M-nets: An algebra of high-level Petri nets, with an application to the semantics of concurrent programming languages

This paper describes a high-level Petri net model called M-nets (for modular multilabelled nets). A distinctive feature of this model is that it allows both: unfolding, as do most other high-level net models; and composition – in particular, synchronisation – in a process algebraic style, turning the set of M-nets into an algebraic domain. It turns out that the composition operations of this domain have various algebraic properties. Moreover, the model is such that composition operations are coherent with unfolding, in the sense that the unfolding of a composite high-level net is the composition of the unfoldings of its components. One of the motivations for M-nets is that they be a vehicle for giving semantics of concurrent programming languages. To illustrate their capability for that, the compositional semantics of – a simple, expressive concurrent programming language – is given. An associated low-level net semantics is described, and the coherence of these high-level and low-level semantics is proved. Received: 20 November 1996 / 13 January 1998     

A multistage parallel-hierarchic network as a model of a neuronlike computation scheme

A three-dimensional network and its application to the analysis of images are described. This multilevel architecture studies partial correlations between structural components of an image. An algorithm is proposed that formalizes a new approach to the decomposition of images. An image is transformed so that each pixel contains information on the spatial structure of its neighborhood. The most correlated information is first formed, which ensures the resistance of the algorithm to small structural changes. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 114–133, March–April, 2000.     

A regularization algorithm for singular controls of parabolic systems

A practically convenient method of regularization is proposed to solve an optimal control problem for a parabolic equation with a delta function on its right-hand side. The corresponding regularized analogue is proved to converge to a delta function in a negative space. The differential characteristics of the performance criterion are analyzed. An algorithm for finding the optimal control is developed for a regularized problem. Results from a numerical testing of the algorithm are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 86–94, January–February 2006.     

Queuing system evolution in a diffusion approximation scheme

An asymptotic diffusion approximation scheme is investigated as applied to the requirement evolution in semi-Markov queuing systems. In proving the diffusion approximation theorem, the compensating operator of the corresponding extended Markov process is used. This problem is solved with the help of a phase merging procedure. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 136–145, May–June 2009. Original article submitted August 19, 2008.     

Merits and limitations of using fuzzy inference system for temporal integration of INS/GPS in vehicular navigation

Most of the present vehicular navigation systems rely on global positioning system (GPS) combined with inertial navigation system (INS) for reliable determination of the vehicle position and heading. Integrating both systems provide several advantages and eliminate their individual shortcomings. Kalman filter (KF) has been widely used to fuse data from both systems. However, KF-based integration techniques suffer from several limitations related to its immunity to noise, observability and the necessity of accurate stochastic models of sensor random errors. This article investigates the potential use of adaptive neuro-fuzzy inference system (ANFIS) for temporal integration of INS/GPS in vehicular navigation. An ANFIS-based module named “P–δP” is designed, developed, implemented and tested for fusing INS and GPS position information. The fusion process aims at providing continuous correction of INS position to prevent its long-term growth using GPS position updates. In addition, it provides reliable prediction of the vehicle position during GPS outages. The P–δP module was examined using real navigation system data compromising an Ashtech Z12 GPS receiver and a Honeywell LRF-III INS. The proposed module proved to be successful as a modeless and platform independent module that does not require a priori knowledge of the navigation equipment utilized. Limitations of the ANFIS module are also discussed.     

An optimal control model for a system of degenerate parabolic integro-differential equations

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 90–102, November–December 2007.     

System approach to mathematical modeling of filtration consolidation

Filtration consolidation is modeled taking into account salt saturation of soil and the nonisothermal and relaxation nature of the filtration process. A boundary-value problem for a soil mass consolidated on an impermeable bed is posed, its approximated solution is obtained, and the results of numerical experiments are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 71–79, November–December 2006.     

Fluctuations of a stochastic system under an asymptotic diffusive perturbation

A stochastic singularly perturbed system is considered. Sufficient conditions of the asymptotic normality are obtained for the dynamic system in the vicinity of its equilibrium point. To this end, a solution to the singular perturbation problem is constructed for an asymptotic representation of the generator of a Markov renewal process. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 104–109, September–October 2008.     

A proof system for distributed processes

Summary A partial correctness proof system for Brinch Hansen’s Distributed Processes (DP) is presented. Two important aspects of the system are: Proofs of individual processes of a DP program are completely isolated from each other; in particular, no assumptions are allowed in the proof of one process about the behavior of the other processes. Secondly a process is characterized by its externally visible behavior, i.e. the sequence of interactions between this process and the other processes of the program. An example demonstrates the use of the system. This paper is an extended version of a paper presented at the Workshop on Logics of Programs, Brooklyn, New York, June 17–19, 1985 and was supported in part by the National Science Foundation under grant ECS-8404725.     

