cs.AISep 24, 2026
SaveHEXIS: Compiling Skills into Extended Finite State Machines
Abstract
Agent skills provide reusable knowledge and instructions, yet agents must repeatedly infer how to apply them and which operation should follow. This couples task reasoning with control decisions, allowing prescribed steps to be omitted or applied incorrectly. We introduce HEXIS, which compiles agent skills into extended finite state machines that separate knowledge from control flow. Skill knowledge is incorporated into local instructions that guide reasoning and generation within states. The machine records execution progress and intermediate results, while explicit transition conditions determine subsequent operations. Our incremental compiler first maps skill clauses and tool interfaces to state operations, local instructions, data bindings, and transitions. It then aligns development traces with existing states to identify missing operations and dependencies. These are incorporated by adding or reusing states and refining their connections. Updates are accepted only after static checks and replay of the current and all previously accepted traces. Across four benchmarks and four executors, HEXIS improves success over Skill + ReAct by 16.1 percentage points on average. Qwen3.8-27B reduces execution tokens by 38.4-88.9% across benchmarks.
Figures & tables
Figure 1: Separating knowledge from control flow. Existing works interprets the whole skill as context or memory. HEXIS separates knowledge and flow within an FSM that controls execution. The detail of the FSM with guards omitted is shown as Appendix F .
Figure 2: Separating knowledge from workflow. In panel (d), HEXIS retains task knowledge and local operations in orange FSM states, while green transitions define the workflow. Panels (a) and (b) provide revised skills or memory as context for the LLM to select tools and control execution. Panel (c) sketches an AFlow program that composes LLM calls.
Figure 3: Skill compilation consists of initialization and trajectory updates. Initialization generates and validates an initial machine from the skill document and tool specifications; updates extract events, align states, modify a copy, and check and replay it to obtain the final machine for execution.
| Benchmark | Method | Qwen3.6-flash | GLM-4.7-FlashX | Qwen3.5-9B | Qwen3.8-27B |
|---|---|---|---|---|---|
| Spreadsheet Bench | Skill + ReAct | 45.6% | 22.8% | 33.3% | 56.1% |
| AWM | 61.4% | 31.6% | 35.1% | 59.6% | |
| ReasoningBank | 43.9% | 15.7% | 33.3% | 63.2% | |
| SkillOpt | 59.6% | 40.4% | 47.4% | 66.7% | |
| AFlow | 36.8% | 22.8% | 38.6% | 73.7% | |
| HEXIS | 75.4% | 47.4% | 38.6% | 71.9% |
Table 1: Success rates (%) on four benchmarks using four execution models. Bold and underline mark the best and second-best result for each benchmark and model.
Figure 4: Full compliance rates (%) across four models and benchmarks.
Figure 5: Reported mean execution tokens per task (k), including input and output tokens. Each benchmark uses its own axis scale.
| Skill document | Execution | Success (%) | Tokens (k) |
|---|---|---|---|
| Original | Skill + ReAct | 45.6% | 213 |
| Original | HEXIS | 75.4% | 223 |
| SkillOpt | Skill + ReAct | 59.6% | 257 |
| SkillOpt | HEXIS | 84.2% | 69 |
Table 2: Combining skill optimization with state machine execution on SpreadsheetBench. Tokens are mean total execution tokens per task.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Figure A.1: The state machine completes tasks through the skill content and operations within its states, connecting execution stages according to stored results. The diagram shows the main progression; a complete machine can also include repair branches, repeated execution, and fallback paths.
| Benchmark | Skill + ReAct | HEXIS Fable 5.1 | HEXIS Sonnet 5 low |
|---|---|---|---|
| SpreadsheetBench | 45.6% | 75.4% | 71.9% |
| LiveMath | 45.0% | 76.7% | 72.7% |
| DABench | 78.4% | 82.4% | 80.4% |
| LongSeal | 7.8% | 21.6% | 19.6% |
Table 3: Success rates with qwen3.6-flash execution. State machines are compiled by Fable 5.1 or Sonnet 5 with the low setting.
