Dynamic Symmetry Reduction

Abstract

Abstract. Symmetry reduction is a technique to combat the state explosion problem in temporal logic model checking. Its use with symbolic representation has suffered from the prohibitively large BDD for the orbit relation. One suggested solution is to pre-compute a mapping from states to possibly multiple representatives of symmetry equivalence classes. In this paper, we propose a more efficient method that determines representatives dynamically during fixpoint iterations. Our scheme preserves the uniqueness of representatives. Another alternative to using the orbit relation is counter abstraction. It proved efficient for the special case of full symmetry, provided a conducive program structure. In contrast, our solution applies also to systems with less than full symmetry, and to systems where a translation into counters is not feasible. We support these claims with experimental results.

SVISS: Symbolic Verification of Symmetric Systems

“…The computation can be done (i) ignoring symmetry, (ii) using dynamic symmetry [5], (iii) using the orbit relation [3] and (iv) by way of multiple representatives [3]. 1 If the result is neither empty nor equal to the entire state space, the set of states (or a few elements of it) can be enumerated.…”

“…Quantitative results from these experiments are available in the cited literature [5,4], which also compares the performance of Sviss's algorithms with alternative approaches to exploiting symmetry. In this paper we share our experiences of applying Sviss to concurrent Linux device-driver software.…”

“…The histograms in figure 1 show time (top left, log-scale) and space (bottom left) demands for safety-checking eight abstract models with a fixed number of ten processes, ignoring (light gray) and exploiting (dark gray) symmetry dynamically [5]. We see tremendous memory savings thanks to symmetry, in all cases.…”

“…In this paper, we present a symbolic model checker with symmetry reduction that never builds this BDD and thus avoids the orbit problem: Sviss (historically, "S ymbolic V erification of I nvariants of S ymmetric S ystems") implements, to our knowledge, the first efficient symbolic realization of symmetry reduction, by dynamically mapping each encountered state to a unique representative of its orbit [5].…”

“…The benefit of a library in a widely known programming language over a specialized input language is flexibility: the library has been used to model systems as diverse as asynchronous communication protocols [5], Boolean abstractions of concurrent software (see section 3), synchronous parallel programs [4], and finitestate machine descriptions of computer hardware. The penalty for this flexibility is that by using C++ constructs outside the library, the user can circumvent restrictions that ensure symmetry, which are therefore not enforced by the tool (a weakness that Sviss shares with other tools exploiting symmetry including Murϕ [7]).…”