Component refinement and CSC-solving for STG decomposition

Abstract

STGs (Signal Transition Graphs) give a formalism for the description of asynchronous circuits based on Petri nets. To overcome the state explosion problem one may encounter during circuit synthesis, a nondeterministic algorithm for decomposing STGs was suggested by Chu and improved by one of the present authors.Here we study how CSC-solving -which is essential for circuit synthesis -can be combined with decomposition. For this purpose, the correctness definition for decomposition is enhanced with internal signals and hierarchical decomposition is proven correct. Based on this, it is shown that speed-independent CSC-solving preserves correctness and can be combined with decomposition.Furthermore, we use our new correctness definition to give the first correctness proof for the decomposition method of Carmona and Cortadella. Finally, we compare three different implementation relations for STGs: one derived from our correctness definition; one defined by Dill based on trace structures; and one derived from I/O-compatibility defined by Carmona and Cortadella.

STG Decomposition: Internal Communication for SI Implementability

“…In this case, the enabling of an input by an internal signal should not be interpreted as a causal but a temporal relation. In [SV07] it was shown that the above correctness notion implies that the STG C in Definition 2.5 is in a sense input proper; in particular, if the solution of a CSC-conflict inserts an internal signal in front of an input, it is not correct in the sense of Definition 2.5. Also, correctness is essentially transitive.…”

“…• consist of local transitions only -including t d -such that the later gyroscope refinement of q with a new internal signal ic is input proper according to [SV07], which means that no input will be delayed by ic. Furthermore,…”

Improved Decomposition of STGs

“…In a companion paper [9], it is shown that the components produced by our method are still a correct decomposition of the original specification after such insertions; for this, the correctness definition had to be extended to internal signals.…”

“…Thus, in [4] CSC is used to find sufficient input signals for each component, while our method is guided by the detection of auto-conflicts. Correctness is not proven in [4] -not even formulated -, but this has recently been proved in [9] w.r.t. the extended correctness definition.…”

“…Often, essentially the same operations have to be performed in different components; DESI should be enabled to reuse the results of some operations. Also, backtracking makes DESI start with a new initial component, while reuse of some operations performed before the backtracking should be possible; [9] also contains the theoretical underpinning for this.…”