16 research outputs found
Partial evaluation in insertion modeling system
The paper relates to practical aspects of insertion modeling. Insertion modeling system is an environment for development of insertion machines, used to represent insertion models of distributed systems. The notions of insertion modeling are stated. The main features of partial evaluation are described in the paper. The concep-tion of partial evaluation in insertion modeling is presented
APS C++ USERβS LIBRARY
The general information about the APS algebraic programming system (terms rewriting system) is briefly described in the present article. It is justified practical necessity of creation of APS C++ Userβs Library, its conception is presented and its main functions are listed. Also it is mentioned few words about the translator APLAN-C++. \ud
ΠΠΎΡΠΎΡΠΊΠΎ ΠΎΠΏΠΈΡΠ°Π½Ρ ΠΎΠ±ΡΠΈΠ΅ ΡΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΎ ΡΠΈΡΡΠ΅ΠΌΠ΅ Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ APS(ΡΠΈΡΡΠ΅ΠΌΠ΅ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠΌΠΎΠ²). ΠΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΎ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ Π² ΡΠΎΠ·Π΄Π°Π½ΠΈΠΈ Π±ΠΈΠ±Π»ΠΈΠΎΡΠ΅ΠΊΠΈ APS C++ Userβs Library, ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½Π° Π΅Π΅ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΡ ΠΈ ΠΏΠ΅ΡΠ΅ΡΠΈΡΠ»Π΅Π½Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΡΡΠ½ΠΊΡΠΈΠΈ. Π£ΠΏΠΎΠΌΡΠ½ΡΡΠΎ ΠΎ ΡΡΠ°Π½ΡΠ»ΡΡΠΎΡΠ΅ APLAN-Π‘++. \u
Use of metods of algebraic programming for the formal verification of legal acts
This article briefly describes the programmable tool for the analysis of a normative legal document. A mechanism for checking legal requirements is presented. The model of the legal document is proposed in the form of a set of special rules. Verification is provided by means of algebraic programming and methods of symbolic transformation. This approach allows us to analyze the legislative base of structural and logical errors, check the contradictions, completeness and integrity of legal acts. Presently, the mechanism of claster analysis of text, which makes it possible to identify the frequency of occurrence of various vague language constructs.Π£ ΡΡΠΉ ΡΡΠ°ΡΡΡ ΠΊΠΎΡΠΎΡΠΊΠΎ ΠΎΠΏΠΈΡΡΡΡΡΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠ½ΠΈΠΉ ΡΠ½ΡΡΡΡΠΌΠ΅Π½Ρ Π΄Π»Ρ Π°Π½Π°Π»ΡΠ·Ρ Π½ΠΎΡΠΌΠ°ΡΠΈΠ²Π½ΠΎ-ΠΏΡΠ°Π²ΠΎΠ²ΠΎΠ³ΠΎ Π΄ΠΎΠΊΡΠΌΠ΅Π½ΡΠ°. ΠΡΠ½ΡΡ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌ ΠΏΠ΅ΡΠ΅Π²ΡΡΠΊΠΈ Π·Π°ΠΊΠΎΠ½Π½ΠΈΡ
Π²ΠΈΠΌΠΎΠ³. ΠΠΎΠ΄Π΅Π»Ρ ΠΏΡΠ°Π²ΠΎΠ²ΠΎΠ³ΠΎ Π΄ΠΎΠΊΡΠΌΠ΅Π½ΡΠ° ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π° Ρ Π²ΠΈΠ³Π»ΡΠ΄Ρ Π½Π°Π±ΠΎΡΡ ΡΠΏΠ΅ΡΡΠ°Π»ΡΠ½ΠΈΡ
ΠΏΡΠ°Π²ΠΈΠ». ΠΠ΅ΡΠΈΡΡΠΊΠ°ΡΡΡ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΡΡΡΡΡΡ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ Π°Π»Π³Π΅Π±ΡΠ°ΡΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΠ³ΡΠ°ΠΌΡΠ²Π°Π½Π½Ρ ΡΠ° ΠΌΠ΅ΡΠΎΠ΄ΡΠ² ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΠ³ΡΠ°ΠΌΡΠ²Π°Π½Π½Ρ. Π¦Π΅ΠΉ ΠΏΡΠ΄Ρ
ΡΠ΄ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΠΏΡΠΎΠ°Π½Π°Π»ΡΠ·ΡΠ²Π°ΡΠΈ Π·Π°ΠΊΠΎΠ½ΠΎΠ΄Π°Π²ΡΡ Π±Π°Π·Ρ Π½Π° Π½Π°ΡΠ²Π½ΡΡΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ Π»ΠΎΠ³ΡΡΠ½ΠΈΡ
