Looped Schedules for Dataflow Descriptions of Multirate Signal Processing Algorithms

References 28 of 29 max_connected(G) The set of maximal connected subgraphs of the SDF graph G. The number of invocations of the source actor of SDF arc α that precede the ith invocation of sink(α) in schedule S. p(α) The number of samples produced onto SDF arc α by one invocation of source(α). periodic schedule A schedule that invokes each actor at least once and produces no net change in the number of samples buffered on any arc. q G The repetitions vector q G of the connected SDF graph G is a vector that is indexed by the nodes in G. q G gives the minimum number of times that each node must be invoked in a periodic schedule for G. restriction Given a looped schedule S and a set of actors Z, the restriction of S to Z, denoted restriction(S, Z), is the looped schedule obtained by removing from S all actors that are not contained in Z, and removing all empty schedule loops that result. Also, given an SDF subgraph G, restriction(S, G) ≡ restriction(S, N(G)). single appearance schedule A looped schedule in which no actor appears more than once. sink(α) The actor at the sink of SDF arc α. source(α) The actor at the source of SDF arc α. subgraph A subgraph of an SDF graph G is the graph formed by any subset Z of nodes in G together with all arcs α in G for which source(α), sink(α) ∈ Z. We denote the sub-graph corresponding to the subset of nodes Z by subgraph(Z, G), or simply by sub-graph(Z) if G is understood from context. subschedule A subschedule of a looped schedule S is a sequence of successive iterands of S or a sequence of successive iterands of a schedule loop contained in S. termination of a schedule If S is not an admissable schedule then some invocation f in S is not fireable immediately after all of its antecedents in the schedule have fired. Thus f does not have sufficient data on at least one of its input arcs. If α is one such input arc, we say that S terminates on α at f. valid schedule A schedule that is a both periodic and admissable. Acknowledgment 27 of 29 these tradeoffs — the existing techniques focus on a small subset of the full range of considerations. A more global objective of the formal …