Darbe nagrinėjamas realiojo laiko sistemų, specifikuotų agregatiniu metodu, verifikavimo uždavinys. Sprendžiant šį uždavinį, naudojama pasiekiamų būsenų grafo sudarymo metodika, leidžianti įvertinti laiko intervalus, kuriais įvyksta sistemoje apibrėžti įvykiai. Darbe nagrinėjami pasiekiamų būsenų grafo sudarymo algoritmai ir pateikta prototipinėse programose naudojama duomenų struktūra. Suformuluoti ir įrodyti teiginiai apie pasiekiamų būsenų grafo sudarymo algoritmo sudėtingumą (maksimalaus vienos būsenos galimų perėjimų skaičiaus; grafo viršūnių skaičiaus augimo priklausomybės nuo įvykių skaičiaus; maksimalaus įvykių skaičiaus elgsenoje laiko intervale; maksimalaus viršūnių skaičiaus laiko intervale.) Pateikta trijų testinių sistemų grafų automatizuoto sudarymo analizė. Parodyta, kad Simplekso optimizavimo procedūra laiko momentų palyginimui gali būti naudojama tik atskirais atvejais. / The work deals with a verification task of real time system specified by aggregate method. While solving the task, a technique for creation a reachable state graph is used. The technique permits to evaluate intervals of time when the defined system events occur. Reachable state graph creation algorithms are analysed in the work. A data structure used in prototype software is presented in the work too. Assertions about a complexity of algorithm for reachable state graph creation are formulated and proved. These assertions concern maximum number of transitions from single state, dependency of number of graph verteles growth on a number of events, maximum number of events in a behaviour during time interval, and maximum number of vertexes during time interval. Analysis of automated creation of graphs for three test systems is presented. It is shown that Simplex optimisation procedure for comparison of time intervals can be used only in certain cases.

The problem of analyzing concurrent systems has been investigated by many researchers, and several solutions have been proposed. Among the proposed techniques, reachability analysis—systematic enumeration of reachable states in a finite-state model—is attractive because it is conceptually simple and relatively straightforward to automate and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. The system validation problem considered here is the problem of verifying that the original specification is itself logically consistent. If, for instance, the specification has a design error, an implementation is expected to pass a conformance test if it contains the same error. A validation for the logical consistency of the system, however, must reveal the design error. An automated analysis of all reachable states in a distributed system can be used to trace obscure logical errors that would be very hard to find manually. This type of validation is traditionally performed by the symbolic execution of a finite state machine model of the system studied. The author presents an overview of the existing validation techniques and methods. Specified and analyzed systems are presented as reachable state graph. The implementation of the aggregate specifications validation system is also presented.

Formalios specifikacijos – tai matematinis programinės ar techninės įrangos aprašymas, kurį galima naudoti sistemos realizacijai. Formalių specifikacijų naudojimas dar negarantuoja specifikacijos teisingumo. Tam naudojami formalaus verifikavimo metodai. Šiame dokumente aptariami formalių specifikacijų validavimo metodai. Du populiaraiausi formalių specifikacijų validavimo metodai yra pasiekiamų būsenų grafo analizė bei invarianto tikrinimas. Pasiekiamų būsenų grafo analizę sudaro pasiekiamų būsenų grafo generavimas ir analizė. Grafo analizės metu ieškoma aklaviečių, uždarų ciklų, nepasiekiamų būsenų, atliekamas būsenų koordinačių apribojimų tikrinimas bei invarianto tikrinimas. Tradiciniai pasiekiamų būsenų grafo sudarymo algoritmai grafo sudarymui naudoja sistemos būsenų eilę. Kiekviena išanalizuota būsena įrašoma į pasiekiamų būsenų grafą. Dokumente aptariamas lygiagretaus programavimo naudojimas būsenų grafo generavimui, kuris analizuoja ir generuoja sistemos būsenas naudodamas lygiagrečias gijas. Eksperimentų su vienkanale aptarnavimo sistema metu nustatyta, kad lygiagretaus algoritmo naudojimas šio uždavinio metu leidžia pagerinti sistemos veikimą iki 35%, priklausomai nuo būsenų skaičiaus. / Arguably the most important task in creation of software is user requirement specification. Accurate requirement specification allows avoidance of errors in late stages of software development. This is extremely important in critical systems, where even vague error can cause great financial losses or even human victims. One of the methods used for precise user requirement specification is use of formal specifications. Formal specification is a mathematical method for describing of software or hardware, which might be suitable for system realization. Nevertheless, the construction of formal specifications does not guarantee the correctness of specification. For this reason formal specification validation is necessary. In this paper methods of formal specification validation are discussed. Two most popular methods of formal specification validation are reachable state graph analysis and invariant checking. Reachable state graph analysis consists of graph generation and graph analysis. Graphs can be analyzed for dead-ends, closed loops, state reach ability checking, coordinate restriction checking or invariant checking. Traditional reachable graph generation algorithm uses unanalyzed states queue to produce reachable state graph. Each step single state is analyzed and depending on results new vertex or edge is added to state graph. An improvement to the algorithm to consider is usage of parallel programming to process multiple states simultaneously. This allows increasing the... [to full text]

With the technological advancement in computer science, Geographic Information Science (GIScience), and transportation, more and more complex path finding queries including category based queries are proposed and studied across diverse disciplines. A category based query, such as Optimal Sequenced Routing (OSR) queries and Trip Planning Queries (TPQ), asks for a minimum-cost path that traverses a set of categories with or without a predefined order in a graph. Due to the extensive computing time required to process these complex queries in a large scale environment, efficient algorithms are highly desirable whenever processing time is a consideration. In Artificial Intelligence (AI), a best first search is an informed heuristic path finding algorithm that uses domain knowledge as heuristics to expedite the search process. Traditional best first searches are single-variate in terms of the number of variables to describe a state, and thus not appropriate to process these queries in a graph. In this dissertation, 1) two new types of category based queries, Category Sequence Traversal Query (CSTQ) and Optimal Sequence Traversal Query (OSTQ), are proposed; 2) the existing single-variate best first searches are extended to multivariate best first searches in terms of the state specified, and a class of new concepts--state graph, sub state graph, sub state graph space, local heuristic, local admissibility, local consistency, global heuristic, global admissibility, and global consistency--is introduced into best first searches; 3) two bivariate best first search algorithms, C* and O*, are developed to process CSTQ and OSTQ in a graph, respectively; 4) for each of C* and O*, theorems on optimality and optimal efficiency in a sub state graph space are developed and identified; 5) a family of algorithms including C*-P, C-Dijkstra, O*-MST, O*-SCDMST, O*- Dijkstra, and O*-Greedy is identified, and case studies are performed on path finding in transportation networks, and/or fully connected graphs, either directed or undirected; and 6) O*- SCDMST is adopted to efficiently retrieve optimal solutions for OSTQ using network distance metric in a large transportation network. / Ph. D.