 

  55. Red’kin, N.P.: Complete detection tests for switching circuits. Metody Diskret. Analiz 39, 80–87 (1983) (in Russian)

    MathSciNet  MATH  Google Scholar 

  56. Red’kin, N.P.: Verifying tests for closed and broken circuits. Metody Diskret. Analiz 40, 87–99 (1983) (in Russian)

    MathSciNet  MATH  Google Scholar 

  57. Red’kin, N.P.: On complete checking tests for circuits of functional elements. Moscow State University Bulletin, Series 1 – Mathematics and Mechanics (1), 72–74 (1986) (in Russian)

    Google Scholar 

  58. Red’kin, N.P.: Single checking tests for schemes with inverse errors of elements. Mathematical Problems of Cybernetics 12, 217–230 (2003) (in Russian)

    Google Scholar 

  59. Roth, J.P.: Diagnosis of automata failures: a calculus and a method. IBM J. Res. Develop. 10, 278–291 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  60. Shevtchenko, V.I.: On the depth of conditional tests for controlling “negation” type faults in circuits of functional gates. Sibirsk. Zh. Issled. Oper. 1(1), 63–74 (1994) (in Russian)

    MathSciNet  Google Scholar 

  61. Shevtchenko, V.I.: On complexity of fault diagnosis of circuits of functional elements. In: Lupanov, O., Chashkin, A. (eds.) Collection of Lectures of Youth Scientific Schools on Discrete Mathematics and its Applications, vol. 2, pp. 111–123. MSU Publishers, Moscow (2001) (in Russian)

    Google Scholar 

  62. Slavík, P.: A tight analysis of the greedy algorithm for set cover. In: Proc. of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 435–441. ACM, New York (1996)

    Chapter  Google Scholar 

  63. Slavík, P.: Approximation algorithms for set cover and related problems. Ph.D. thesis, State University of New York at Buffalo (1998)

    Google Scholar 

  64. Slepyan, V.: The parameters of the distribution of dead-end tests and the information weights of columns in binary tables. Diskret. Analiz 14, 28–43 (1969) (in Russian)

    MATH  Google Scholar 

  65. Slepyan, V.: The length of minimal test for a certain class of tables. Diskret. Analiz 23, 59–71 (1973) (in Russian)

    MATH  Google Scholar 

  66. Soloviev, N.: On certain property of tables with dead-end tests of equal length. Diskret. Analiz 12, 91–95 (1968) (in Russian)

    Google Scholar 

  67. Soloviev, N.: On tables containing trivial dead-end tests. Diskret. Analiz 12, 96–114 (1968) (in Russian)

    Google Scholar 

  68. Soloviev, N.A.: Tests (Theory, Construction, Applications), Nauka, Novosibirsk (1978) (in Russian)

    Google Scholar 

  69. Vaintsvaig, M.N.: Pattern recognition learning algorithm Kora. In: Pattern Recognition Learning Algorithms, pp. 110–116. Sovetskoe Radio, Moscow (1973) (in Russian)

    Google Scholar 

  70. Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications 16, 264–280 (1971)

    Article  MATH  Google Scholar 

  71. Vasilevskii, M.P.: Failure diagnosis of automata. Cybernetics and Systems Analysis 9(4), 653–665 (1973)

    MathSciNet  Google Scholar 

  72. Vasilevskii, M.P.: Concerning the decoding of automata. Cybernetics and Systems Analysis 10(2), 213–218 (1974)

    Google Scholar 

  73. Yablonskii, S.V.: On the construction of dead-end multiple experiments for automata. Trudy Mat. Inst. Steklov. 83, 263–272 (1973) (in Russian)

    Google Scholar 

  74. Yablonskii, S.V.: Some problems of reliability and diagnosis in control systems. Mathematical Problems of Cybernetics 1, 5–25 (1988) (in Russian)

    MathSciNet  Google Scholar 

  75. Yablonskii, S.V., Chegis, I.A.: On tests for electric circuits. Uspekhi Mat. Nauk 10, 182–184 (1955) (in Russian)

    Google Scholar 

  76. Zhuravlev, Y.I.: A class of partial Boolean functions. Diskret. Analiz 2, 23–27 (1964) (in Russian)

    Google Scholar 

  77. Zhuravlev, Y.I., Petrov, I.B., Ryazanov, V.V.: Discrete methods of diagnosis and analysis of medical information. In: Medicine in the Mirror of Informatics, Nauka Moscow, pp. 113–123 (2008) (in Russian)

    Google Scholar 

  78. Zielosko, B., Moshkov, M., Chikalov, I.: Decision rule optimization on the basis of dynamic programming methods. Vestnik of Lobachevsky State University of Nizhny Novgorod 6, 195–200 (2010) (in Russian)

    Google Scholar 

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Authors and Affiliations

  1. Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Building 1 4700, 23955-6900, Thuwal, Saudi Arabia

    Igor Chikalov

  2. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, United Kingdom

    Vadim Lozin & Irina Lozina

  3. Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, 23955-6900, Thuwal, Saudi Arabia

    Mikhail Moshkov & Beata Zielosko

  4. Institute of Mathematics, The University of Warsaw, Banacha St. 2, 02-097, Warsaw, Poland

    Hung Son Nguyen

  5. Institute of Mathematics, Warsaw University, Banacha 2, 02097, Warsaw, Poland

    Andrzej Skowron

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  1. Igor Chikalov
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Chikalov, I. et al. (2013). Test Theory: Tools and Applications. In: Three Approaches to Data Analysis. Intelligent Systems Reference Library, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28667-4_1

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