ΠΏΠΎΠΌΠΈΠ»ΠΎΠΊ, ΠΏΠ΅ΡΠ΅Π²ΡΡΡΡΠΈ ΠΏΡΠ°Π²ΠΎΠ²Ρ Π²ΠΈΠΌΠΎΠ³ΠΈ Π½Π° ΠΏΡΠΎΡΠΈΡΡΡΡΡ, ΠΏΠΎΠ²Π½ΠΎΡΡ ΡΠ° ΡΡΠ»ΡΡΠ½ΡΡΡΡ.Π ΡΡΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΠΊΡΠ°ΡΠΊΠΎ ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΡΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΡΠΉ ΠΈΠ½ΡΡΡΡΠΌΠ΅Π½Ρ Π΄Π»Ρ Π°Π½Π°Π»ΠΈΠ·Π° Π½ΠΎΡΠΌΠ°ΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΏΡΠ°Π²ΠΎΠ²ΠΎΠ³ΠΎ Π΄ΠΎΠΊΡΠΌΠ΅Π½ΡΠ°. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌ ΠΏΡΠΎΠ²Π΅ΡΠΊΠΈ ΡΡΠΈΠ΄ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ΅Π±ΠΎΠ²Π°Π½ΠΈΠΉ. ΠΠΎΠ΄Π΅Π»Ρ ΡΡΠΈΠ΄ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄ΠΎΠΊΡΠΌΠ΅Π½ΡΠ° ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π° Π² Π²ΠΈΠ΄Π΅ Π½Π°Π±ΠΎΡΠ° ΡΠΏΠ΅ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΠΏΡΠ°Π²ΠΈΠ». ΠΠ΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°Π΅ΡΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π½Π°ΠΌ Π°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ Π·Π°ΠΊΠΎΠ½ΠΎΠ΄Π°ΡΠ΅Π»ΡΠ½ΡΡ Π±Π°Π·Ρ Π½Π° Π½Π°Π»ΠΈΡΠΈΠ΅ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ-Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΎΡΠΈΠ±ΠΎΠΊ, ΠΏΡΠΎΠ²Π΅ΡΡΡΡ ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠΈΡ, ΠΏΠΎΠ»Π½ΠΎΡΡ ΠΈ ΡΠ΅Π»ΠΎΡΡΠ½ΠΎΡΡΡ ΠΏΡΠ°Π²ΠΎΠ²ΡΡ
Π°ΠΊΡΠΎΠ²
Simple non-deterministic rewriting in verification
Abstract. We discuss the non-deterministic rewriting in application for engine functions of Verification of Formal Specification (VFS) system in this paper. VFS β are tools to prove properties of systems described as formal specifications (basic protocols), such as the completeness (the system behavior has a possible continuation at each of its stages) and consistency (the system behavior is deterministic at each stage), safety (something bad will never happened), or the correspondence of the specified behavior to given scenarios. Together these tools constitute a powerful environment for the formal verification of formal specifications expressed through message sequence charts
Deductive verification of requirements for event-driven architecture
The current paper presents the technology of processing of requirements for systems with event-driven architecture. The technology consists of the stages of formalization, formal verification and conversion to design specifications. The formalization is the formal description of events as formal specifications called basic protocols. The consistency and completeness of basic protocols, safety properties and user-defined properties are verified. The deductive tools for dynamic and static checking are used for detection of properties violation. The method of enlargement allows reducing the complexity of proving and solving. Formal presentation of requirements allows converting them to SDL\UML specifications and generating the test suite. The technology is realized in IMS system and applied in more than 50 projects of telecommunication, networking, microprocessing and automotive systems
Satisfiability For Symbolic Verification in VRS
Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π»ΠΎΠ³ΠΈΠΊΠΈ ΠΏΠ΅ΡΠ²ΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΠ° Π² ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΠΎΠΉ Π²Π΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΡΠΏΠ΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΉ ΡΡΠ΅Π±ΠΎΠ²Π°Π½ΠΈΠΉ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠ³ΠΎ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ, ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΡΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠΈΡΡΠ΅ΠΌ, ΠΊΠΎΡΠΎΡΡΠ΅ Π΅ΡΡΡ ΡΡΠ°Π½Π·ΠΈΡΠΈΠΎΠ½Π½ΡΠΌΠΈ ΡΠΈΡΡΠ΅ΠΌΠ°ΠΌΠΈ Ρ ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΡΠΌΠΈ ΡΠΎΡΡΠΎΡΠ½ΠΈΡΠΌΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π½ΡΡ
