Analysis of Algorithms: An Example of a Sort Algorithm

Open access

Summary

We analyse three algorithms: exponentiation by squaring, calculation of maximum, and sorting by exchanging in terms of program algebra over an algebra.

[1] Grzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007. doi:10.2478/v10037-007-0011-x.

[2] Grzegorz Bancerek. Program algebra over an algebra. Formalized Mathematics, 20(4): 309-341, 2012. doi:10.2478/v10037-012-0037-6.

[3] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

[4] Grzegorz Bancerek. Sorting by exchanging. Formalized Mathematics, 19(2):93-102, 2011. doi:10.2478/v10037-011-0015-4.

[5] Grzegorz Bancerek. Institution of many sorted algebras. Part I: Signature reduct of an algebra. Formalized Mathematics, 6(2):279-287, 1997.

[6] Grzegorz Bancerek. Complete lattices. Formalized Mathematics, 2(5):719-725, 1991.

[7] Grzegorz Bancerek. Free term algebras. Formalized Mathematics, 20(3):239-256, 2012. doi:10.2478/v10037-012-0029-6.

[8] Grzegorz Bancerek. Terms over many sorted universal algebra. Formalized Mathematics, 5(2):191-198, 1996.

[9] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[10] Grzegorz Bancerek. König’s lemma. Formalized Mathematics, 2(3):397-402, 1991.

[11] Grzegorz Bancerek. Joining of decorated trees. Formalized Mathematics, 4(1):77-82, 1993.

[12] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Formalized Mathematics, 6(1):93-107, 1997.

[13] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[14] Grzegorz Bancerek and Artur Korniłowicz. Yet another construction of free algebra. Formalized Mathematics, 9(4):779-785, 2001.

[15] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. FormalizedMathematics, 5(4):485-492, 1996.

[16] Ewa Burakowska. Subalgebras of many sorted algebra. Lattice of subalgebras. FormalizedMathematics, 5(1):47-54, 1996.

[17] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[18] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990.

[19] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.

[20] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[21] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[22] Czesław Bylinski. Galois connections. Formalized Mathematics, 6(1):131-143, 1997.

[23] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[24] Małgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Formalized Mathematics, 5(1):61-65, 1996.

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

[26] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.

[27] Takashi Mitsuishi and Grzegorz Bancerek. Lattice of fuzzy sets. Formalized Mathematics, 11(4):393-398, 2003.

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

[29] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.

[30] Andrzej Trybulec. A scheme for extensions of homomorphisms of many sorted algebras. Formalized Mathematics, 5(2):205-209, 1996.

[31] Andrzej Trybulec. Many sorted algebras. Formalized Mathematics, 5(1):37-42, 1996.

[32] Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.

[33] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.

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

[35] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. FormalizedMathematics, 1(2):387-393, 1990.

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

[37] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.

[38] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.

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

Formalized Mathematics

(a computer assisted approach)

Journal Information

SCImago Journal Rank (SJR) 2017: 0.119
Source Normalized Impact per Paper (SNIP) 2017: 0.237



Target Group

researchers in the fields of formal methods and computer-checked mathematics

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 38 38 10
PDF Downloads 12 12 5