Trace Spaces: An Efficient New Technique for State-Space Reduction

Abstract

State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing loops, which is "as reduced as possible" in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partial-order reduction techniques.

Geometric and combinatorial views on asynchronous computability

“…These papers have explored the use of precubical sets and Higher-Dimensional Automata (which are labeled precubical sets equipped with a distinguished beginning vertex) [33,35], begun to suggest possible homology theories [22,18] and pushed the development of a specific homotopy theory, part of a general directed algebraic topology [24]. On the practical side, directed topological models have found applications to deadlock and unreachable state detection [12], validation and static analysis [20,7,10], state-space reduction (as in e.g. modelchecking) [21], serializability and correctness of databases [25] (see also [19,13] for a panorama of applications).…”

From Geometric Semantics to Asynchronous Computability

“…The intuition is that, given two points x, y ∈ X such that x ≤ y, y cannot be reached before x. The encoding can be done in a quite general manner [8,9]. Here, for the sake of simplicity, we define directly the pospace that gives the semantics we are looking for.…”

“…These papers have explored the use of precubical sets and Higher-Dimensional Automata (which are labeled precubical sets equipped with a distinguished beginning vertex) [28,30], begun to suggest possible homology theories [13,16] and pushed the development of a specific homotopy theory, part of a general directed algebraic topology [19]. On the practical side, directed topological models have found applications to deadlock and unreachable state detection [6], validation and static analysis [4,8,15] state-space reduction (as in e.g. model-checking) [17], serializability and correctness of databases [20] (see also [7,14] for a panorama of applications).…”

Simplicial models for trace spaces II: General higher dimensional automata

“…For these restricted class of models, the resulting algorithm has meanwhile been implemented with encouraging results; see Fajstrup et al [8].…”

“…It is probably easier to get hold on periodicity properties in this setting. This line is currently being investigated by several colleagues; see Fajstrup [7] and Fajstrup et al [8].…”