ࡱ> Y bjbjWW .$==P]....8zBffvvv?BABABABABABAB$0C$EeB# eB$..vvf$$$.vv?B....?B$$+oA6h?BvL.տ'BValidation and Test Case Generation for MSCs using a Propositional SAT Solver K. Meinke Dept. of Numerical Analysis and Computer Science, Royal Institute of Technology, 100 44 Stockholm, and Prover Technology AB, Alstrmergatan 22, 112 47 Stockholm e-mail: karlm@prover.com 2000-06-07 Abstract We describe the results of a pilot project to construct a validation and test case generation tool for MSCs based on a SAT solver for propositional logic known as Prover Plug-In(. We give a metric temporal logic semantics to MSCs which allows us to interface existing MSC editing tools to a constraint solver for metric temporal logic. In this way, we are able to use the results of constraint solving to carry out validation analysis of problems such as race and performance. The output from constraint solving can also be annotated and saved for the purposes of test case generation. Introduction Message Sequence Charts (MSCs) are gaining acceptance as a commercially useful requirements capture language for real-time and distributed systems, both within and outside the world of telecommunications. Similar formalisms, such as UML Sequence Diagrams, together with the spread of object-oriented software engineering (OOSE) further increase the interest in this type of formalism. Independently of which systems development model is used (V model, spiral model etc.) there is a need for computer assistance with the validation activity during the requirements capture phase. By validation, we mean the (somewhat open-ended) activities of: investigating whether the user requirements as written down (typically in the form of MSCs and natural language text) coincide with the product that the end user actually wants, and certifying that the user requirements, as written down, are: internally consistent, unambiguous, complete (unless there is an intentional lack of information), and to the extent that this can be predicted at an early stage, technically feasible. Well known statistics indicate the significant number and subsequent high-cost of errors which slip through the validation process. It is important to distinguish between the process of validation, as described above, and the process of verification, where we check agreement between a set of requirements and an implementation. These differences between verification and validation reflect themselves in the different types of algorithms that are used for each. For verification one can apply automated reasoning (theorem proving) algorithms to compare an implementation with its requirements. This has been a traditional area of academic and industrial research into formal methods for many years. For validation of high-level requirements, it is not possible to carry out this kind of comparative analysis. On the other hand, simulating the system requirements can provide a rich source of information about the validity of a set of MSC requirements. In fact, by going beyond conventional state based simulation, and using constraint solving techniques such as those given by a SAT algorithm, we can obtain quite deep analyses of the information content of a set of MSCs. Such analyses, we claim, provide insight into the validation problem: are we building the right system? In this paper we describe the results of a pilot project to develop validation and test case generation tools for MSCs using a commercially developed satisfiability algorithm. Prover Plug-In( is a commercial implementation of Stlmarcks satsifiability algorithm for propositional logic (Stlmarck [1989]), which is marketed by Prover Technology AB. We will describe an extension of Prover Plug-In that consists of a compiler from MSCs into temporal logic formulas. An existing application then allows us to compile the temporal logic model of a set of MSCs into propositional logic and execute the satisfiability algorithm. This algorithm either returns a satisfying assignment (that we decompile back into an MSC simulation) or a refutational proof (that can be returned for debugging purposes). Over a decade of industrial application, Stlmarcks algorithm has proven itself to have efficient run-time and memory requirements, even though the satisfiability problem for propositional logic is NP-complete. The structure of this paper is as follows. In Section 1 we outline the semantical model of MSCs that we use to carry out analysis. In Section 2, we explain the basic principles of compiling MSCs and validation properties into temporal logic formulas. Effectively, we give a semantics for MSCs using a metric temporal logic. In Section 3, we describe the architecture, functionality and performance of our MSC analysis tool. In Section 4, we briefly compare our approach to other MSC tool development projects described in the literature. Finally in Section 5 we present some conclusions. 