ΡΠΎΡΠΌΡΠ»ΠΎΠΉ Π»ΠΎΠ³ΠΈΠΊΠΈ ΠΏΠ΅ΡΠ²ΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΠ°. ΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½Ρ ΠΌΠ΅ΡΠΎΠ΄Ρ Satisfiability Modulo Theory Π²ΠΌΠ΅ΡΡΠΎ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π²ΡΠ²ΠΎΠ΄Π° Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠ΅ΠΌ ΠΈΡΡΠΈΡΠ»Π΅Π½ΠΈΠΈ Π΄Π»Ρ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΡ
Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ Π² ΠΏΡΠ΅Π΄ΠΈΠΊΠ°ΡΠ½ΡΡ
ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ΅ΡΠ°Ρ
.This paper demonstrates the use of the first order logic in symbolic verification of the requirement specifications of reactive software systems. We consider symbolic models of a specified system which are transition systems with symbolic states represented by formulae of the first order logic. To efficiently compute predicate transformers the Satisfiability Modulo Theory methods are used instead of the logical inference in the corresponding calculi.Π ΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π»ΠΎΠ³ΡΠΊΠΈ ΠΏΠ΅ΡΡΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΡ Ρ ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΡΠΉ Π²Π΅ΡΠΈΡΡΠΊΠ°ΡΡΡ ΡΠΏΠ΅ΡΠΈΡΡΠΊΠ°ΡΡΠΉ Π²ΠΈΠΌΠΎΠ³ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠ½ΠΎΠ³ΠΎ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ, ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠΈΡΡΠ΅ΠΌ, ΡΠΊΡ Ρ ΡΡΠ°Π½Π·ΠΈΡΡΠΉΠ½ΠΈΠΌΠΈ ΡΠΈΡΡΠ΅ΠΌΠ°ΠΌΠΈ Π· ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΠΈΠΌΠΈ ΡΡΠ°Π½Π°ΠΌΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΈΠΌΠΈ ΡΠΎΡΠΌΡΠ»ΠΎΡ Π»ΠΎΠ³ΡΠΊΠΈ ΠΏΠ΅ΡΡΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΡ. ΠΠΈΠΊΠΎΡΠΈΡΡΠ°Π½ΠΎ ΠΌΠ΅ΡΠΎΠ΄ΠΈ Satisfiability Modulo Theory Π·Π°ΠΌΡΡΡΡ Π»ΠΎΠ³ΡΡΠ½ΠΎΠ³ΠΎ Π²ΠΈΠ²ΠΎΠ΄Ρ Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΈΡ
ΡΠΈΡΠ»Π΅Π½Π½ΡΡ
Π΄Π»Ρ Π΅ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΎΠ±ΡΠΈΡΠ»Π΅Π½Π½Ρ Ρ ΠΏΡΠ΅Π΄ΠΈΠΊΠ°ΡΠ½ΠΈΡ
ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ΅ΡΠ°Ρ
ΠΠΎΠ΄Ρ ΠΎΠ΄ ΠΊ ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅ΡΡΠΎΠ²ΡΡ ΡΡΠ΅Π½Π°ΡΠΈΠ΅Π² Π² ΡΠ°ΠΌΠΊΠ°Ρ ΡΠ΅Ρ Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠΌΡΡΠ»Π΅Π½Π½ΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΡΡ ΠΏΡΠΎΠ΅ΠΊΡΠΎΠ²
In this paper we propose an approach to efficient automating test technology for industrial software projects, that uses a formal model of the system, automatically performs a symbolic verification, generation and concretization of the symbolic traces, the generation of test suites for concretized traces, and also includes tools for analysis of the testing results, allowing users to automate the full cycle of testing. Particular emphasis is placed on the presentation of the algorithm concretization and setting of test scenarios.ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΊ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠΉ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠΌΡΡΠ»Π΅Π½Π½ΡΡ
ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΡΡ
ΠΏΡΠΎΠ΅ΠΊΡΠΎΠ², ΠΊΠΎΡΠΎΡΡΠΉ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅Ρ ΡΠΎΡΠΌΠ°Π»ΡΠ½ΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠΈΡΡΠ΅ΠΌΡ, Π²ΡΠΏΠΎΠ»Π½ΡΠ΅Ρ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈ ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΡΡ Π²Π΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ, Π³Π΅Π½Π΅ΡΠ°ΡΠΈΡ ΠΈ ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΡΡ
