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...te reachability analysis can be as bad as enumerative methods. Hence, we are planning to incorporate more recent symbolic techniques such as clustering [17] and saturation-based reachability analysis =-=[18, 19]-=- in our current implementation. These techniques will certainly improve computation of state predicates such as program invariant and fault-span. However, due to the dynamic nature of synthesis, since...

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...ch was not always practical. [11] avoids the Kronecker encoding by conjunctively partitioning the transition relation of each event into groups, encoded by matrix diagrams with an identity reduction. =-=[5]-=- allows an even finer partition, where conjuncts can share state variables, resulting in a more efficient computation for the symbolic encoding of the transition relation. Fully-reduced decision diagr...

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...C-MOAN). Contribution and related work. In the area of quantitative evaluation, symbolic techniques already exist. The Petri Net based tool SMART [5] implements a powerful technique called saturation =-=[6]-=-. Also, symbolic techniques have been developed for a stochastic process algebra and implemented in the tool CASPA [7, 8]. The most general algorithm is the one used in SMART. But, it does not have su...

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...it events, potentially leading to exponential growth of the node sizes or of the number of events. A more recent version of saturation allows the conjuncts to be functions of multiple state variables =-=[12]-=-, but we limit our discussion to the original version for simplicity (the findings of this paper are equally applicable to this general version of saturation). We say that level k does not depend on e...

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...., non-safe Petri nets and software protocols) have variable domains with a priori unknown or very large upper bounds. These bounds must then be discovered “on the fly” during the symbolic iterations =-=[10]-=-, and MDDs are preferable to BDDs when using this approach, due to the ease with which MDD nodes and variable domains can be extended. A second advantage, related to the present paper, is that our cha...

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...encoding Nt which is reached by following the edge labeled i from the root and then the edge labeled i ′ from the resulting node. To improve over breadth-first iterations, we have proposed algorithms =-=[12,13]-=- that exploit chaining [33] and event locality. Chaining is based on the observation that the number of symbolic iterations might be reduced if the application of asynchronous events (transitions) is ...

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...4 ·10 7 0.13 4.36 1.00 ·10 8 1.42 34.28 1.02 ·10 3 1.46 35.46 [12] 15 2.27 ·10 11 0.91 21.90 7.83 ·10 11 91.57 1415.63 - - - bitshift 20 1.56 ·10 2 0.01 0.11 4.08 ·10 7 0.01 0.50 4.19 ·10 6 0.02 0.54 =-=[10]-=- 70 1.56 ·10 2 0.02 0.26 3.60 ·10 16 0.09 3.37 4.72 ·10 21 0.14 4.15 bqueue 5 2.37 ·10 7 1.08 24.53 1.82 ·10 8 22.02 408.38 1.58 ·10 4 22.47 414.68 [19] 10 2.99 ·10 7 1.13 24.31 - - - - - - bubsort 5 ...

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...d its fully-identity reduced equivalent (right). another reduction rule of nodes, different than the two already presented in definitions 4 on page 4 and 5 on page 4: the full-identity reduction from =-=[8]-=-. An example of such an identity pattern and its full-identity reduction is shown in Figure 5. In this figure, edges leading to terminal 0 are omitted for clarity. Table 1 shows the execution time wit...

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...bles (reducing the number of decision diagram levels) or splitting events (increasing the size of E), which can be inefficient. Work is under way to employ the general next-state function encoding of =-=[13]-=- and represent N as a disjunction (over E) of the conjunction of a set of arbitrary decision diagrams defined over (usually small) subsets of the levels. Bounded CTL model checking. In cases where the...