Solution of parallel language equations for logic synthesis
Bibliographic record
Abstract
The problem of designing a component that combined with a known part of a system, conforms to a given overall specification arises in several applications ranging from logic synthesis to the design of discrete controllers. We cast the problem as solving abstract equations over languages. Language equations can be defined with respect to several language composition operators such as synchronous composition, , and parallel composition,; conformity can be checked by language containment. In this paper we address parallel language equations. Parallel composition arises in the context of modeling delayinsensitive processes and their environments. The parallel composition operator models an exchange protocol by which an input is followed by an output after a finite exchange of internal signals. It abstracts a system with two components with a single message in transit, such that at each instance either the components exchange messages or one of them communicates with its environment, which submits the next external input to the system only after the system has produced an external output in response to the previous input. We study the most general solutions of the language equation � � � �, and define the language operators needed to express them. Then we specialize such equations to languages associated with important classes of automata used for modeling systems, e.g., regular languages and FSM languages. In particular, for � � � �, we give algorithms for computing: the largest FSM language solution, the largest complete solution, and the largest solution whose composition with � yields a complete FSM language. We solve also FSM equations under bounded parallel composition. In this paper, we give concrete algorithms for computing such solutions, and state and prove their correctness. 1
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".