메뉴 건너뛰기




Volumn 32, Issue 4, 2009, Pages 480-504

Formal verification of tail distribution bounds in the HOL theorem prover

Author keywords

Higher order logic; Mechanization of proofs; Probabilistic analysis of algorithms; Probability theory; Theorem proving

Indexed keywords

MACHINERY; MECHANIZATION; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; QUALITY ASSURANCE; RANDOM PROCESSES; RELIABILITY ANALYSIS; THEOREM PROVING;

EID: 62449314897     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1055     Document Type: Article
Times cited : (12)

References (31)
  • 3
    • 0001341735 scopus 로고    scopus 로고
    • Introduction to Monte Carlo methods
    • Learning in Graphical Models, Kluwer Academic Press: Dordrecht
    • MacKay DJC. Introduction to Monte Carlo methods. Learning in Graphical Models. NATO Science Series. Kluwer Academic Press: Dordrecht, 1998; 175-204.
    • (1998) NATO Science Series , pp. 175-204
    • MacKay, D.J.C.1
  • 4
    • 22444455170 scopus 로고    scopus 로고
    • Assessing the reliability of statistical software: Part I
    • McCullough BD. Assessing the reliability of statistical software: Part I. The American Statistician 1998; 52(4): 358-366.
    • (1998) The American Statistician , vol.52 , Issue.4 , pp. 358-366
    • McCullough, B.D.1
  • 5
    • 0033468677 scopus 로고    scopus 로고
    • Assessing the reliability of statistical software: Part II
    • McCullough BD. Assessing the reliability of statistical software: Part II. The American Statistician 1999; 53(2):149-159.
    • (1999) The American Statistician , vol.53 , Issue.2 , pp. 149-159
    • McCullough, B.D.1
  • 6
    • 35348827909 scopus 로고    scopus 로고
    • Verification of expectation properties for discrete random variables in HOL
    • Theorem Proving in Higher-order Logics, Springer: Berlin
    • Hasan O, Tahar S. Verification of expectation properties for discrete random variables in HOL. Theorem Proving in Higher-order Logics. Lecture Notes in Computer Science, vol. 4732. Springer: Berlin, 2007; 119-134.
    • (2007) Lecture Notes in Computer Science , vol.4732 , pp. 119-134
    • Hasan, O.1    Tahar, S.2
  • 9
    • 35148895911 scopus 로고    scopus 로고
    • Formalization of the continuous probability distributions
    • Automated Deduction, Springer: Berlin
    • Hasan O, Tahar S. Formalization of the continuous probability distributions. Automated Deduction. Lecture Notes in Artificial Intelligence, vol. 4603. Springer: Berlin, 2007; 3-18.
    • (2007) Lecture Notes in Artificial Intelligence , vol.4603 , pp. 3-18
    • Hasan, O.1    Tahar, S.2
  • 10
    • 35348861893 scopus 로고    scopus 로고
    • Formal verification of expectation and variance for discrete random variables
    • Technical Report, Concordia University, Montreal, Canada, June, Available from
    • Hasan O, Tahar S. Formal verification of expectation and variance for discrete random variables. Technical Report, Concordia University, Montreal, Canada, June 2007. Available from: http://hvg.ece.concordia.ca/ Publications/ TECH-REP/FVEVDR-TR07.
    • (2007)
    • Hasan, O.1    Tahar, S.2
  • 11
    • 35348859118 scopus 로고    scopus 로고
    • Verification of tail distribution bounds in a theorem prover
    • American Institute of Physics: Corfu, Greece
    • Hasan O, Tahar S. Verification of tail distribution bounds in a theorem prover. Numerical Analysis and Applied Mathematics, vol. 936. American Institute of Physics: Corfu, Greece, 2007; 259-262.
    • (2007) Numerical Analysis and Applied Mathematics , vol.936 , pp. 259-262
    • Hasan, O.1    Tahar, S.2
  • 15
    • 33646394869 scopus 로고    scopus 로고
    • Quantitative temporal logic mechanized in HOL
    • International Colloquium Theoretical Aspects of Computing, Springer: Berlin
    • Celiku O. Quantitative temporal logic mechanized in HOL. International Colloquium Theoretical Aspects of Computing. Lecture Notes in Computer Science, vol. 3722. Springer: Berlin, 2005; 439-453.
    • (2005) Lecture Notes in Computer Science , vol.3722 , pp. 439-453
    • Celiku, O.1
  • 16
    • 33746092487 scopus 로고    scopus 로고
    • Proofs of randomized algorithms in Coq
    • Mathematics of Program Construction, Springer: Berlin
    • Audebaud P, Paulin-Mohring C. Proofs of randomized algorithms in Coq. Mathematics of Program Construction. Lecture Notes in Computer Science, vol. 4014. Springer: Berlin, 2006; 49-68.
    • (2006) Lecture Notes in Computer Science , vol.4014 , pp. 49-68
    • Audebaud, P.1    Paulin-Mohring, C.2
  • 17
    • 35148840872 scopus 로고    scopus 로고
    • Verification of probabilistic properties in HOL using the cumulative distribution function
    • Integrated Formal Methods, Springer: Berlin
    • Hasan O, Tahar S. Verification of probabilistic properties in HOL using the cumulative distribution function. Integrated Formal Methods. Lecture Notes in Computer Science, vol. 4591. Springer: Berlin, 2007; 333-352.
    • (2007) Lecture Notes in Computer Science , vol.4591 , pp. 333-352
    • Hasan, O.1    Tahar, S.2
  • 20
    • 33646427778 scopus 로고    scopus 로고
    • Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems
    • American Mathematical Society: Providence, RI
    • Rutten J, Kwaiatkowska M, Normal G, Parker D. Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems. CRM Monograph Series, vol. 23. American Mathematical Society: Providence, RI, 2004.
    • (2004) CRM Monograph Series , vol.23
    • Rutten, J.1    Kwaiatkowska, M.2    Normal, G.3    Parker, D.4
  • 24
    • 0003180840 scopus 로고
    • A formulation of the simple theory of types
    • Church A. A formulation of the simple theory of types. Journal of Symbolic Logic 1940; 5:56-68.
    • (1940) Journal of Symbolic Logic , vol.5 , pp. 56-68
    • Church, A.1
  • 25


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.