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Formalized Mathematics

(a computer assisted approach)

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Volume 15, Issue 3 (Jan 2007)

Issues

Mizar Analysis of Algorithms: Preliminaries

Grzegorz Bancerek
  • Department of Theoretical Computer Science, Białystok Technical University, Poland
Published Online: 2008-06-09 | DOI: https://doi.org/10.2478/v10037-007-0011-x

Mizar Analysis of Algorithms: Preliminaries

Algorithms and its parts - instructions - are formalized as elements of if-while algebras. An if-while algebra is a (1-sorted) universal algebra which has 4 operations: a constant - the empty instruction, a binary catenation of instructions, a ternary conditional instruction, and a binary while instruction. An execution function is defined on pairs (s, I), where s is a state (an element of certain set of states) and I is an instruction, and results in states. The execution function obeys control structures using the set of distinguished true states, i.e. a condition instruction is executed and the continuation of execution depends on if the resulting state is in true states or not. Termination is also defined for pairs (s, I) and depends on the execution function. The existence of execution function determined on elementary instructions and its uniqueness for terminating instructions are shown.

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  • [17] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.

  • [18] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras. Formalized Mathematics, 4(1):23-27, 1993.

  • [19] Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.

  • [20] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

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  • [24] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.

  • [25] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

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  • [32] Małgorzata Korolkiewicz. Homomorphisms of algebras. Quotient universal algebra. Formalized Mathematics, 4(1):109-113, 1993.

  • [33] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.

  • [34] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

  • [35] Jarosław Kotowicz, Beata Madras, and Małgorzata Korolkiewicz. Basic notation of universal algebra. Formalized Mathematics, 3(2):251-253, 1992.

  • [36] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

  • [37] Beata Perkowska. Free universal algebra construction. Formalized Mathematics, 4(1):115-120, 1993.

  • [38] Beata Perkowska. Free many sorted universal algebra. Formalized Mathematics, 5(1):67-74, 1996.

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  • [46] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.

  • [47] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

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  • [49] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

  • [50] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

About the article


Published Online: 2008-06-09

Published in Print: 2007-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0011-x. Export Citation

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