scholarly journals DEDUCTIVE VERIFICATION OF PREDICATE PROGRAM OF BINARY SEARCH OF AN ARBITRARY TYPE OBJECT

2019 ◽  
pp. 45-64
Author(s):  
Shelekhov Vladimir ◽  
Author(s):  
Vladimir Ivanovich Shelekhov ◽  

Deductive verification of the classical J.Williams heapsort algorithm for objects of an arbitrary type was conducted. In order to simplify verification, non-trivial transformations, replacing pointer arithmetic operators by an array element constructs, were applied. The program was translated to the predicate programming language. Deductive verification of the program in the tools Why3 and Coq appears to be complicated and time consuming.


2009 ◽  
Vol 29 (2) ◽  
pp. 500-502
Author(s):  
Deng PAN ◽  
Da-fang ZHANG ◽  
Kun XIE ◽  
Ji ZHANG

2021 ◽  
pp. 1-1
Author(s):  
Kyle Berney ◽  
Henri Casanova ◽  
Ben Karsin ◽  
Nodari Sitchinava
Keyword(s):  

Axiomathes ◽  
2021 ◽  
Author(s):  
Andrew Powell

AbstractThis article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy of ordinal recursive functionals of arbitrary type that can be reduced by substitution to natural number functions.


Cryptography ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 4
Author(s):  
Bayan Alabdullah ◽  
Natalia Beloff ◽  
Martin White

Data security has become crucial to most enterprise and government applications due to the increasing amount of data generated, collected, and analyzed. Many algorithms have been developed to secure data storage and transmission. However, most existing solutions require multi-round functions to prevent differential and linear attacks. This results in longer execution times and greater memory consumption, which are not suitable for large datasets or delay-sensitive systems. To address these issues, this work proposes a novel algorithm that uses, on one hand, the reflection property of a balanced binary search tree data structure to minimize the overhead, and on the other hand, a dynamic offset to achieve a high security level. The performance and security of the proposed algorithm were compared to Advanced Encryption Standard and Data Encryption Standard symmetric encryption algorithms. The proposed algorithm achieved the lowest running time with comparable memory usage and satisfied the avalanche effect criterion with 50.1%. Furthermore, the randomness of the dynamic offset passed a series of National Institute of Standards and Technology (NIST) statistical tests.


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