1. Semantics of MSCs In order to validate a set of MSCs it is first necessary to understand what they mean as a set of requirements, i.e. their semantics. Several different approaches to the semantics of MSCs can be found in the literature, including: Ladkin and Leue [1993, 1995], Mauw and Reniers [1994], Alur et al [1996] and Broy [1996]. The process algebraic semantics developed by Mauw has provided the basis for a standardised semantics proposed by the ITU in ITU [1995]. From the point of view of constraint solving, the most appropriate semantic model proposed in the literature seems to be the partial ordering semantics developed in Alur et al [1996]. Partial ordering semantics seems to come closest to capturing the informal semantics normally used to describe MSCs. From the point of view of tool use, this clear relationship between formal and informal semantics is very important. The requirements analyst must be able to understand the errors diagnosed by a tool in an intuitive way, in order to be able to correct them. Semantic models that are complex and unintuitive will hinder the effectiveness of any tool set that is built on top of them. In fact, Alur et al [1996] introduce a framework for different semantic models of MSCs. The fundamental constraints on the sending and receipt of messages can be extended in a variety of different ways, for example by making different assumptions about channel behaviours. We will extend the semantic framework presented in Alur et al [1996] by introducing explicit simulations of MSCs as semantic objects. The aim is to automatically generate such simulations by constraint solving. Ultimately, we are even interested in timing and performance analysis. Therefore, our approach differs somewhat from Alur et al, since they place emphasis on efficient computation of the transitive closure of event orderings and use quite different algorithmic techniques for this. Definition A partial order model ( of a message sequence chart M is a structure consisting of: A finite non-empty set P of processes, A finite set E of events, which can be partitioned into two disjoint subsets, S ( E of send events and R ( E of receive events, A labelling function L : E ( P, which associates each event with the process where it occurs. (A send event occurs at the sending process, a receive event occurs at the receiving process.) Thus we can define the set Ep of events occurring at p, for each process p ( P, by Ep = { e ( E | L(e) = p } A compatibility relation C ( S ( R, such that: (a) for each send event s ( S there exists at most one receive event r ( R such that C(s, r), and (b) for each receive event r ( R there exists at most one send event s ( S such that C(s, r). For each process p ( P, a total ordering < vis,p ( Ep ( Ep on the (cartesian product of the) events occurring at p, called the visual order. The visual order < vis,p represents the order in which the events at p appear visually, as drawn or written on the page. Since MSCs are normally drawn with the time axis moving down the page, then e1 < vis,p e2 if, and only if, e1 is drawn above e2 in the diagram, or mentioned before e2 in an equivalent MSC text specification. We let < vis denote the corresponding (partial) visual ordering of all events, (implies). In addition, the language allows integer expressions to be built up in the usual way from integer constants 0, 1, -1, and variables chosen from some set X, and the usual arithmetic operations, +, -, *. Then, if exp1 and exp2 are integer expressions, ( exp1 < exp2 ), ( exp1 = exp2 ) are both propTRIO formulas. Furthermore, if ( is a propTRIO formula, and exp is an integer expression, then Dist( (, exp ) is a propTRIO formula. The operator Dist is termed the distance or shift operator. Intuitively, the truth value of Dist((, exp) at time t is the truth value of ( shifted a distance of exp time units from t. Finally, since the integer expression exp may contain variables, we would like to be able to quantify over these, so that temporal modalities can be expressed. Thus if ( is a propTRIO formula, and x is an integer variable, then ( (x ( ), ( (x ( ) are propTRIO formulas. A temporal structure S for this language, consists of a family of functions pS : Z ( B, one for each propositional literal p, where Z = { , -1, 0, 1, 2, } denotes the set of integers, and B = { true, false } denotes the set of Booleans. Then for each propTRIO formula (, and for any temporal structure S, any integer variable assignment ( : X ( Z, and