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AutoDRI: Bridging the Semantic Gap for Automated Design Rule Integration in CP-SAT-Based Cell Synthesis under Multi-Patterning
Yuhao Ren, Yucheng Wang, Zihao Chen, Chung-Kuan Cheng, Zhiang Wang
TL;DR
Design-rule integration is a manual bottleneck, and existing low-level representations cannot express some context-dependent and colored cut-mask rules. AutoDRI uses semantic abstractions, conflict-set encoding, constructive multicolor-cut modeling, and multi-agent translation; it achieves 32/33 and 33/33 correct integrations in the reported experiments.
Problem
Manual rule translation and limited low-level representations hinder CP-SAT-based synthesis, especially for context-dependent metal-length and colored cut-mask spacing rules.
Method
AutoDRI combines geometric semantic variables, standardized conflict sets, constructive multicolor-cut modeling, and a multi-agent flow to translate natural-language rules into executable CP-SAT constraints.
Results
The full framework reached 33/33 correct integrations with Gemini-3-pro and 32/33 with GPT-5.4 in the reported experiments.
Takeaways & Limitations
AutoDRI supports reliable automated rule integration across reasoning engines and preserves comparable block-level PPA while eliminating standard-cell metal design-rule violations.
Takeaways & Limitations
Existing endpoint-based formulations cannot represent colored cut-mask spacing rules, and commercial nodes may mix cut-based and metal-based rule encodings.
Abstract
from arXiv · showhide
Design-rule integration (DRI) remains a major bottleneck for scalable (Constraint Programming with SAT) CP-SAT-based standard cell synthesis and rapid technology enablement at advanced nodes. It still depends heavily on manual effort and domain expertise. Moreover, existing low-level rule encodings are not expressive enough for emerging constraints such as cut-based rules under multi-patterning technology. This paper presents \textbf{AutoDRI}, a multi-agent framework for automated design-rule integration in standard cell synthesis. AutoDRI combines a geometric semantic library, a standardized conflict-set encoding, a constructive multicolor-cut modeling method, and a feedback-driven multi-agent flow to bridge the semantic gap between natural-language design rules and executable CP-SAT constraints. In the reported experiments, AutoDRI achieves near-perfect rule-integration correctness across 41 cell benchmarks under 10+ complex rules, including colored cut-mask spacing rules, reaching 33/33 correct integrations with Gemini-3-pro and 32/33 with GPT-5.4, while maintaining runtime comparable to manual hard-coding and passing KLayout DRC and Cadence LVS.
1 Introduction
AutoDRI targets the manual, expertise-intensive design-rule integration bottleneck that limits portable CP-SAT-based standard cell synthesis. It bridges the semantic gap between natural-language rules and executable constraints with structured abstractions and multi-agent automation.
- Existing tools are tightly coupled to individual PDKs, making cross-node migration labor-intensive and rule encoding difficult to transfer across tools.
- Manual design-rule translation remains a primary bottleneck because it must be repeated, debugged, and re-validated for each new node or rule revision.
- The semantic gap arises because rule integration must connect spatial geometry, Boolean logic, and solver-specific encoding without a structured intermediate representation.
- Existing variables inadequately express context-dependent metal-length rules and cannot represent colored cut-mask spacing rules under multi-patterning.
- AutoDRI combines reusable geometric semantics, conflict-set normalization, constructive multicolor-cut modeling, and LLM-driven code generation for automated rule integration.
2 Preliminaries
The paper models standard-cell layouts on a three-dimensional routing grid and distinguishes metal-based from cut-based manufacturing rules. It identifies missing geometric and cut-level representations that motivate AutoDRI’s semantic abstractions.
- Natural-language design rules are translated into executable constraints integrated into CPCell, producing layouts that satisfy the entire rule set simultaneously.
- The layout uses a three-dimensional routing grid whose edges represent metal segments or vias, with M0 and M2 horizontal and M1 vertical.
- Metal-based processes define discrete segments directly, whereas cut-based processes form segments by severing continuous tracks with colored cut masks.
- Under multi-patterning, cut-mask spacing rules are defined per color, while some metal-endpoint rules may become implicitly satisfied by cut geometry.
- Existing endpoint indicators cannot capture some context-dependent metal-length rules and provide no variables for cut masks or their color assignments.
- AutoDRI addresses these gaps with interval-level semantic variables and constructive multicolor-cut modeling within a unified CP-SAT formulation.
3 Semantic Rule Representation
AutoDRI introduces reusable geometric semantics and constructive multicolor-cut modeling to express design rules that existing encodings cannot represent, including colored cut-mask constraints.
- Geometric Semantic Library: AutoDRI lifts primitive edge variables into reusable higher-level semantic variables over the routed grid.The library supports rule expression independently of low-level grid encodings.
- Rule Integration: The resulting semantic representation closes coverage gaps for context-dependent metal-length rules and abstraction gaps for colored cut-mask spacing rules.Colored cut-mask spacing constraints are expressed directly over the constructed cut-mask variables, whose contiguous activated states become physical mask geometries.
