On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency

Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal verification techniques. Among these, symbolic techniques have been shown to be particularly effective at finding concurrency-related bugs because they can leverage highly optimized decision procedures such as SAT/SMT solvers. This paper gives new fundamental results on partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency. In particular, we give the theoretical basis for a decision procedure that can handle a fragment of concurrent programs endowed with least fixed point operators. In addition, we show that a certain partial order semantics of relaxed sequential consistency is equivalent to the conjunction of three extensively studied weak memory axioms by Alglave et al. An important consequence of this equivalence is an asymptotically smaller symbolic encoding for bounded model checking which has only a quadratic number of partial order constraints compared to the state-of-the-art cubic-size encoding.Comment: 15 pages, 3 figure

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

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

Symbolic Partial-Order Execution for Testing Multi-Threaded Programs

We describe a technique for systematic testing of multi-threaded programs. We combine Quasi-Optimal Partial-Order Reduction, a state-of-the-art technique that tackles path explosion due to interleaving non-determinism, with symbolic execution to handle data non-determinism. Our technique iteratively and exhaustively finds all executions of the program. It represents program executions using partial orders and finds the next execution using an underlying unfolding semantics. We avoid the exploration of redundant program traces using cutoff events. We implemented our technique as an extension of KLEE and evaluated it on a set of large multi-threaded C programs. Our experiments found several previously undiscovered bugs and undefined behaviors in memcached and GNU sort, showing that the new method is capable of finding bugs in industrial-size benchmarks.Comment: Extended version of a paper presented at CAV'2

Abstract Hidden Markov Models: a monadic account of quantitative information flow

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs: for that, we recast them as `abstract' HMM's, computations in the Giry monad $\mathbb{D}$, and we equip them with a partial order of increasing security. However to encode the monadic type with hiding over some state $\mathcal{X}$ we use $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ rather than the conventional $\mathcal{X}{\to}\mathbb{D}\mathcal{X}$ that suffices for Markov models whose state is not hidden. We illustrate the $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ construction with a small Haskell prototype. We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, with characteristic analytic properties for them, and show how the new entropies interact with the order of increasing security. Furthermore, we give a `backwards' uncertainty-transformer semantics for HMM's that is dual to the `forwards' abstract HMM's - it is an analogue of the duality between forwards, relational semantics and backwards, predicate-transformer semantics for imperative programs with demonic choice. Finally, we argue that, from this new denotational-semantic viewpoint, one can see that the Dalenius desideratum for statistical databases is actually an issue in compositionality. We propose a means for taking it into account

Theorem proving support in programming language semantics

We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational semantics, axiomatic semantics, and abstract interpretation. Descriptions as recursive functions are also provided whenever suitable, thus yielding a a verification condition generator and a static analyser that can be run inside the theorem prover for use in reflective proofs. Extraction of an interpreter from the denotational semantics is also described. All different aspects are formally proved sound with respect to the natural semantics specification.Comment: Propos\'e pour publication dans l'ouvrage \`a la m\'emoire de Gilles Kah

Size-Change Termination as a Contract

Termination is an important but undecidable program property, which has led to a large body of work on static methods for conservatively predicting or enforcing termination. One such method is the size-change termination approach of Lee, Jones, and Ben-Amram, which operates in two phases: (1) abstract programs into "size-change graphs," and (2) check these graphs for the size-change property: the existence of paths that lead to infinite decreasing sequences. We transpose these two phases with an operational semantics that accounts for the run-time enforcement of the size-change property, postponing (or entirely avoiding) program abstraction. This choice has two key consequences: (1) size-change termination can be checked at run-time and (2) termination can be rephrased as a safety property analyzed using existing methods for systematic abstraction. We formulate run-time size-change checks as contracts in the style of Findler and Felleisen. The result compliments existing contracts that enforce partial correctness specifications to obtain contracts for total correctness. Our approach combines the robustness of the size-change principle for termination with the precise information available at run-time. It has tunable overhead and can check for nontermination without the conservativeness necessary in static checking. To obtain a sound and computable termination analysis, we apply existing abstract interpretation techniques directly to the operational semantics, avoiding the need for custom abstractions for termination. The resulting analyzer is competitive with with existing, purpose-built analyzers