Abstract-Computer system reliability is conventionally modeled and analyzed using techniques such as fault tree analysis (FTA) and reliability block diagrams (RBD), which provide static representations of system reliability properties. A recent extension to RBD, called dynamic reliability block diagrams (DRBD), defines a framework for modeling dynamic reliability behavior of computer-based systems. However, analyzing a DRBD model in order to locate and identify design errors, such as a deadlock error or faulty state, is not trivial when done manually. A feasible approach to verifying it is to develop its formal model, and then analyze it using programmatic methods. In this paper, we first define a reliability markup language (RML) that can be used to formally describe DRBD models. Then we present an algorithm that automatically converts a DRBD model into a colored Petri net (CPN). We use a case study to illustrate the effectiveness of our approach and demonstrate how system properties of a DRBD model can be verified using an existing Petri net tool. Our formal modeling approach is compositional, thus it provides a potential solution to automated verification of DRBD models. Index Terms-System

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Aims  Isoetes L. is an ancient, primitive genus of heterosporous lycopsids characterized by a strongly reduced plant. The genus occupies a unique position in plant evolution as the closest relatives of the famous tree lycopods. Hybridization and allopolyploid speciation as well as habitat preference are regarded as having played an important role in the evolution of the genus Isoetes. However, it is still uncertain what factors have impacted upon hybridization and allopolyploid speciation of the genus Isoetes. Our understanding of the origin, evolution and modern distribution pattern of Isoetes in East Asia would benefit from investigations into the relationship between the unique geographical location and topographic features and the existing fossil record in the region. Methods  The chromosome number was determined from known 81 populations of 10 species of Isoetes in East Asia. The altitude was obtained in location of every population. T‐test was used to evaluate the altitude difference between diploid and polyploid populations. Data of Japanese Isoetes from Takamiya et al. was used in the study. Results  There are 10 known species of Isoetes with four diploids and six polyploids in East Asia. The four diploid species (2n = 22) are found at high altitudes (mean altitude = 2649.67 ± 1396.16 m, n = 18) and isolated from each other. In contrast, the six polyploid species widely occur in low altitude regions (mean altitude = 182.62 ± 181.44 m, n = 63) and are partially sympatric. Highly significant differences (P < 0.001) were observed between the mean altitude of locations of populations of diploids and polyploids. Main conclusions  The polyploidy speciations of Isoetes in East Asia might originate and develop from Holocene (Quaternary). The present pattern of distribution of Isoetes in East Asia is the result of allopatric speciation derived from vicariance, dispersal and combinations of both, and significantly correlative with the geological history and geographical changes. The change of altitude might have played an important role in allopolyploid speciation and the pattern of distribution of the genus Isoetes in East Asia by exerting a considerable influence on dispersal and hybridization opportunities of Isoetes species.

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