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

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

Rethinking Pointer Reasoning in Symbolic Execution

Symbolic execution is a popular program analysis technique that allows seeking for bugs by reasoning over multiple alternative execution states at once. As the number of states to explore may grow exponentially, a symbolic executor may quickly run out of space. For instance, a memory access to a symbolic address may potentially reference the entire address space, leading to a combinatorial explosion of the possible resulting execution states. To cope with this issue, state-of-the-art executors concretize symbolic addresses that span memory intervals larger than some threshold. Unfortunately, this could result in missing interesting execution states, e.g., where a bug arises. In this paper we introduce MemSight, a new approach to symbolic memory that reduces the need for concretization, hence offering the opportunity for broader state explorations and more precise pointer reasoning. Rather than mapping address instances to data as previous tools do, our technique maps symbolic address expressions to data, maintaining the possible alternative states resulting from the memory referenced by a symbolic address in a compact, implicit form. A preliminary experimental investigation on prominent benchmarks from the DARPA Cyber Grand Challenge shows that MemSight enables the exploration of states unreachable by previous techniques

Shadow symbolic execution for better testing of evolving software

In this idea paper, we propose a novel way for improving the testing of program changes via symbolic execution. At a high-level, our technique runs two different program versions in the same symbolic execution instance, with the old version effectively shadowing the new one. In this way, the technique can exploit precise dynamic value information to effectively drive execution toward the behaviour that has changed from one version to the next. We discuss the main challenges and opportunities of this approach in terms of pruning and prioritising path exploration, mapping elements across versions, and sharing common symbolic state between versions. Copyright © 2014 ACM

Integrating Abstract Caches with Symbolic Pipeline Analysis

Static worst-case execution time analysis of real-time tasks is based on abstract models that capture the timing behavior of the processor on which the tasks run. For complex processors, task-level execution time bounds are obtained by a state space exploration which involves the abstract model and the program. Partial state space exploration is not sound. Symbolic methods using binary decision diagrams (BDDs) allow for a full state space exploration of the pipeline, thereby maintaining soundness. Caches are too large to admit an efficient BDD representation. On the other hand, invariants of the cache state can be computed efficiently using abstract interpretation. How to integrate abstract caches with symbolic-state pipeline analysis is an open question. We propose a semi-symbolic domain to solve this problem. Statistical data from industrial-level software and WCET tools indicate that this new domain will enable an efficient analysis

Lex-Partitioning: A New Option for BDD Search

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n) ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n). The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

Subsumer-First: Steering Symbolic Reachability Analysis

Abstract. Symbolic reachability analysis provides a basis for the veri-fication of software systems by offering algorithmic support for the ex-ploration of the program state space when searching for proofs or coun-terexamples. The choice of exploration strategy employed by the anal-ysis has direct impact on its success, whereas the ability to find short counterexamples quickly and—as a complementary task—to efficiently perform the exhaustive state space traversal are of utmost importance for the majority of verification efforts. Existing exploration strategies can optimize only one of these objectives which leads to a sub-optimal reach-ability analysis, e.g., breadth-first search may sacrifice the exploration ef-ficiency and chaotic iteration can miss minimal counterexamples. In this paper we present subsumer-first, a new approach for steering symbolic reachability analysis that targets both minimal counterexample discovery and efficiency of exhaustive exploration. Our approach leverages the re-sult of fixpoint checks performed during symbolic reachability analysis to bias the exploration strategy towards its objectives, and does not require any additional computation. We demonstrate how the subsumer-first ap-proach can be applied to improve efficiency of software verification tools based on predicate abstraction. Our experimental evaluation indicates the practical usefulness of the approach: we observe significant efficiency improvements (median value 40%) on difficult verification benchmarks from the transportation domain.

Context-aware counter abstraction

The trend towards multi-core computing has made concurrent software an important target of computer-aided verification. Unfortunately, Model Checkers for such software suffer tremendously from combinatorial state space explosion. We show how to apply counter abstraction to real-world concurrent programs to factor out redundancy due to thread replication. The traditional global state representation as a vector of local states is replaced by a vector of thread counters, one per local state. In practice, straightforward implementations of this idea are unfavorably sensitive to the number of local states. We present a novel symbolic exploration algorithm that avoids this problem by carefully scheduling which counters to track at any moment during the search. We have carried out experiments on Boolean programs, an abstraction promoted by the success of the Slam project. The experiments give evidence of the applicability of our method to realistic programs, and of the often huge savings obtained in comparison to plain symbolic state space exploration, and to exploration optimized by partial-order methods. To our knowledge, our tool marks the first implementation of counter abstraction to programs with non-trivial local state spaces, resulting in a Model Checker for concurrent Boolean programs that promises true scalabilit