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First, actual path constraints are typically not terribly long.
They are, after all, written by humans for the purpose of reasoning formally about constraints that arise naturally. Second, it is possible that the predicates that arise in this domain might lend themselves to specialized analyses with good performance. Of course, this is a claim that is likely to be made about any intractable problem, but at least here it can be formalized.
The complexity of the path-checking problem in our case arises, of course, from the variable-binding extension, but in particular it arises from nesting these binders. All of the intractable examples we have seen, such as the transformed formula in the QBF reduction, involve arbitrarily deeply nested variable bindings. The following theorem shows that model-checking a path constraint over a path is intractable only to the extent that variables are nested without bound. The correctness of the algorithm follows easily from the semantics of path constraints. Note that in the case where there are no variable assignments, this algorithm reduces to the algorithm for LTL.
Thus no column is filled more than m d times, where d is the maximum variable-nesting depth of c p. In practice, it seems unlikely that variable bindings will often be very deeply nested, since software architects are unlikely to be naturally interested in such convoluted constraints. This chapter thus addresses research claim 2 from section 1. A result of PSPACE-completeness establishes a tight upper and lower bound on both the time complexity and space complexity of verifying path constraints.
This is the best sort of result we could hope for in undertaking a theoretical evaluation like this one. In another sense, though, the practical relevance of these results is somewhat murky. The PSPACE-completeness result (theorem 2) suggests that verifying path constraints may be intractable for large problem sizes, and the polynomial-time result for the case in which the variable-nesting depth is bounded (theorem 3) suggests that the problem may become tractable provided that rigid variables are not deeply nested.
But how are we to apply these theoretical results in practical contexts? Is path constraint verification computationally practical for the problem sizes and constraint specifications that are likely to emerge in realistic architecture evolution scenarios? This dissertation does not provide final answers to these questions. Fully settling them would require performance tests of tools implementing our approach.
Thus, although these theoretical results provide a final and decisive answer to the question of the computational complexity of path constraint essay custom writing verification, they do not provide an entirely satisfying answer to the question of practical performance. The theoretical results proved in this chapter are 39 3 Theoretical results on evolution path constraint verification of relevance to anyone using such a logic to verify formulas over finite paths. Thus, it is my hope that the results here will be useful to other researchers beyond the domain of architecture evolution, apart from their relevance to my own thesis. One reason for this is that missions at JPL can last for decades, and software systems must evolve to support them continuously. The Voyager mission launched in 1977, and 36 years later it is still running—and transmitting telemetry that must continue to be processed by software on the ground.
The flight software and ground software associated with this mission have required continuous maintenance to keep them up essay custom writing and running for 36 continuous years.
As new missions make use of a multimission platform, the platform must evolve to support the new capabilities and qualities that the new missions require. Over a long period of time, a multimission system can change drastically, ultimately to the point where it bears little resemblance to its ancestral form. The system has been used for many prominent NASA missions, and continues to be used today. Among the systems that make up AMMOS are elements responsible for uplink and downlink of spacecraft telemetry, for planning command sequences, for processing spacecraft telemetry, for navigation, and so on. The system suffered from architectural inconsistencies and redundancies and lacked a coherent overarching architecture. The goal was to develop a modern deep-space information systems architecture based on principles of composability, 42 4. The MDAS element was an attractive choice for several reasons. First, it was undergoing a major restructuring to meet specific goals. Third, it presented interesting trade-offs and unanswered questions that might be usefully addressed by an architecture evolution analysis. Fourth, I had good access to staff who were familiar with the system and with the evolution, who could provide architectural information beyond that available in official documentation.
At the time of this case study, engineers were in the process of adapting and refining the architecture of MPCS for multimission use.
In this section, I describe the initial MPCS architecture (as used by MSL), the motivations for evolving it, and the planned future architecture. Components could be attached to or detached from the message bus freely (by subscribing to or publishing the appropriate kind of event) provided that they adhered to application protocols and did not violate architectural constraints, allowing for plug-and-play reconfiguration of the system. This event-driven, bus-mediated architecture gave MPCS a degree of architectural flexibility. An important example of the architectural variability of MPCS is that it could be deployed with different configurations in different environments.
This database was queried by a number of analysis components. The purpose of these programs was to retrieve data from the database and output the data in a standard format. Together, help write an essay online these components effectively formed a standard MPCS workflow. Although MPCS was flexible enough to be configured in many different ways, this workflow describes the way MPCS works most of the time, in typical environments. However, as MPCS was to be developed for reuse in future missions, engineers faced the need to evolve the system to improve qualities such as performance and usability, support additional needed capabilities, and better integrate with other ground data systems. In this case study, I focused on two particular proposed features of MPCS that project architects hoped to introduce in future versions: integrated commanding (ICMD) and timeline integration.