ΡΡΠ°ΡΡ, Π³Π΅Π½Π΅ΡΠ°ΡΠΈΡ ΡΠ΅ΡΡΠΎΠ²ΡΡ
Π½Π°Π±ΠΎΡΠΎΠ² ΠΏΠΎ ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΠΌ ΡΡΠ°ΡΡΠ°ΠΌ, Π° ΡΠ°ΠΊΠΆΠ΅ Π²ΠΊΠ»ΡΡΠ°Π΅Ρ ΡΡΠ΅Π΄ΡΡΠ²Π° Π°Π½Π°Π»ΠΈΠ·Π° ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΠΈΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ ΡΠ΅ΡΡΠΎΠ², ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΠΏΠΎΠ»Π½ΡΠΉ ΡΠΈΠΊΠ» ΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΡΠΎΠ±ΡΠΉ Π°ΠΊΡΠ΅Π½Ρ ΡΠ΄Π΅Π»Π°Π½ Π½Π° ΠΈΠ·Π»ΠΎΠΆΠ΅Π½ΠΈΠΈ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π½Π°ΡΡΡΠΎΠΉΠΊΠΈ ΡΠ΅ΡΡΠΎΠ²ΡΡ
ΡΡΠ΅Π½Π°ΡΠΈΠ΅Π²
ΠΠΎΠ΄Ρ ΠΎΠ΄ ΠΊ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·Π°ΡΠΈΠΈ ΠΎΡΠ»Π°Π΄ΠΊΠΈ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΡΠ΅ΡΠΊΠΈΡ ΡΡΠ΅Π½Π°ΡΠΈΠ΅Π²
The paper presents two approaches to debugging the application model behavior scenarios: semi-automatic and automatic. The first approach allows a user to automatize the process of finding the place in a concrete behavioral scenario that is suspicious of being a cause of an error. The second approach allows, in a single cycle of the analysis, to automatically identify not only the place, but also possible causes of errors in a given set of generated behavioral symbolic scenarios.Π ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ Π΄Π²Π° ΠΌΠ΅ΡΠΎΠ΄Π°, Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΡΡ
Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ Π·Π°Π΄Π°ΡΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·Π°ΡΠΈΠΈ ΠΎΡΠ»Π°Π΄ΠΊΠΈ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ΅Π½Π°ΡΠΈΠ΅Π² ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΡ: ΠΏΠΎΠ»ΡΠ°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ. ΠΠ΅ΡΠ²ΡΠΉ Π΄Π°Π΅Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Ρ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΠΏΠΎΠΈΡΠΊ ΡΠ΅Ρ
ΠΌΠ΅ΡΡ Π² Π²ΡΠ±ΡΠ°Π½Π½ΠΎΠΌ ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΠΎΠΌ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΡΠ΅ΡΠΊΠΎΠΌ ΡΡΠ΅Π½Π°ΡΠΈΠΈ, Π² ΠΊΠΎΡΠΎΡΡΡ
ΠΊΡΠΎΠ΅ΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½Π°Ρ ΠΏΡΠΈΡΠΈΠ½Π° ΠΎΡΠΈΠ±ΠΊΠΈ. ΠΡΠΎΡΠΎΠΉ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π² Π΅Π΄ΠΈΠ½ΠΎΠΌ ΡΠΈΠΊΠ»Π΅ Π°Π½Π°Π»ΠΈΠ·Π° Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°ΡΡ Π½Π΅ ΡΠΎΠ»ΡΠΊΠΎ ΠΌΠ΅ΡΡΠ°, Π½ΠΎ ΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ ΠΏΡΠΈΡΠΈΠ½Ρ ΠΎΡΠΈΠ±ΠΎΠΊ Π² Π·Π°Π΄Π°Π½Π½ΠΎΠΌ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π΅ ΡΠ³Π΅Π½Π΅ΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠΈΠΌΠ²ΠΎΠ»ΡΠ½ΡΡ
ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ΅Π½Π°ΡΠΈΠ΅Π²
PM DIRECTORY INTEGRATED ENVIRONMENT ANALYTICAL GEOMETRY COURSE FOR HIGHER EDUCATION.
The work by PM Directory integrated environment Analytical Geometry course for higher education, show the properties of language Aplan and the possibility of its use to solve various problems associated with arithmetic calculations, conversion and parsing complicated expressions. From the perspective of software applications submitted language. Thoroughly reviewed mathematical kernel module directory ISA software Analytical Geometry. Displaying architecture and directory capabilities and examples of problems that may decide his help
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