ELEMENTS EVALUATION OF SOFT-HARDWARE OBJECTS WITH COMPLEX PHYSICAL, INFORMATION STRUCTURES LINKS

It is offered to consider the index of element importance for multi-element soft-hardware objects with complex structure physical, information links. Elements evaluation is carried out in the planning of implementation of diagnostic tests. The methodological basis is based on the use of formal objects "network of uniformity soft-hardware devices", "processes operating environment", the diagnostic model of inter-process communication tract.


Introduction
Technical diagnostics soft-hardware objects with complex structure physical, information links (the object of diagnosis, OD) should be carried out taking into account the systemic role of their elements. The methodological basis of technical systems' analysis with a sequential, sequential-parallel, parallel-sequential structure of elements is sufficiently developed and tested. At the same time, evaluation of elements soft-hardware objects with a more complex structural organization requires further research.
A perspective approach to evaluating of the structural properties of elements of multi-element soft-hardware objects is their consideration as elements of the cybernetic system [3,10].
Cybernetic system is an abstract model of a technical system as a set of related objects (elements) capable to receive, store, process, and exchange information. The scientific research of cybernetic systems is aimed to determine the most common patterns for all such objects [5,8]:  structurea set of elements and relations between them;  statea set of states of elements and connections between them;  the complexity is due to the dimensional (the number of parameters which describe elements' states), number and variety of relationships between elements. The presentation of OD as a set of physical, informational complex structures of links cybernetic system connections allows us to use a wide range of interpretations for complex networks. The theory of complex networks offers the most developed approach to description and evaluation of the structural properties of multi-element technical objects [2,4].

Formulation of the problem
Based on the foregoing, the model of the selected OD is the formal object "network of uniformity soft-hardware devices". The assumption of "uniformity" is accepted on the basis of analysis of trends, principles of practical implementation (modularity, multilevel, unification) software, hardware support of Open System Interconnection (OSI) and inter-process communication.
It is offered to evaluate the element importance to support physical, informational connectivity of multi-element softwarehardware ODs. The multipliers of additive index χ i E are the relative weights of element inclusion in the structures of physical, informational connectivity on the observation interval χ . The initial data are the adjacency matrix of the formal object "network of uniformity soft-hardware devices" in the observation interval χ : for the graph of physical links ij u  , for the graph of information links ij w  .

The network of uniformity soft-hardware devices
The network of uniformity soft-hardware devices is a formal object based on a one-to-one mapping of physical and information connectivity of OD elements to the set of nodes complex network and relationships between them ( Fig. 1): Notation: is a set of uniformity soft-hardware devices; U is a relation of physical connectivity; W is a relation of informational connectivity;  A process is a unit for planning computing work of a softhardware device and the subject of access to resources. The algorithm of process software implementation in RAM determines the computational work of soft-hardware device on the time interval for its execution.
The basis for building a process of software implementation in RAM is the loadable module of a program. The memory address space required for the process is isolated from unforeseen I/O (Input/Output) operations.
The operating system kernel is a software implementation of control algorithms for scheduling and allocation of CPU time, address space RAM, I/O devices between processes, providing their access to system services. The role and place of the kernel of operating system is to provide inter-process communication in the context of the I/O operations. Its software implementation is provided by functionality of OSI levels: transport, network, data link. For this, its software implementation includes: firstly, the functionality of the transport, network, data link layer; secondly, the provision of FIFO service discipline, stream multiplexing, error control, etc.
Vectors of parameter values and settings of functional components of a uniformity soft-hardware device, i vV  , is a set of parameters and settings of DCE device components, is a set of options and settings of software implementation kernel components to provide inter-process communication, , , , , The role and place of kernel components of soft-hardware device are considered in the context of formal object ″processes operating environment″ (Fig. 2): , , , , , , , : where ine x  is access matrix for transferring data blocks between where ine x  is access matrix for transferring data blocks of kernel  Principles to evaluate the element importance of OD on the basis of a formal object "network of uniformity softhardware devices":  the relation of nodes' physical connectivity U is mapping of operability physical connection between OD's elements (data transmission channel);  the relation of nodes' information connectivity W is mapping of operability information links between processes OD's elements (inter-process communication tract);  the graphs of physical, information links between elements of OD are mapping of technical state of inter-process communication tracts and data transmission channels in their composition.
Predicates of physical connectivity , 1, , where ij u  is the relationship matrix of nodes physical connectivity for formal object "network of uniformity softhardware devices" is an equivalent to the adjacency matrix of graph of physical connections between the elements Predicates of information connectivity , where ij w  is the relationship matrix of nodes information connectivity for formal object "the network of uniformity softhardware devices" is an equivalent to the adjacency matrix of graph of information links between OD's elements () W MV  on the observation interval χ (inter-process communication [1,4,9] that a graph is a set of nodes (vertices) and their ordered (unordered) pairs. An ordered pair of nodes (vertices) is called an edge; an unordered pair is called an arc. A pair of nodes (vertices) can be connected by two or more edges (arcs). Common graphs naming in applied research and engineering tasks is complex network. The element of the graph adjacency matrix is a mapping of links number between nodes, the element of the graph incidence matrixnodes which are incidental to links. The graph node degree is mapping of edges number that is incidental to the node of the graph. The sum of the graph edges is equal to the sum of the degrees of its nodes.
Two nodes of the graph are called connected if there is a route between them. A route is a finite sequence edges to move from one node to another. Cartesian product of sets is mapping binary relation of elements connectivity and can be given in terms of the predicate calculus. A binary relation is any subset of ordered pairs of Cartesian product.
The truth of the predicate indicates the existence of a relationship. The truth of the predicate indicates the validity of a binary relation connectivity as a result of the Cartesian product.
To define a relation means to set a predicate (method) of selecting a subset of ordered pairs from the set of results of Cartesian product. A visual representation of binary relations is the relation matrix, an oriented (undirected) graph or its adjacency matrix.

The formal axiomatic apparatus
for determining the technical state of inter-process communication tract The prevailing index of the element OD's importance ( 0,17 r E   ) is explained by the obvious transit role of this OD's element. The main element of the tracts inter-process communication is the functional component r vV  described by the formal object ″processes operating environment″.

Conclusions
Adequacy of the element OD importance index (24-25) is based on generally accepted interpretation of a node degree of a graph (complex network), it is informative, invariant, and resistant to evaluation interference.
Formal objects "network of uniformity soft-hardware devices" (1-2, 10-15), ″process's operating environment″ (3)(4)(5)(6)(7)(8)(9) are the basis of a new scientific approach to the synthesis and analysis of multi-element soft-hardware objects with a complex structure of physical, information links. The formal axiomatic apparatus (16-23) is a logical conclusion system about the technical state of an inter-process communication tracts. The conclusion about the technical state of "network of uniformity soft-hardware devices" can be made after performing diagnostic tests based on a comparison of their results using index of the element OD importance (24-25).
Further research is aimed to develop a model of diagnostic parameter of inter-process communication tracts and methods of evaluation of technical state network of uniformity softhardware devices.