- Geometric Semantic Library: Metal continuation and metal empty variables encode continuous segments and metal-free intervals along same-track paths.Both interval-level variables are derived from primitive edge variables.
- Multicolor-Cut Modeling: Color-specific cut-mask variables extend the semantic library to cut-based multi-patterning rules.These variables represent physical cut masks by color and require explicit construction rather than direct reading from primitive edge variables.
- Multicolor-Cut Modeling: The two-step construction first selects color-independent cuts inside valid metal-breaking intervals, then lifts them into color-specific cut-mask variables.A valid interval contains no metal between facing segment boundaries; exactly one cut is selected when legal candidates exist, and activated cuts must be justified by an interval.
- Multicolor-Cut Modeling: Node intrinsic colors are assigned from cyclic layer color order and track indices, supporting color-aware cut-mask modeling.In practice, the cyclic order uses colorA and colorB.
- Multicolor-Cut Modeling: Color lifting allows a cut mask to extend across off-color nodes when anchored by a neighboring same-color cut selection.This handles physical masks whose span crosses nodes with differing intrinsic colors.
4 Automated Design Rule Integration
AutoDRI represents design rules as standardized conflict sets over geometric semantic variables, then uses a feedback-driven multi-agent flow to compile natural-language rules into executable CP-SAT code.
- Framework overview: AutoDRI combines standardized conflict-set encoding with a multi-agent flow that translates natural-language rules into executable CP-SAT code.The framework separates semantic representation from code generation.
- Conflict-set encoding: Each conflict set contains forbidden local Boolean patterns representing concrete violation scenarios; any pattern whose literals are all true is prohibited.This converts rule enforcement into forbidding local assignments.
- Conflict-set encoding: Rule translation uses local enumeration: select a reference node, enumerate nearby violation scenarios, and emit one semantic-variable pattern per scenario.The procedure avoids directly deriving handcrafted constraints over primitive solver variables.
- Conflict-set encoding: Four local scenarios capture parallelRun_rule violations when adjacent-track parallel overlap is shorter than the required threshold D.The scenarios use overlap endpoints and continuous metal segments on adjacent tracks.
- Feedback mechanisms: The Teacher–Translator Loop refines conflict-set translations using demonstrations, diagnostic feedback, and persistent guidance distilled from accumulated tips.TipsRefiner maintains rule-specific tip memory and re-evaluates tips according to empirical usefulness.
- Feedback mechanisms: Verifier Feedback executes generated code in synthesis, checks compilation and runtime behavior, and uses DRC and post-layout evidence to revise the responsible integration stage.Reported DRC violations are converted into the gridded representation used by CPCell synthesis before comparison with encoded forbidden cases.
5 Experimental Results
AutoDRI integrates complex design rules into CP-SAT cell synthesis through semantic abstractions and multi-agent feedback, achieving high correctness across benchmarks, supporting distinct encodings, and preserving practical runtime and block-level validity.
- Evaluation Setup: 41 standard-cell masters and 11 complex rules, including rules from PROBE3 and commercial 7nm specifications, define the evaluation scope.Each configuration is tested with Gemini-3-pro and GPT-5.4 across three runs.
- Overall Correctness: 32/33 and 33/33 correct integrations are achieved by GPT-5.4 and Gemini-3-pro, respectively, under the full multi-agent framework.Correctness requires successful compilation, violation-free synthesis for all 41 cells, and passing LVS.
- Process Migration: Two rule encodings, including colored cut-mask spacing, are integrated by extending the semantic library without changing the core AutoDRI flow.All 41 cell benchmarks pass KLayout DRC and Cadence LVS under both encodings.
- Process Migration: The two encodings produce substantially different AOI21_X2 physical layouts: segmented metal tracks for metal spacing versus continuous colored tracks severed by cut masks.The layouts are confirmed DRC-clean under their respective encodings.
- Runtime and Efficiency: 0.96× average runtime is obtained by the semantic conflict-set formulation across 14 complex cells, making runtime overall comparable to hard-coded at-most-one constraints.CP-SAT presolve can collapse deduplicated conflict sets and helper-variable relationships before branching.
- Block-Level Validation: At block level, AutoDRI-generated cells maintain PPA comparable to baseline cells while eliminating cell-metal design-rule violations in gcd, aes, and jpeg_encoder.The comparison uses PDKs generated from the unmodified CPCell flow and the automated rule-integration flow.
6 Conclusions
AutoDRI automates design-rule integration in CP-SAT-based standard-cell synthesis by combining semantic modeling, conflict-set encoding, multicolor-cut modeling, and multi-agent translation. Future work extends the framework toward multimodal rule understanding and broader DTCO/STCO workflows.
- Conclusion: AutoDRI translates complex design rules into executable CP-SAT constraints within the CPCell framework using semantic and multi-agent components.Its components include a geometric semantic library, standardized conflict-set encoding, constructive multicolor-cut modeling, and a multi-agent integration flow.
- Future Work: Future work targets multimodal rule understanding from foundry figures and diagrams and expansion into a foundational DTCO/STCO workflow module.These are identified as the paper’s two main future directions.