Functionally Linear Decomposition and Synthesis of Logic Circuits for FPGAs
Bibliographic record
Abstract
This paper presents a novel XOR-based logic synthesis approach called functionally linear decomposition and synthesis (FLDS). This approach decomposes a logic function to expose an XOR relationship by using Gaussian elimination. It is fundamentally different from the traditional approaches to this problem, which are based on the work of Ashenhurst and Curtis. FLDS utilizes binary decision diagrams to efficiently represent logic functions, making it fast and scalable. This technique was tested on a set of 99 MCNC benchmarks, mapping each design into a network of four input lookup tables. On the 25 of the benchmarks, which have been classified by previous researchers as XOR-based logic circuits, our approach provides significant area savings. In comparison to the leading logic synthesis tools, ABC and BDS-PGA 2.0, FLDS produces XOR-based circuits with 25.3% and 18.8% smaller area, respectively. The logic circuit depth is also improved by 7.7% and 14.5%, respectively.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".