In cases where signal processing involves arrays of data interrelated in a larger data space, models of dataflow in which actors produce and consume series of patterned subspaces of these data spaces have certain advantages over dataflow models that simply act on streams of independent tokens. Such models can utilize these patterns and traversals of space to intuitively structure computations in which the structure of the data space is meaningfully related to the computation. In this kind of a model, optimizations can also be made in scheduling to minimize the use of buffers and to pipeline processing.

While several specifications have been made for the semantics of static multidimensional models, including GMDSDF and ArrayOL, with differing constraints imposed on them, many problems still exist in how these specifications can be optimally implemented to minimize buffer space, handle feedback, and pipeline scheduling. Questions also exist with regards to generating efficient code from these models. I am beginning to explore some of these questions in multidimensional static dataflow.

The possibility also exists for more generalized, dynamic versions of these semantics to be developed. In dynamic models, patterns and traversals of data space could be made modal or parametric. The expressive potential of such models would be expanded in a manner useful in many applications. However, the scheduling and optimization of these dynamic models will be significantly more complicated than the static case. In particular, I am exploring possible ways of dynamically handling dependency relationships between actors efficiently. I am also interested in the effect of imposing on a more general model different sets of constraints limiting the kinds of variability in patterns and traversals to special classes that allow further optimizations.

Influenced by previous work in which combinator expressions are used to represent block-diagrams with certain semantic details about systems they constitute, I am developing a general method of representing a broad class of dataflow ptolemy models with a generalized combinator syntax. In such a syntax, functional blocks with enumerable sets of input and output ports are composed in parallel and connected in series to form models. This type of syntax serves as an alternative to syntaxes in which ports are bound to names and connections are unstructured sets of statements specifying by names the connections between these ports. In such a syntax, a canonical form can uniquely or nearly uniquely represent textually a model as an expression. Hierarchy in the syntax would be reflected naturally in subexpression.

In addition to having a combinator representation generated from ptolemy models, a combinator syntax would provide a non-graphical secondary means to author models or edit them. The analysis utilized to formulate this syntactic representation could itself be useful in doing various other syntactic analyses on models such as deducing compositional properties between groupings of actors. This analysis could also be useful in generating both functional and sequential code from models.

In order to explore this kind of syntactic representation, I have been working on an algorithm to translate a large class of suitable ptolemy models into combinator expressions through a set of intermediate transformations on a representative 'syntactic graph' generated from a model. The modularity of this algorithm will allow different variations on syntactic code generation to be explored.