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Domain expertise can aid significantly in planning evolution, and so domain specialization is an important part of the approach proposed here. Domain specialization is achieved by means of evolution styles, which encapsulate architectural expertise about a domain of software evolution. An evolution style provides common properties, operators, constraints, and evaluation functions to support modeling and reasoning about a broad class of evolutions. For example, consider the following domains of evolution: 1. Evolutions to improve the security of a service-oriented architecture 4.

Evolutions from a legacy version of IBM WebSphere to the most recent version Each of these examples refers to a class of evolutions addressing a recurring, domain- specific architecture evolution problem. Each embodies certain constraints—for example, that the set of essential services should not become unavailable during the evolution.

Finally, although they share many commonalities, the specific details of how those evolutions should be carried out may well be influenced by concerns such as the time it takes to do the transformation, the available resources to carry it out, etc. We can take advantage of these characteristics of system evolution. Evolution styles are defined by analogy with the traditional concept of architectural styles in software architecture. An architectural style is a class of architectures that share common element types and properties, such as the pipe-and-filter architectural best college essay editing service style and the service-oriented architecture style. In a similar way, an evolution style defines a vocabulary of evolution operators, together with constraints governing how they may be composed into paths. Before turning to this empirical work, however, it is useful to conduct a theoretical analysis of some of the properties of our modeling apparatus. In this chapter, therefore, I evaluate our path constraint language by establishing a theoretical foundation for it and then using this foundation to evaluate its tractability (more precisely, the computational complexity of evaluating a path constraint). Other parts are either trivial and uninteresting (e. Such a simple definition will not work for our evolution path constraint language. So in college essay online help defining a syntax, we need to recognize that there are atomic formulas other than merely propositional symbols. In this respect, it is similar to first-order predicate logic (FOL), and so in formalizing the syntax for our path constraint language, we take a cue from FOL, giving separate, inductive definitions for terms, atomic formulas, and finally formulas: Definition 1 (path constraint syntax). To make this definition more concrete, let us analyze the example formula from section 2. When it appears alone, as in the first occurrence of system in the formula above, is is a nullary function: it takes no arguments and behaves as a term. But in a temporal context, constant is not a very good word for a nullary function, because a nullary function can refer to different states depending on the current state, just as a nullary predicate—a proposition—can have a different truth value from state to state. The predicates in our temporal path constraints, then, can be specified as conventional architectural constraints, using the facilities provided by the architecture modeling language. This is the only predefined function that currently exists in the path constraint language—in our experiences defining path constraints thus far, it has been sufficient on its own for expressing constraints that are of interest—but other predefined functions (or user-defined functions) could be added in principle without affecting the formalization in this chapter, such as a unary successor function that returns the next intermediate architecture in the temporal sequence.

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There are various ways to formalize the semantics of LTL.

In the following formalization, we identify a state with an interpretation of the propositional symbols.

Alternatively we could externalize an interpretation function as a map from states to sets of propositions. There are a number of things we must change to obtain a semantics for our path constraint language.

We, best college essay editing service however, are interested in expressing constraints over a finite sequence best college essay editing service of states: the evolution path, which comprises finitely many intermediate software architectures. So the first modification we will need to make to the definition of the semantics of LTL is to restrict ourselves to a finite sequence of states. In propositional logic, an interpretation is simply an assignment of truth or falsehood to each proposition symbol. But in FOL, an interpretation is a map that assigns a function to each function symbol and a relation to each predicate symbol. We also need a way to keep track of what states the variables are binding to.

After making all these changes, we obtain the following semantics. As in LTL, we define a state to be an interpretation, but now each state o, is a function that maps each function symbol to a function over states and each predicate symbol to a relation over states. A variable assignment s: V — S is a function that maps variables to states.

Indeed, there are several logics that are similar to ours with respect to our introduction into LTL of variables that retain their values across states. Another related logic has been developed to model real-time systems. A natural way to specify real-time systems is with LTL, but one problem that arises is the incorporation of hard real-time requirements. There are a couple of differences, which I describe under the next subhead. First, unlike Richardson, Alur and Henzinger, and us, who were devising specification languages for particular domains (object-oriented data models, real-time systems, and software architecture, respectively), Goranko is philosophically motivated. A nominal is an atomic symbol with the special property that it is true at exactly one state.

Another discussion of related logics is given by Demri et al.

How our evolution path constraint language differs.

Our language fits comfortably within this family of related logics. However, there are some ways in which our path constraint language distinguishes itself semantically from its cousins. Although these distinctions are subtle, they turn out to have, in some cases, major theoretical consequences. Although the existing literature is rich, it is also somewhat patchy.

There are interesting problems that have yet to be tackled. Notably, the question of the complexity of model-checking a path, which we discuss below and resolve in section 3. In the remainder of this section, I will discuss the differences between our path constraint language and other logics.

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