Research Interests

In general, my research is concerned with: (1) the study of mathematical models for concurrent systems, and (2) the use of these models, to define the semantics of concurrent programming languages, to devise specification and proof techniques for concurrent systems, and to determine the capabilities and limitations of such systems under various assumptions. I am particularly interested in the use of ideas from abstract algebra and category theory to systematize the study of concurrency.

Much of my work for the past several years has centered around the study of a particular paradigm for parallel computing, called ``dataflow networks.'' Such networks consist of a collection of concurrently and asynchronously executing processes that communicate by sending messages over FIFO channels. ``Determinate'' dataflow networks are those in which each process computes a function from inputs to outputs; the behavior of such networks has been fairly well understood for some time. Of greater current research interest are the less well-understood ``indeterminate'' networks, in which processes need not compute functions. One topic I have investigated concerns the power of indeterminate dataflow networks to perform various computational tasks, such as the merging of two input sequences into a single output sequence. Another area I have investigated is concerned with finding compositional semantics for indeterminate networks, which nicely generalize the classical denotational semantics (based on continuous functions between domains of ``streams'') for determinate networks.

Recently, I have been trying to bring research on dataflow networks into closer contact with mainstream work in concurrency theory; in particular, with Milner's Calculus of Communicating Systems (CCS). Towards this end, I have designed a formal calculus for dataflow networks with uninterpreted processes, with a structured operational semantics in the CCS style. I have investigated a bisimulation-based equivalence for this calculus, and have proved the soundness and completeness of an equational axiomatization.