Parallel symbolic state-space exploration is difficult, but what is the alternative?

Abstract

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Evaluating Machine-Independent Metrics for State-Space Exploration

“…Through this evaluation, PRSS was shown to be effective (some speedups more than 100x) for exploring various concurrent programs using JPF version 3.1.2 across a reasonably small number (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) of parallel machines. However, it is not Paper Metric(s) Search Type Used Randomness Machine Configuration CAPP [8] Transitions Stateful Yes Cluster CAPP [8] Schedules Stateless Yes Cluster Controlling Factors [2] States Stateful Yes Cluster CTrigger [18] Time Stateless No Single machine Depth Bounding [11] States, Transitions, Time, Memory Stateful No Not specified Distributed Reachability [15] Time Stateless Yes Cluster Gambit [7] Time, Memory Hybrid Yes Not specified ICB [4] States, Time Hybrid No Not specified PENELOPE [19] Time Stateless No Not specified PRSS [3] States Stateful Yes Cluster Random Backtracking [12] States, Transitions Stateful Yes Not specified Swarm [5] States, Time, Memory Stateful Yes Single machine clear whether similar results could be obtained for (i) other concurrent programs, (ii) stateless exploration, (iii) different search strategy, or (iv) the latest version of JPF which incorporates many new optimizations.…”

“…We use an implementation of the ICB strategy in the ReEx framework [8], [13] for some of our experiments. Other techniques include those that parallelize a single exploration by partitioning the exploration into non-overlapping subspaces [14], [15] and those that exploit diversity among different (potentially overlapping) complete explorations by performing them in parallel [3], [5].…”

Sylvan: multi-core framework for decision diagrams

“…Parallel symbolic reachability (after 2000) After 2000, research attention shifted from parallel implementations of BDD operations towards the use of BDDs for symbolic reachability in distributed [15,33] or shared memory [18,28]. Here, BDD partitioning strategies such as horizontal slicing [15] and vertical slicing [35] were used to distribute the BDDs over the different computers.…”

Coupling simulation and model checking to examine selected mechanical constraints of automated production systems

“…A reason for that is that symbolic model checkers can only work locally on one computer. The possibility to distribute work among multiple computers is missing [8]. However, many approaches have shown that explicit-state model checking scales well in a distributedmemory environment [9,10].…”