An approach for the formal verification of DSP designs using Theorem proving
Bibliographic record
Abstract
This paper proposes a framework for the incorporation of formal methods in the design flow of digital signal processing (DSP) systems in a rigorous way. In the proposed approach, DSP descriptions were modeled and verified at different abstraction levels using higher order logic based on the higher order logic (HOL) theorem prover. This framework enables the formal verification of DSP designs that in the past could only be done partially using conventional simulation techniques. To this end, a shallow embedding of DSP descriptions in HOL at the floating-point (FP), fixed-point (FXP), behavioral, register transfer level (RTL), and netlist gate levels is provided. The paper made use of existing formalization of FP theory in HOL and a parallel one developed for FXP arithmetic. The high ability of abstraction in HOL allows a seamless hierarchical verification encompassing the whole DSP design path, starting from top-level FP and FXP algorithmic descriptions down to RTL, and gate level implementations. The paper illustrates the new verification framework on the fast Fourier transform (FFT) algorithm as a case study.
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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 | 0.011 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".