Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution traces. We have implemented the approach in Isabelle/HOL as a lightweight concurrency verification tool that supports reasoning about the control and data flow of concurrent programs with shared variables at different levels of abstraction. This is illustrated on two simple verification examples

An Event Structure Model for Probabilistic Concurrent Kleene Algebra

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures, which combines ideas from Katoen's work on probabilistic concurrency and Varacca's probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala's probabilistic simulation. Finally, the algebraic properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules.Comment: Submitted and accepted for LPAR19 (2013

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

Event correlation with boxed pomsets

Abstract. This paper proposes a diagnosis framework for distributed systems based on pomset languages. Diagnosis is performed by projecting these models on a collection of observable labels and then synchronization with an observation. This paper first proposes a new model called boxed pomset languages, which extends classical pomset-based languages as so called High-level Message Sequence Charts. It can describe infinite scenarios, and has good properties with respect to projections. We then give a solution for the event correlation problem (knowing whether two observed alarms are causally related) for pomset languages.

Emptiness is Decidable for Asynchronous Cellular Machines

. We resume the investigation of asynchronous cellular automata. Originally, these devices were considered in the context of Mazurkiewicz traces, and later generalized to run on arbitrary pomsets without autoconcurrency by Droste and Gastin [DG96]. While the universality of the accepted language is known to be undecidable [Kus98], we show here that the emptiness is decidable. Our proof relies on a result due to Finkel and Schnoebelen [FS98b] on well-structured transition systems. 1 Introduction In a distributed system, some events may occur concurrently, meaning that they may occur in any order or simultaneously or even that their executions may overlap. This is the case in particular when two events use independent resources. On the other hand, some events may causally depend on each other. For instance, the receiving of a message must follow its sending. Therefore, a distributed behavior may be abstracted as a directed acyclic graph (dag), that is a set of events together wit..

A model theoretic proof of Büchi-type theorems and first-order logic for N-free pomsets

We give a uniform proof for the recognizability of sets of finite words, traces, or N-free pomsets that are axiomatized in monadic second order logic. This proof method uses Shelah's composition theorem for bounded monadic theories. Using this method, we can also show that elementary axiomatizable sets are aperiodic. In the second part of the paper, it is shown that width-bounded and aperiodic sets of N-free pomsets are elementary axiomatizable

A Kleene iteration for parallelism

This paper extends automata-theoretic techniques to unbounded parallel behaviour, as seen for instance in Petri nets. Languages are defined to be sets of (labelled) series-parallel posets --- or, equivalently, sets of terms in an algebra with two product operations: sequential and parallel. In an earlier paper, we restricted ourselves to languages of posets having bounded width and introduced a notion of branching automaton. In this paper, we drop the restriction to bounded width. We define rational expressions, a natural generalization of the usual ones over words, and prove a Kleene theorem connecting them to regular languages (accepted by finite branching automata). We also show that recognizable languages (inverse images by a morphism into a finite algebra) are strictly weaker