We present a novel algorithm for generating state spaces of asynchronous systems using Multi–valued Decision Diagrams. In contrast to related work, we encode the next–state function of a system not as a single Boolean function, but as cross–products of integer functions. This permits the application of various iteration strategies to build a system’s state space. In particular, we introduce a new elegant strategy, called saturation, and implement it in the tool SMART. On top of usually performing several orders of magnitude faster than existing BDD–based state–space generators, our algorithm’s required peak memory is often close to the final memory needed for storing the overall state space.

Reo is an exogenous coordination language for compositional construction of component connectors based on a calculus of channels. Building automated tools to address such concerns as equivalence or containment of the behavior of two given connectors, verification of the behavior of a connector, etc. requires an operational semantic model suitable for model checking. In this paper we introduce constraint automata and propose them as a semantic model for Reo.

In previous work, we proposed a "saturation" algorithm for symbolic state-space generation characterized by the use of multi-valued decision diagrams, boolean Kronecker operators, event locality, and a special iteration strategy. This approach outperforms traditional BDDbased techniques by several orders of magnitude in both space and time but, like them, assumes a priori knowledge of each submodel's state space. We introduce a new algorithm that merges explicit local statespace discovery with symbolic global state-space generation. This relieves the modeler from worrying about the behavior of submodels in isolation.

Abstract not found

We describe the main features of SmArT, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. SmArT can combine dierent formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL model-checking algorithms, are available. For the study of stochastic and timing behavior, both sparse-storage and Kronecker numerical solution approaches are available when the underlying process is a Markov chain. In addition,

We present a new method for the symbolic construction of shortest paths in reachability graphs. Our algorithm relies on a variant of edge-valued decision diagrams that supports efficient fixed-point iterations for the joint computation of both the reachable states and their distance from the initial states. Once the distance function is known, a shortest path from an initial state to a state satisfying a given condition can be easily obtained. Using a few representative examples, we show how our algorithm is vastly superior, in terms of both memory and space, to alternative approaches that compute the same information, such as ordinary or algebraic decision diagrams.

Abstract. In previous work, we showed how structural information can be used to efficiently generate the state-space of asynchronous systems. Here, we apply these ideas to symbolic CTL model checking. Thanks to a Kronecker encoding of the transition relation, we detect and exploit event locality and apply better fixed-point iteration strategies, resulting in orders-of-magnitude reductions for both execution times and memory consumption in comparison to well-established tools such as NuSMV. 1

Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting high-level structure and regularity in the models to which they are applied, increasing the size of the state spaces which can be tackled. In general, this is done by using data structures which provide compact storage but which are still efficient to manipulate, usually based on binary decision diagrams (BDDs) or their extensions. In this paper we focus on BDDs, multi-valued decision diagrams (MDDs), multi-terminal binary decision diagrams (MTBDDs) and matrix diagrams. 1

Abstract not found

this paper, we propose a compact representation of logic functions using Multi-valued Decision Diagrams (MDDs) called heterogeneous MDDs. In a heterogeneous MDD, each variable may take a different domain. By partitioning binary input variables and representing each partition as a single multi-valued variable, we can produce a heterogeneous MDD with 16% smaller memory size than a Reduced Ordered Binary Decision Diagram (ROBDD), and with comparable memory size to Free Binary Decision Diagrams (FBDDs). And also, heterogeneous MDDs have shorter Average Path Length (APL) than ROBDDs and FBDDs. We minimized a large number of benchmark functions to show the compactness of heterogeneous MDDs