| Benchmark | States | Edges | Recovery | Fallback | Retry events | Steps | Revisits | |
|---|---|---|---|---|---|---|---|---|
| (tasks) | (tasks) | (total) | (mean) | (mean) | ||||
| SpreadsheetBench | 57 | 17 | 35 | 0 (0.0%) | 0 (0.0%) | 0 | 24.56 | 10.60 |
| LiveMath | 120 | 12 | 19 | 3 (2.5%) | 1 (0.8%) | 3 | 9.04 | 0.11 |
| DABench | 51 | 15 | 29 | 0 (0.0%) | 0 (0.0%) | 0 | 13.57 | 1.57 |
| LongSeal | 51 | 16 | 30 | 1 (2.0%) | 1 (2.0%) | 1 | 30.20 | 17.31 |
Table 4: Sizes and execution diagnostics of compiled state machines using qwen3.6-flash . Retry events count runtime recovery actions, while revisits count repeated visits to non-fallback machine states.
| State | Assigned operation | Ordered outgoing rules |
|---|---|---|
| s1 | Model: analyze the question, hypotheses, option support, and relative strength; write analysis . | Always |
| s2 | Model: select an option using request , analysis , and ; write answer_letter and justification . | ; else |
| s2m | Judge: check whether the selected option covers the stated conclusion; write . | , ; else |
| s3 | Model: generate write_cmd to write the selected letter in the required boxed format to output_path , using edit_log when available. | ; ; else |
| s4 | Tool: execute bash with command=write_cmd ; bind the returned stdout to edit_log . | ; else , |
| s5 | Tool: execute read with filePath=output_path ; bind the returned stdout to file_content . | ; ; else , |
Table 5: The actual LiveMath v11 machine. Outgoing rules are evaluated from top to bottom after the state’s operation; “else” is the stored unconditional edge. Counter increments occur only when the corresponding edge is taken. , , and abbreviate END_VERIFIED , END_UNVERIFIED , and FALLBACK .
| Benchmark | Success | Full compliance | ||||
|---|---|---|---|---|---|---|
| Skill + ReAct | Prompt-only | HEXIS | Skill + ReAct | Prompt-only | HEXIS | |
| SpreadsheetBench | 45.6% | 63.2% | 75.4% | 96.5% | 75.4% | 100.0% |
| LiveMath | 45.0% | 33.9% | 76.7% | 45.5% | 82.6% | 91.7% |
| DABench | 78.4% | 80.4% | 82.4% | 88.2% | 96.1% | 98.0% |
| LongSeal | 7.8% | 11.8% | 21.6% | 33.3% | 19.6% | 96.1% |
Table 6: Success and request-level full compliance with qwen3.6-flash . Both metrics are reported as percentages.
Figure H.1: Per-group success during incremental compilation on LiveMath with Qwen3.6-flash. The star marks the document-initialized machine . The shaded region denotes groups 21–49, which reuse the same refined machine. All development groups are shown without smoothing or repeated evaluation of previously processed tasks. Groups contain different tasks, so fluctuations also reflect task composition.
| Resource | License | URL |
| SpreadsheetBench ( Ma et al., 2024 ) | CC BY-SA 4.0 | https://huggingface.co/datasets/KAKA22/SpreadsheetBench |
| LiveMathematicianBench ( He et al., 2026 ) | Available online | https://huggingface.co/datasets/LiveMathematicianBench/ |
| InfiAgent-DABench ( Hu et al., 2024 ) | Apache 2.0 | https://github.com/InfiAgent/InfiAgent |
| SealQA ( Pham et al., 2026 ) | Apache 2.0 | https://huggingface.co/datasets/vtllms/sealqa |
| SigLeak skills ( Geng et al., 2026 ) | Available online | https://anonymous.4open.science/r/SigLeak-D1DB |
| Pandas Pro ( Jeffallan, 2026 ) | MIT | https://github.com/jeffallan/claude-skills |
Table 7: Resource licenses and URLs.