## 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.