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1
Content available An algebraic model of the subsystem for the computer generation of elimination operation
Ovsyak V., Ovsyak O., Kozelko M., Petrushka J.
Measurement Automation Monitoring
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2018
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Vol. 64, No. 3
48--52
EN
A brief analysis of the known methods of non-algebraic and algebraic descriptions of algorithms has been presented. The features of the elimination operation being a term of the algorithm algebra have been shown. An algebraic model of the computer generation of the elimination operation has been synthesized by means of the algorithm algebra. The model has been implemented with the help of software on the platform Microsoft Visual Studio.NET. The models of subsystem as a graph and a diagram of sequences have been designed as well.
2
Content available Presentation of Mathematical Induction by Formula of Algebra of Algorithms
Ovsyak V., Ovsyak O., Petrushka J.
Measurement Automation Monitoring
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2016
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Vol. 62, No. 11
367--370
EN
The analysis of the axiom of mathematical induction, which is given by the formula of mathematical logics is presented in the paper. It has been established that the famous formula of mathematical induction is executed only in case of ordered values of the variable linked by a quantifier. This ordering is not described analytically. Algebra of algorithms is applied for an analytical description of ordering of the variable values. The axiom of mathematical induction is described by the formula of algebra of algorithms.
3
Content available Optimization of abstract algorithm
Ovsyak V.
Measurement Automation Monitoring
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2016
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Vol. 62, No. 1
37--39
EN
The optimization of the known abstract algorithm has been done by means of algebra of algorithms. The optimization criterion is the number of abstract operators. The optimization has been done on the basis of operation features of algebra of algorithms.
4
Content available Models of a Computer System with an Abstract Graphic Element
Ovsyak V., Ovsyak O., Kozelko M., Petrushka J.
Measurement Automation Monitoring
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2016
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Vol. 62, No. 10
345--347
EN
A general model of a computer system with an abstract graphic element and a model of formation of an element form have been designed using the means of algebra of algorithms, the system of algorithmic algebras and platforms.
5
Content available The general model of the system decomposition and the model of the system interface fragment
Ovsyak V., Ovsyak O.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 5
148--150
EN
There have been built a fragment of three-level model of the formulas processing system of algebra of algorithms (SOFAL) by means of the modified algorithms algebra. The model of the first level is formed by subsystems. At the second level of decomposition the model is created by graphic and functional parts of subsystems of the first level of decomposition. The third level of decomposition is the model of the system user interface.
6
Content available Models of information system layers
Ovsyak V., Ovsyak O.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 5
151--153
EN
Models of information system layers as a scheme, algebraic expressions and computer model were created. Algebraic model of information system layers is synthesized by means of algebraic algorithms and modified systems of algorithmic algebras. A computer model of layers is created in environment Microsoft Visual Studio .NET. A four-layer model of abstract information system in the form of diagrams, mathematical formulas and models of computer system was created. Comparison of object models is performed.
7
Content available Models of alternative selection
Ovsyak V., Ovsyak O.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 4
101--103
EN
Models of a number of eliminations in conditions have been presented. In particular, the models of a number of eliminations in the form of a block diagram of the algorithm, the instructions if() and switch() of algorithmic programming languages, systems of algorithmic algebras and its modifications, as well as two models of algebraic algorithms have been constructed.
8
Content available Decomposition of the GUI by means of modified algorithm algebra
Ovsyak V., Ovsyak O.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 8
413--415
EN
Using operations of cyclic sequencing and cyclic paralleling of the modified algebra of algorithms we have built compact model of decomposition of the formulas processing system of algebra of algorithms. We have developed the generalized abstract model of user graphic interface of a computer system. Based on the generalized model we have created the model of a user interface fragment for formulas processing of algorithm algebra.
9
Content available Carriers of algebra of algorithms
Ovsyak V., Ovsyak O.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 4
98--100
EN
Operations of modified system of algorithm algebras [10, 11] and algebra of algorithms [12-15] are presented in the paper. The paper shows operations of mathematical logic on the three-meaning alphabet. It considers converting of logical to operator values that are performed in the system of algorithmic algebras and its modifications. It presents constants, variables and operators, which are components of models of algorithms and systems, as predicates. It gives a comparative assessment of mono- and polycarrier algebras of algorithms.
