AutoDRI: Bridging the Semantic Gap for Automated Design Rule Integration in CP-SAT-Based Cell Synthesis under Multi-Patterning

• Existing tools are tightly coupled to individual PDKs, making cross-node migration labor-intensive and rule encoding difficult to transfer across tools.Source: §1 · p. 1
• Manual design-rule translation remains a primary bottleneck because it must be repeated, debugged, and re-validated for each new node or rule revision.Source: §1 · p. 1
• The semantic gap arises because rule integration must connect spatial geometry, Boolean logic, and solver-specific encoding without a structured intermediate representation.Source: §1 · p. 2
• Existing variables inadequately express context-dependent metal-length rules and cannot represent colored cut-mask spacing rules under multi-patterning.Source: §1 · p. 2
• AutoDRI combines reusable geometric semantics, conflict-set normalization, constructive multicolor-cut modeling, and LLM-driven code generation for automated rule integration.Source: §1 · p. 2

• Natural-language design rules are translated into executable constraints integrated into CPCell, producing layouts that satisfy the entire rule set simultaneously.Source: §2 · p. 2
• The layout uses a three-dimensional routing grid whose edges represent metal segments or vias, with M0 and M2 horizontal and M1 vertical.Source: §2.1 · p. 2
• Metal-based processes define discrete segments directly, whereas cut-based processes form segments by severing continuous tracks with colored cut masks.Source: §2.2 · p. 2
• Under multi-patterning, cut-mask spacing rules are defined per color, while some metal-endpoint rules may become implicitly satisfied by cut geometry.Source: §2.2 · p. 3
• Existing endpoint indicators cannot capture some context-dependent metal-length rules and provide no variables for cut masks or their color assignments.Source: §2.2 · p. 3
• AutoDRI addresses these gaps with interval-level semantic variables and constructive multicolor-cut modeling within a unified CP-SAT formulation.Source: §2.2 · p. 3

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.Source: §3 · p. 3, §3.1 · p. 3

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.Source: §3 · p. 3, §3.2 · p. 4

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.Source: §3.1 · p. 3

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.Source: §3.1 · p. 3
• 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.Source: §3.2 · pp. 3–4
• 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.Source: §3.2 · pp. 3–4
• 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.Source: §3.2 · p. 4

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.Source: §4 · p. 5, §4.2 · p. 5

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.Source: §4.1 · p. 5
• 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.Source: §4.1 · p. 5
• 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.Source: §4.1 · p. 5, Figure 5 · p. 5

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.Source: §4.2 · pp. 5–6
• 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.Source: §4.2 · p. 6

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.Source: §5 · p. 6, §5.1 · p. 6

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.Source: §5.1 · p. 7

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.Source: §5.2 · pp. 7–8
• 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.Source: §5.2 · pp. 7–8, Figure 7 · p. 7

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.Source: §5.3 · p. 8

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.Source: §5.4 · pp. 8–9

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.Source: §6 · p. 9

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.Source: §6 · p. 9