Detecting and Measuring Fine Roots in Minirhizotron Images Using Matched Filtering and Local Entropy Thresholding

An approach to automate the extraction and measurement of roots in minirhizotron images is presented. Two-dimensional matched filtering is followed by local entropy thresholding to produce binarized images from which roots are detected. After applying a root classifier to discriminate fine roots from unwanted background objects, a root labeling method is implemented to identify each root in the image. Once a root is detected, its length and diameter are measured using Dijkstra’s algorithm for obtaining the central curve and the Kimura–Kikuchi–Yamasaki method for measuring the length of the digitized path. Experimental results from a collection of peach (Prunus persica) root images demonstrate the effectiveness of the approach.     

Simulation of Diversified Economic Growth

An optimal growth algorithm is developed for a diversified economic growth model with piecewise-linear production functions. Numerical results are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 147–155, September–October 2005.     

An approach to expert assessment in software engineering

An approach is proposed to the solution of formalized problems of assessment of the activity that produces and maintains software systems (SSs). Such assessment is realized by using expertises that form a new assessment process adequate to the activity needs and specifics with an environment common to the expertises. The following mathematical apparatus is elaborated for expertises: a framework (target functions and executing mechanisms), a model and methods (formalisms for improving the quality and reusing the results of expertises) of an assessment process, and tools for integrating the apparatus into software development management processes. The approach is theoretically justified. Prospects of developing the proposed approach are described. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 151–168, July–August 2009.     

Choosing the parameter of a modified additive-averaged splitting algorithm

The problem-solving time and the solution accuracy are expressed as functions of a parameter. An optimization problem of choosing the parameter using a “time cost–solution accuracy” criterion is considered. A Pareto-optimal set of solutions is obtained. The best value of the parameter is chosen by the ideal-point method. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 98–105, July–August 2009.     

Translation of Algebraic Programs into Executable Codes

An approach to the problem of translation of algebraic programs into executable codes is presented. In particular, an algorithm for translation of algebraic programs represented in the language Aplan into C codes is proposed. An algorithm of reconstruction of types in Aplan is considered that also checks the absence of features used for dynamic specification of procedures in a code. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 168–176, September–October 2005.     

Transformational approach to the development of software architectures on the basis of fuzzy graph models

An approach to the creation of software architectures is examined that is based on the model-oriented paradigm that opens up the way to the implementation of transformational evolution of software systems. The emphasis is on the formalization of fuzzy graphs, fuzzy graph models, and rules of their transformation. A theoretical categorical representation of fuzzy software architectures is developed, which allows one to manage the process of their transformations on the basis of making decisions in a fuzzy modeling space on the functionality of the target platform-specific system. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 139–150, September–October 2008.     

Identification models of a one-dimensional space-time process

Problems of constructing linear and polynomially nonlinear mathematical models are solved for distributed space-time processes with discretely-continuously observable states under distributed space-time perturbations that create such states. The cases of exact and optimal (with respect to the mean-square criterion) identification of kernels of such models are considered. The identifiability conditions are specified for the process and accuracy conditions are established for its mathematical models. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 111–128, September–October 2007.     

An asymptotic estimate of the error of eigenvalues in the method of finite elements for the sturm-liouville problem

A scheme of the second order of accuracy for the Sturm—Liouville problem is constructed by the method of finite elements with the use of a special basic system of compact functions. The convergence of the method of finite elements is proved. An exact formula for estimating errors of eigenvalues is obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 28–36, March–Apni, 2000.     

Synthesis of a robust optimal system for stabilizing a plant with failing elements

An original performance functional is proposed for problems of synthesis of highly accurate stabilizing systems, which consist of an element that is a measure of the sensitivity of the closed-loop system to arbitrary changes of the controlled plant. A new spectral algorithm is considered for the synthesis of optimal stabilizing systems. An analytical example of the synthesized system is given to illustrate the high efficiency of the synthesis procedure. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 151–158, May–June, 2000.     

Direct methods of solving systems of linear algebraic ef ions with complex a-matrices

Algorithms of computer algebra are proposed for solving systems of linear algebraic equations with complex á- matrices. An analysis of roundoff errors for the computational schemes considered is given. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 144–156, March–April, 2000.     

Iterative procedure for solution of sylvester generalized matrix equation

An iteration procedure for solving Sylvester generalized matrix equation is proposed in this paper. The sufficient conditions of stability of the iteration procedure for solving this equation are obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 183–186, May–June, 2000.