Relaxed Operational Semantics of Concurrent Programming Languages

We propose a novel, operational framework to formally describe the semantics of concurrent programs running within the context of a relaxed memory model. Our framework features a "temporary store" where the memory operations issued by the threads are recorded, in program order. A memory model then specifies the conditions under which a pending operation from this sequence is allowed to be globally performed, possibly out of order. The memory model also involves a "write grain," accounting for architectures where a thread may read a write that is not yet globally visible. Our formal model is supported by a software simulator, allowing us to run litmus tests in our semantics.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Evidence for Fixpoint Logic

For many modal logics, dedicated model checkers offer diagnostics (e.g., counterexamples) that help the user understand the result provided by the solver. Fixpoint logic offers a unifying framework in which such problems can be expressed and solved, but a drawback of this framework is that it lacks comprehensive diagnostics generation. We extend the framework with a notion of evidence, which can be specialized to obtain diagnostics for various model checking problems, behavioural equivalence and refinement checking problems. We demonstrate this by showing how our notion of evidence can be used to obtain diagnostics for the problem of deciding stuttering bisimilarity. Moreover, we show that our notion generalizes the existing notions of counterexample and witness for LTL and ACTL* model checking

Reflections on a Geometry of Processes

Contains fulltext : 32919.pdf (publisher's version ) (Open Access)Algebraic Process Calcul

Sequencing and intermediate acceptance: Axiomatisation and decidability of bisimilarity

The Theory of Sequential Processes includes deadlock, successful termination, action prefixing, alternative and sequential composition. Intermediate acceptance, which is important for the integration of classical automata theory, can be expressed through a combination of alternative composition and successful termination. Recently, it was argued that complications arising from the interplay between intermediate acceptance and sequential composition can be eliminated by replacing sequential composition by sequencing. In this paper we study the equational theory of the recursion-free fragment of the resulting process theory modulo bisimilarity, proving that it is not finitely based, but does afford a ground-complete axiomatisation if a unary auxiliary operator is added. Furthermore, we prove that bisimilarity is decidable for processes definable by means of a finite guarded recursive specification over the process the

Equivalence checking for weak bi-kleene algebra∗

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable

Brzozowski goes concurrent - A kleene theorem for pomset languages

Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this paper makes an important step towards an answer. We present a new automaton model and a Kleene-like theorem that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours

A process algebra with global variables

In standard process algebra, parallel components do not share a common state and communicate through synchronisation. The advantage of this type of communication is that it facilitates compositional reasoning. For modelling and analysing systems in which parallel components operate on shared memory, however, the communication-through-synchronisation paradigm is sometimes less convenient. In this paper we study a process algebra with a notion of global variable. We also propose an extension of Hennessy-Milner logic with predicates to test and set the values of the global variables, and prove correspondence results between validity of formulas in the extended logic and stateless bisimilarity and between validity of formulas in the extended logic without the set operator and state-based bisimilarity. We shall also present a translation from the process algebra with global variables to a fragment of mCRL2 that preserves the validity of formulas in the extended Hennessy-Milner logic.Comment: In Proceedings EXPRESS/SOS 2020, arXiv:2008.1241

Equivalence checking for weak bi-Kleene algebra

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable

Partially-commutative context-free languages

The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are commutative according to a binary independence relation, very much like in trace theory. The class has been recently proposed as a robust class subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We identify a natural corresponding automaton model: stateless multi-pushdown automata. We show stability of the class under natural operations, including homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to two other relevant classes: CFL extended with shuffle and trace-closures of CFL. Among technical contributions of the paper are pumping lemmas, as an elegant completion of known pumping properties of regular languages, CFL and commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244