Transition System Models for Concurrency

Labelled transition systems can be extended to faithfully model concurrency by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step, We can characterize a subclass of these step transition systems, called PN-transition systems, which describe the behaviour of Petri nets.This correspondence is formally described in terms of a coreflection between a category of PN-transition systems and a category of Petri nets.In this paper, we show that we can define subcategories of PN-transition systems whose objects are safe PN-transition systems and elementary PN-transition systems such that there is a coreflection between these subcategories and subcategories of our category of Petri nets corresponding to safe nets and elementary net systems.We also prove that our category of elementary PN-transition systems is equivalent to the category of (sequential) elementary transition systems defined by Nielsen, Rozenberg and Thiagarajan, thereby establishing that the concurrent behaviour of an elementary net system can be completely recovered from a description of its sequential behaviour. Finally, we establish a coreflection between our category of safe PN-transition system and a subcategory of asynchronous transition systems which has been shown by Winskel and Nielsen to be closely linked to safe nets

CCS, Locations and Asynchronous Transition Systems

Our aim is to provide a simple non-interleaved operational semantics for CCS in terms of a model that is easy to understand - asynchronous transition systems. Our approach is guided by the requirement that the semantics should identify the concurrency present in the system in a natural way, in terms of events occurring at independent locations in the system.We extend the standard interleaving transition system for CCS by introducing labels on the transitions with information about the locations of events. We then show that the resulting transition system is an asynchronous transition system which has the additional property of being elementary, which means that it can also be represented by a 1-safe net. We establish a close correspondence between our semantics and other approaches in terms of foldings.We also introduce a notion of bisimulation on asynchronous transition systems which preserves independence. We conjecture that the induced equivalence on CCS processes coincides with the notion of location equiualence proposed by Boudol et al

2008 Abstracts Collection -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science

This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS)

A Local-Time Semantics for Negotiations

Negotiations, introduced by Esparza et al., are a model for concurrent systems where computations involving a set of agents are described in terms of their interactions. In many situations, it is natural to impose timing constraints between interactions -- for instance, to limit the time available to enter the PIN after inserting a card into an ATM. To model this, we introduce a real-time aspect to negotiations. In our model of local-timed negotiations, agents have local reference times that evolve independently. Inspired by the model of networks of timed automata, each agent is equipped with a set of local clocks. Similar to timed automata, the outcomes of a negotiation contain guards and resets over the local clocks. As a new feature, we allow some interactions to force the reference clocks of the participating agents to synchronize. This synchronization constraint allows us to model interesting scenarios. Surprisingly, it also gives unlimited computing power. We show that reachability is undecidable for local-timed negotiations with a mixture of synchronized and unsynchronized interactions. We study restrictions on the use of synchronized interactions that make the problem decidable.Comment: A shorter version appears in FORMATS 202

A logical characterization of well branching event structures

AbstractWe develop a tense logic for reasoning about the occurrences of events in a subclass of prime event structures called well branching event structures. The well branching property ensures that two events being in conflict can always be traced back—via the causality relation—to two events being in minimal conflict. Two events are in minimal conflict if they are in conflict and their “unified” past is conflict-free. Thus the minimal conflict relation captures the branching points of the computations supported by the event structure. Our logical language has explicit modalities for talking about causality, conflict, concurrency and minimal conflict. We define the semantics of this logic using well branching event structures as Kripke frames. Our main result is a sound and complete axiomatization of the valid formulas over the chosen class of frames

Generalising Projection in Asynchronous Multiparty Session Types

Multiparty session types (MSTs) provide an efficient methodology for specifying and verifying message passing software systems. In the theory of MSTs, a global type specifies the interaction among the roles at the global level. A local specification for each role is generated by projecting from the global type on to the message exchanges it participates in. Whenever a global type can be projected on to each role, the composition of the projections is deadlock free and has exactly the behaviours specified by the global type. The key to the usability of MSTs is the projection operation: a more expressive projection allows more systems to be type-checked but requires a more difficult soundness argument. In this paper, we generalise the standard projection operation in MSTs. This allows us to model and type-check many design patterns in distributed systems, such as load balancing, that are rejected by the standard projection. The key to the new projection is an analysis that tracks causality between messages. Our soundness proof uses novel graph-theoretic techniques from the theory of message-sequence charts. We demonstrate the efficacy of the new projection operation by showing many global types for common patterns that can be projected under our projection but not under the standard projection operation

Model checking time-constrained scenario-based specifications

We consider the problem of model checking message-passing systems with real-time requirements. As behavioural specifications, we use message sequence charts (MSCs) annotated with timing constraints. Our system model is a network of communicating finite state machines with local clocks, whose global behaviour can be regarded as a timed automaton. Our goal is to verify that all timed behaviours exhibited by the system conform to the timing constraints imposed by the specification. In general, this corresponds to checking inclusion for timed languages, which is an undecidable problem even for timed regular languages. However, we show that we can translate regular collections of time-constrained MSCs into a special class of event-clock automata that can be determinized and complemented, thus permitting an algorithmic solution to the model checking problem

Towards a Theory of Regular MSC Languages

Message Sequence Charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the earlydesign stages in domains such as telecommunication software. It isfruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, weprovide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called boundedmessage-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending andreceiving messages over bounded FIFO channels. We also provide alogical characterization in terms of a natural monadic second-orderlogic interpreted over MSCs.A commonly used technique to generate a collection of MSCs isto use a Message Sequence Graph (MSG). We show that the class oflanguages arising from the so-called locally synchronized MSGs constitute a proper subclass of the languages which are regular in our sense.In fact, we characterize the locally synchronized MSG languages asthe subclass of regular MSC languages that are finitely generated

A theory of regular MSC languages

Message sequence charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, we provide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called bounded message-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending and receiving messages over bounded FIFO channels. We also provide a logical characterization in terms of a natural monadic second-order logic interpreted over MSCs. A commonly used technique to generate a collection of MSCs is to use a hierarchical message sequence chart (HMSC). We show that the class of languages arising from the so-called bounded HMSCs constitute a proper subclass of the class of regular MSC languages. In fact, we characterize the bounded HMSC languages as the subclass of regular MSC languages that are finitely generated