Relational Semantics of Non-Deterministic Dataflow

We recast dataflow in a modern categorical light using profunctors as a generalization of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preservemuch of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially theusual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higher-order dataflow as a biproduct,essentially by following the geometry of interaction programme

Compositional semantics of dataflow networks with query-driven communication of exact values

We develop and study the concept of dataflow process networks as used for exampleby Kahn to suit exact computation over data types related to real numbers, such as continuous functions and geometrical solids. Furthermore, we consider communicating these exact objectsamong processes using protocols of a query-answer nature as introduced in our earlier work. This enables processes to provide valid approximations with certain accuracy and focusing on certainlocality as demanded by the receiving processes through queries. We define domain-theoretical denotational semantics of our networks in two ways: (1) directly, i. e. by viewing the whole network as a composite process and applying the process semantics introduced in our earlier work; and (2) compositionally, i. e. by a fixed-point construction similarto that used by Kahn from the denotational semantics of individual processes in the network. The direct semantics closely corresponds to the operational semantics of the network (i. e. it iscorrect) but very difficult to study for concrete networks. The compositional semantics enablescompositional analysis of concrete networks, assuming it is correct. We prove that the compositional semantics is a safe approximation of the direct semantics. Wealso provide a method that can be used in many cases to establish that the two semantics fully coincide, i. e. safety is not achieved through inactivity or meaningless answers. The results are extended to cover recursively-defined infinite networks as well as nested finitenetworks. A robust prototype implementation of our model is available

Semantics of query-driven communication of exact values

We address the question of how to communicate among distributed processes valuessuch as real numbers, continuous functions and geometrical solids with arbitrary precision, yet efficiently. We extend the established concept of lazy communication using streams of approximants by introducing explicit queries. We formalise this approach using protocols of a query-answer nature. Such protocols enable processes to provide valid approximations with certain accuracy and focusing on certain locality as demanded by the receiving processes through queries. A lattice-theoretic denotational semantics of channel and process behaviour is developed. Thequery space is modelled as a continuous lattice in which the top element denotes the query demanding all the information, whereas other elements denote queries demanding partial and/or local information. Answers are interpreted as elements of lattices constructed over suitable domains of approximations to the exact objects. An unanswered query is treated as an error anddenoted using the top element. The major novel characteristic of our semantic model is that it reflects the dependency of answerson queries. This enables the definition and analysis of an appropriate concept of convergence rate, by assigning an effort indicator to each query and a measure of information content to eachanswer. Thus we capture not only what function a process computes, but also how a process transforms the convergence rates from its inputs to its outputs. In future work these indicatorscan be used to capture further computational complexity measures. A robust prototype implementation of our model is available

Typed event structures and the p-calculus

We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of con uence to systems that allow nondeterminism. Ours is the rst typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the p-calculi with internal mobility. The semantics we provide is the rst event structure semantics of the p-calculus and generalises Winskel's original event structure semantics of CCS

A formal model of non-determinate dataflow computation

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1983.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGVita.Bibliography: leaves 75-78.by Jarvis Dean Brock.Ph.D

Doctor of Philosophy

dissertationMessage passing (MP) has gained a widespread adoption over the years, so much so, that even heterogeneous embedded multicore systems are running programs that are developed using message passing libraries. Such a phenomenon is a shift in computing practices, since, traditionally MP programs have been developed specifically for high performance computing. With growing importance and the complexity of MP programs in today's times, it becomes absolutely imperative to have formal tools and sound methodologies that can help reason about the correctness of the program. It has been demonstrated by many researchers in the area of concurrent program verification that a suitable strategy to verify programs which rely heavily on nondeterminism, is dynamic verification. Dynamic verification integrates the best features of testing and model checking. In the area of MP program verification, however, there have been only a handful of dynamic verifiers. These dynamic verifiers, despite their strengths, suffer from the explosion in execution scenarios. All existing dynamic verifiers, to our knowledge, exhaustively explore the nondeterministic choices in an MP program. It is apparent that an MP program with many nondeterministic constructs will quickly inundate such tools. This dissertation focuses on the problem of containing the exponential space of execution scenarios (or interleavings) while providing a soundness and completeness guarantee over safety properties of MP programs (specifically deadlocks). We present a predictive verification methodology and an associated framework, called MAAPED(Messaging Application Analysis with Predictive Error Discovery), that operates in polynomial time over MP programs to detect deadlocks among other safety property violations. In brief, we collect a single execution trace of an MP program and without re-running other execution schedules, reliably construct the artifacts necessary to predict any mishappening in an unexplored execution schedule with the aforementioned formal guarantee. The main contributions of the thesis are the following: The Functionally Irrelevant Barrier Algorithm to increase program productivity and ease in verification complexity. A sound pragmatic strategy to reduce the interleaving space of existing dynamic verifiers which is complete only for a certain class of MPI programs. A generalized matches-before ordering for MP programs. A predictive polynomial time verification framework as an alternate solution in the dynamic MP verification landscape. A soundness and completeness proof for the predictive framework's deadlock detection strategy for many formally characterized classes of MP programs. In the process of developing solutions that are mentioned above, we also collected important experiences relating to the development of dynamic verification schedulers. We present those experiences as a minor contribution of this thesis

Kahn Process Networks and a Reactive Extension

Kahn and MacQueen have introduced a generic class of determinate asynchronous data-flow applications, called Kahn Process Networks (KPNs) with an elegant mathematical model and semantics in terms of Scott-continuous functions on data streams together with an implementation model of independent asynchronous sequential programs communicating through FIFO buffers with blocking read and non-blocking write operations. The two are related by the Kahn Principle which states that a realization according to the implementation model behaves as predicted by the mathematical function. Additional steps are required to arrive at an actual implementation of a KPN to take care of scheduling of independent processes on a single processor and to manage communication buffers. Because of the expressiveness of the KPN model, buffer sizes and schedules cannot be determined at design time in general and require dynamic run-time system support. Constraints are discussed that need to be placed on such system support so as to maintain the Kahn Principle.We then discuss a possible extension of the KPN model to include the possibility for sporadic, reactive behavior which is not possible in the standard model. The extended model is called Reactive Process Networks. We introduce its semantics, look at analyzability and at more constrained data-flow models combined with reactive behavior