Correctness of programs over poor signatures

1991 ◽  
pp. 109-120
Author(s):  
Hardi Hungar
Keyword(s):  
Correctness Of Programs

Retrieval System and Dynamic Algorithm Looking for Axioms of Notions Defined by Programs

1993 ◽  
Vol 19 (3-4) ◽  
pp. 275-301
Author(s):  
Andrzej Biela
Keyword(s):  
Theorem Proving ◽  
Dynamic Process ◽  
Functional Equations ◽  
Automated Theorem Proving ◽  
Retrieval System ◽  
Formal System ◽  
Dynamic Algorithm ◽  
Algorithmic Logic ◽  
Correctness Of Programs

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

Investigations of properties of programs by means of the extended algorithmic logic I

1977 ◽  
Vol 1 (1) ◽  
pp. 93-119
Author(s):  
Lech Banachowski
Keyword(s):  
Mathematical Model ◽  
Mathematical Tool ◽  
Methods Of Analysis ◽  
Semantic Correctness ◽  
Algorithmic Logic ◽  
Correctness Of Programs

The present paper contains investigations concerning the semantic correctness of programs. Presented methods of analysis of programs are appropriate for every domain of computation. Algorithmic logic extended by classical quantifiers is a fundamental mathematical tool used in the paper. Interrelations between properties of programs and properties of descriptions of programs are studied (a description of a program is a mathematical model of the notion of a documentation of a program).

scholarly journals A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 512 ◽  
Author(s):  
Erdal Karapınar ◽  
Panda Kumari ◽  
Durdana Lateef
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nash Equilibria ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
New Approach ◽  
Correctness Of Programs

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach.

Review of Software Fault-Tolerance Methods for Reliability Enhancement of Real-Time Software Systems

2016 ◽  
Vol 6 (3) ◽  
pp. 1031
Author(s):  
Anjushi Verma ◽  
Ankur Ghartaan ◽  
Tirthankar Gayen
Keyword(s):  
Fault Tolerance ◽  
Real Time ◽  
Cost Effective ◽  
Software Systems ◽  
Real Time Systems ◽  
Cost Effective Approach ◽  
Functional Correctness ◽  
Operational Errors ◽  
Correctness Of Programs ◽  
Time Systems

Real time systems are those systems which must guarantee to response correctly within strict time constraint or within deadline. Failures can arise from both functional errors as well as timing bugs. Hence, it is necessary to provide temporal correctness of programs used in real time applications in addition to providing functional correctness. Although, there are several researches concerned with achieving fault tolerance in the presence of various functional and operational errors but many of them did not address the problem concerned with the timing bugs which is an important issue in real time systems. As for real time systems, many times it becomes a necessity for a given service to be delivered within the specified time deadline. Therefore, this paper reviews the existing approaches from the perspective of  real time systems to analyse the shortcomings of these approaches to  present a versatile and cost effective approach in the presence of timing bugs for providing fault tolerance to enhance the reliability of the real time software applications.

Model Checking for SpaceWire Error Detection Module

2012 ◽  
Vol 241-244 ◽  
pp. 3020-3025
Author(s):  
Ling Ling Dong ◽  
Yong Guan ◽  
Xiao Juan Li ◽  
Zhi Ping Shi ◽  
Jie Zhang ◽  
...  
Keyword(s):  
Model Checking ◽  
Formal Verification ◽  
Temporal Logic ◽  
Error Detection ◽  
System Model ◽  
Linear Search ◽  
Kripke Structure ◽  
Mathematical Methods ◽  
Safety Critical ◽  
Correctness Of Programs

Considerable attention has been devoted to prove the correctness of programs. Formal verification overcomes the incompleteness by applying mathematical methods to verify a design. SpaceWire is a well known communication standard. For safety-critical applications an approach is needed to validate the completeness of SpareWire design. This paper addresses formal verification of SpareWire error detection module. The system model was constructed by Kripke structure, and the properties were presented by linear temporal logic (LTL). Compared the verification of LTL with CTL (branch temporal logic), LTL properties could improve the verification efficiency due to its linear search. The error priority was checked using simulation guided by model checking. After some properties were modified, all possible behaviors of the module satisfied the specification. This method realizes complete validation of the error detection module.

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