Software testing and mathematical error finding model

Program testing is important to audit the quality of the program and its compliance with the initial specifications, reliability requirements, functionality, fullness of the complex, etc. Recently taking into account the compliance of the software product with consumer and market conditions is also relevant. This requires new approaches and methods, tools and technologies for verifying and testing programs in real code and real operation mode. This work is devoted to system analysis of testing environments and modeling of the debugging and testing process. Using general system methods (analysis-synthesis, composition-decomposition, modeling, etc.), mathematical modeling the following results were obtained: 1) an analysis of goals, types, testing methods was carried out; 2) classification of methods was carried out; 3) with certain initial hypotheses regarding the distribution of errors in the software system, a mathematical model for estimating the number of errors (vulnerabilities) in the software system, their dynamics using the apparatus of the class of ordinary differential equations "with saturation" was built and investigated. There are presented variants for development of problem statements (hypotheses), models, algorithms for identification of models for improvement of evidence and coverage of a wider class of test situations. Research results can be used for practical audit, control of the testing process.