Galimullin, Rustam

English

Tomsk State University Repository

ИЗВЕСТИЯ ВЫСШИХ УЧЕБНЫХ ЗАВЕДЕНИЙТ. 55, № 8/3 ФИЗИКА 2012УДК 519.7R.F. GALIMULLINON SEPARATING UML SPECIFIED NON-DETERMINISTIC FINITE STATE MACHINESWITH TIME-OUTSUML state machine diagrams are briefly discussed and two approaches for deriving separating sequences for timedFinite State Machines are compared.Keywords: non-deterministic finite state machines with time-outs, state machine diagram.IntroductionNowadays the complexity of various discrete systems, such as computers, cell phones, embeddedcontrollers, etc., is extremely high, and thus, it is essential to provide high-quality testing at every stage ofthe system development. Moreover, since technical failures are very expensive, the system testing andverification at early stages, especially at the design stage, is of great importance [1]. Many of such sys-tems are formally described using the UML (the Unified Modeling Language) [2]. The UML being a vis-ual modeling language allows obtaining the comprehensive and detailed information about a system un-der design, as well as provides a possibility for convenient update of the system. Correspondingly, theUML is widely used in software engineering, business project development, hardware design and in anumber of other applications. It is also fruitful to use the UML for the integration of fresh employees andcross-national collaboration. There are some approaches for verifying systems described by UML. One ofthem is based on extracting a formal model from the UML description. In our paper, we use a timed fi-nite-state machine model (TFSM) that is an extension of a classical finite-state machine (FSM). By defi-nition, a FSM is described as a finite set of states and transitions between them. Every transition is labeledby an ‘input/output’ pair, where an input triggers the transition and an output is a system response to agiven input. A FSM is deterministic if at each state for each input, there is at most one transition labeledby this input, otherwise, a FSM is non-deterministic. If transitions depend on a time of applying an input,FSM is called timed FSM, and in our paper we deal with a certain type of timing constraints, so-calledtime-outs [3]. If no input is applied at a current state during an appropriate time period (time-out), thetimed FSM can move to another prescribed state. In this paper, we propose an approach how to distin-guish two timed FSMs extracted from UML descriptions.UML StatechartsIn this section we briefly describe UML notations. Being a multipurpose language the UML al-lows using state machine diagrams that are perfectly tailored to the FSM representation. Each state ma-chine diagram is supposed to include at least one state that can be additionally specified by the entry, cur-rent or exit activity (entry/do/exit). A transition may be either blank or can be labeled with a guard condi-tion, a timeout, or both of them. The UML description may contain some special states, so-called pseudo-states, that are used for initiating or finishing the execution (initiation pseudostate, final state, terminatenode), for joining or forking transitions (fork vertex, join vertex), etc. In order to extend state machinepossibilities composite states are added. Composite states contain one (orthogonal composite state) ormore regions which are executed simultaneously. An output of a composite state may include a join ver-tex. In this case the transition is executed when one of the regions reaches a final state. Otherwise, waitall condition becomes true. Composite states are very useful due to the ability to model and test a systemat different levels of abstraction, i.e., it is possible to model certain parts of a system as well as the overallsystem. Nevertheless, it is unknown how to distinguish two UML diagrams, e.g., the specification and acertain implementation. However, as it was mentioned above, state machine diagrams allow the transfor-mation of UML descriptions to timed, possibly non-deterministic, FSMs. In order to distinguish twotimed FSMs separating sequences are constructed [4].Deriving Separating Sequences for FSMs with timeoutsTwo approaches for deriving separating sequences were elaborated. The first approach is basedon a proper modification of the algorithm for deriving a separating sequence for classic FSMs. It is basedR.F. Galimullin228on a truncated successor tree constructed for the intersection of two timed FSMs describing the commonbehavior of both machines. For a current node, specified by the set of pairs <statei, timei>  there are edgeslabeled by each input, and for each input the set of all possible successors labels a node at the next level.A node is terminal if there are no successors for the given input (Rule 1), or the set of correspondingitems contains a set of items of the node at a higher level of the tree (Rule 2). If the tree has a node that isterminal due to Rule 1, a separating sequence exists. A separating sequence is a sequence of inputs label-ing a path from the root to the terminal node tailed by the current input. For TFSMs the algorithm ismodified by adding extra edges labeled by the minimum of time-outs. Thus, a separating sequence fortwo timed FSMs consists of <input, time> pairs. The second approach does not need any modification ofthe above mentioned algorithm. Instead of this, there is an additional step, namely, the transformation of atimed FSM into a classical FSM. The main point is that time-labeled transition (n time instances, for in-stance) is represented as n sequential transitions with a special input 1 (wait for one time instance) and aspecial output N. Correspondingly, the number of states increases compared with a timed FSM.  After thetransformation the intersection of two FSMs is constructed in order to derive a separating sequence.Comparing two approaches following remarks can be made. The successor tree for the first approachseems to be smaller, as a corresponding FSM has more states than the initial TFSM. On the other hand,the software implementation of the second approach is rather simpler and thus, we may expect that aseparating sequence can be derived faster.For more detailed comparison, both approaches were implemented and computer experiments withsoftware implementations were performed. TFSMs with 20–100 states and 10–750 inputs were randomlygenerated. For each pair of parameters 10 pairs of TFSMs were generated and average length of a sepa-rating sequence (if sequence exists) was calculated. The results are following (Fig. 1 and 2).   Fig. 1. States – length plot.                                  Fig. 2. Inputs – length plot.The experimental results show, that for randomly generated TFSMs separating sequences derivedusing the first approach are shorter. Moreover, when the number of input increases almost every ran-domly generated TFSM has a separating sequence of length 1.REFERENCES1. K a r p o v  Y .  Model Checking. – BHV-Saint-Petersburg, 2010. – 552 p. (in Russian)2. B o o c h  G .  The Unified Modeling Language User Guide, Second Edition / J a c o b s o n  I . ,  R u m b a u g h  J .  –Addison Wesley, 2005. – 496 p.3. G r o m o v  M . ,  E l - F a k i h  K . ,  S h a b a l d i n a  N . ,  a n d  E v t u s h e n k o  N .  // Formal Techniques for Dis-tributed Systems. – Germany: Springer, 2009. – P. 137–151.4. G a l i m u l l i n  R .  a n d  S h a b a l d i n a  N .  // Proceedings of the 5th Spring/Summer Young Researchers’ Collo-quium on Software Engineering (SYRCoSE 2011). – Ekaterinburg, USU, 2011. – P. 100–104.Tomsk State University, Tomsk, Russia Поступила в редакцию 15.06.12.E-mail: nihilkhaos@gmail.com_______________Rustam Galimullin, student.

On separating UML specified non-deterministic finite state machines with time-outs

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On separating UML specified non-deterministic finite state machines with time-outs

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