# Mizar Analysis of Algorithms: Preliminaries

Formalized Mathematics (2007)

- Volume: 15, Issue: 3, page 87-110
- ISSN: 1426-2630

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topGrzegorz Bancerek. "Mizar Analysis of Algorithms: Preliminaries." Formalized Mathematics 15.3 (2007): 87-110. <http://eudml.org/doc/266833>.

@article{GrzegorzBancerek2007,

abstract = {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.},

author = {Grzegorz Bancerek},

journal = {Formalized Mathematics},

language = {eng},

number = {3},

pages = {87-110},

title = {Mizar Analysis of Algorithms: Preliminaries},

url = {http://eudml.org/doc/266833},

volume = {15},

year = {2007},

}

TY - JOUR

AU - Grzegorz Bancerek

TI - Mizar Analysis of Algorithms: Preliminaries

JO - Formalized Mathematics

PY - 2007

VL - 15

IS - 3

SP - 87

EP - 110

AB - 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.

LA - eng

UR - http://eudml.org/doc/266833

ER -

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## Citations in EuDML Documents

top- Grzegorz Bancerek, Mizar Analysis of Algorithms: Algorithms over Integers
- Grzegorz Bancerek, Sorting by Exchanging
- Grzegorz Bancerek, Algebraic Approach to Algorithmic Logic
- Grzegorz Bancerek, Analysis of Algorithms: An Example of a Sort Algorithm
- Piotr Rudnicki, Lorna Stewart, Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph
- Grzegorz Bancerek, Program Algebra over an Algebra

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