any temporal instant i ( Z, we can define the satisfaction relation (S, (, i) |= (, (read ( is true in S under ( at time i) by induction on the complexity of formulas, (S, (, i) |= p ( pS(i) = true, (S, (, i) |= ( exp1 < exp2 ) ( eval((exp1) < eval((exp2) (S, (, i) |= ( exp1 = exp2 ) ( eval((exp1) = eval((exp2) (S, (, i) |= ( ( & ( ) ( (S, (, i) |= ( and (S, (, i) |= ( (S, (, i) |= ( ( | ( ) ( (S, (, i) |= ( or (S, (, i) |= ( (S, (, i) |= ~ ( ( not (S, (, i) |= ( (S, (, i) |= ( ( -> ( ) ( (S, (, i) |= ( implies (S, (, i) |= ( (S, (, i) |= Dist( (, exp ) ( (S, (, i + eval((exp) ) |= ( (S, (, i) |= ( (x ( ) ( (S, ([x/j], i) |= ( for all j ( Z, (S, (, i) |= ( (x ( ) ( (S, ([x/j], i) |= ( for some j ( Z, Here, eval((exp) is the integer value obtained by evaluating the expression exp under the assignment ( : X ( Z recursively, while ([x/j] : X ( Z is the variable assignment which agrees with ( everywhere except on x, where ([x/j](x) = j. Notice above how the distance operator Dist( . , . ) shifts the evaluation of its formula argument. The advantage of having a temporal language with a single shift operator is that we can use it to encode most of the commonly used temporal modalities. To compile MSCs into propTRIO in a semantically transparent way, we require the following modalities: Always( ( ) ( (x Dist( ( , x) Sometime( ( ) ( (x Dist( (, x) SometimeFuture( ( ) ( (x ( x > 0 & Dist( (, x) ) AlwaysFuture( ( ) ( (x ( x > 0 -> Dist( (, x) ) Before( (, ( ) ( Always( ( -> SometimeFuture(( ) ) OccursOnce( ( ) ( Always ( ( -> AlwaysFuture( ~ ( ) ) Within( (, exp ) ( (x ( x < exp & Dist((, x) ) It is instructive to decode these modalities according to the semantics given above. For example, Before( (, ( ) means that for any integer time point i ( Z, if ( is true at i, then at some point in the future relative to i, ( is true. OccursOnce( ( ) means that for every integer time point i ( Z, if ( is true at time i then ~ ( is true for ever in the future after i. With these operators formalised, we can give a metric temporal logic semantics to an MSC which coincides with its partial ordering semantics, for the various different semantic models proposed in Section 1. 2.1. Definition Let ( = ( P, E = S ( R, L, C, Dist( r, ((p, q) ) Intuitively the formula Timing(,(p,q) forces all messages from p to q to incur a delay of exactly ((p, q) units. Notice that the formula Timing( subsumes the formula Before(,< in the sense that every temporal structure S which satisfies Timing( also satisfies Before(,<. Many different generalisations and refinements of this timed delay semantics are possible. For example, we can specify a channel delay of no more than (1(p, q) time units, or no less than (2(p, q) time units (or even both). We leave this as an exercise for the interested reader. Given an MSC M, its partial ordering semantics <, any associated channel delay information (, and the corresponding temporal logic semantics ( we can consider generating temporal structures which satisfy ( according to the satisfaction relation |= defined above. However, such structures are infinite, and therefore can neither be generated nor stored in the finite memory of a computer. Nevertheless, it is possible to approximate the infinite model semantics of propTRIO with a finite model semantics, in a way that preserves the validity of the kinds of formulas we are usually interested in. A finite model semantics defines the truth values of literals over a contiguous but finite segment of the infinite timeline. Such a semantics can be defined in various different ways. The approach used in the temporal logic front end to Prover Plug-In is defined in Morzenti et al [1992]. What is the utility of generating such satisfying temporal structures? At the very least we can say that each such structure provides an abstract simulation of a possible implementation of the system. Simulation alone is often enough to debug the more obvious errors in a set of requirements, such as errors of omission. On the other hand, the number of satisfying temporal structures is likely to be extremely large, and random exploration of this space becomes less productive as the space grows. Instead, we would like to add further constraints that force requirements errors to manifest themselves within simulations. Let us describe two such examples. As we have already discussed in Section 1, a deceptive aspect of the graphical structure of an MSC is that the visual ordering that it implies may disagree with the actual semantic ordering. Thus we can consider focussing on those temporal structures for which the visual ordering disagrees with the semantic ordering. 2.3. 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