10
Content available A sequential method for the synthesis of formulae of algorithms
Ovsyak V., Ovsyak O.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 1
21--23
EN
New method for the synthesis of algorithm formulae based on the concept of algorithm algebra is presented. The concept of algorithm algebra there is shown in papers [1-4]. The synthesis is performed in two stages. First, all sequences are formulated, which is followed by the bonding the sequences by conditions. This operation is termed by elimination. If the algorithm contains a cyclic operations, then each cyclic operation is considered as a complex one, over which the synthesis of sequences and eliminations are successively performed. Additionally, the algorithm algebra tools for transformation and minimization of algorithms are illustrated by a simple but instructive example.
11
Content available The analysis of algorithm algebra formulae in xml-format
Ovsyak V., Ovsyak O.
Pomiary Automatyka Kontrola
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2014
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R. 60, nr 5
313--316
EN
Analysis of formulae of algebra algorithms (AA) written in xml - format is described in the paper. A specific editor uses the xml - format for AA formulae writing to and reading from the computer memory. The xml – format contains operation types, operation orientations, operation uniterm separation, and AA operation uniterms. There are shown features of algorithm formula transforms, the result of which are 5 times shorter algorithms while saving all algorithm functionalities.
PL
Istniejąca algebra algorytmów (AA) zawiera specjalne znaki operacji, jakich nie ma wśród znaków matematycznych. Znaki mają skomplikowane formy. Znaki operacji mogą być stworzone z wykorzystaniem istniejących edytorów, takich jak na przykład Word. Jednak proces ich tworzenia jest bardzo skomplikowany i czasochłonny. Z tego powodu dla komputerowego edytowania formuł algebry algorytmów został stworzony specjalny edytor, którego główne okienko przedstawiono na rys.1. Dla zapisu formuł algebry algorytmów w pamięci komputera został stworzony specjalny format xml. Opisano format xml, służący do zapisu formuł algebry algorytmów do pamięci komputera. Zbudowano dwie formuły do analizy formatu xml, wykorzystane do identyfikacji i zapisu typów, orientacji i separatorów oraz unitermów operacji algebry algorytmów. Udowodniono, że te formuły umożliwiają wykonanie analizy formatu xml. Pokazano możliwości przekształcenia formuł algorytmów. W wyniku przekształceń możliwe jest 5 – krotne zmniejszenie liczby unitermów, przy zachowaniu wszystkich funkcjonalności formuły algorytmu.
12
Content available Models of layers of information systems
Ovsyak V., Ovsyak O.
Pomiary Automatyka Kontrola
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2014
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R. 60, nr 6
388--390
EN
Model of information system layers as a scheme, algebraic expressions and computer model were created. Algebraic model of information system layers is synthesized by means of algebraic algorithms and modified systems of algorithmic algebras. A computer model of layers is created in environment Microsoft Visual Studio .NET. A four-layer model of abstract information system in the form of diagrams, mathematical formulas and models of computer system were created. Comparison of object models is performed.
PL
W pracy zaprezentowano metodę uproszczenia złożoności projektowania systemu informacyjnego, polegającą na jego podziale na warstwy, z których każda zawiera jeden lub więcej podsystemów. Metoda jest oparta na wykorzystaniu zmodyfikowanego systemu algebr algorytmicznych, opracowanego przez autora [1, 2]. Przedstawiono ogólny model algebry algorytmów w postaci warstw algorytmu, który zaimplementowano w programie komputerowym. Omówiono modele warstw systemu informatycznego utworzone w postaci schematu, wykresów algebraicznych i modelu komputerowego. W programie komputerowym warstwy są reprezentowane w formie zagnieżdżonych prostokątów (rys. 8). Modele algebraiczne warstw systemu informatycznego zostały zsyntezowane przy zastosowaniu zasobów algebry algorytmów i zmodyfikowanego systemu algebr algorytmicznych (tab. 1). Model komputerowy warstw zbudowano w środowisku Microsoft Visual Studio. NET. Utworzono czteropoziomowy model warstw informatycznego systemu abstrakcyjnego w postaci schematów, wykresów matematycznych i modelu systemu komputerowego. Pokazano wyniki porównania utworzonych modeli.
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