2nd/10_Wiki/Topics/Architecture/Program Dependence Graph.md

---
id: wiki-2026-0508-program-dependence-graph
title: Program Dependence Graph
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [PDG, Program Dependence Graph, 프로그램 의존성 그래프]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [compiler, static-analysis, ir, slicing]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: compiler-ir
  framework: static-analysis
---

# Program Dependence Graph

## 매 한 줄
> **"매 control + data dependence를 매 한 그래프로"**. Program Dependence Graph (PDG)는 Ferrante, Ottenstein, Warren (1987) 이 매 제안한 매 IR — 매 statement node 사이에 매 control dependence edge와 매 data dependence edge를 매 함께 표현. Program slicing, parallelization, change impact analysis의 매 backbone.

## 매 핵심

### 매 두 종류 edge
- **매 Data dependence**: 매 statement A가 매 정의한 var를 매 B가 매 사용 → A → B (def-use).
- **매 Control dependence**: 매 A의 매 결과가 매 B의 매 실행 여부를 매 결정 → A → B.
- **매 Region node**: 매 unconditional block 매 그룹화 (선택적).

### 매 CDG vs DDG vs PDG
- **CDG**: control dependence만 (post-dominator frontier 기반).
- **DDG**: data dependence만 (def-use chain).
- **PDG**: 매 둘 모두를 매 single graph로.
- **SDG (System DG)**: PDG + interprocedural call/parameter edge.

### 매 응용
1. Program slicing (Weiser 1981 + Horwitz et al. 1990).
2. Change impact analysis.
3. Loop parallelization (data dep 없으면 매 parallel-safe).
4. Code clone detection (subgraph isomorphism).
5. Differential testing / fuzzing.

## 💻 패턴

### PDG 구축 sketch (Python AST)
```python
import ast
from collections import defaultdict

class PDGBuilder(ast.NodeVisitor):
    def __init__(self):
        self.defs = defaultdict(list)   # var -> [stmt_id]
        self.data_edges = []
        self.ctrl_edges = []

    def visit_Assign(self, node):
        sid = id(node)
        for n in ast.walk(node.value):
            if isinstance(n, ast.Name):
                for prev in self.defs[n.id]:
                    self.data_edges.append((prev, sid))
        for tgt in node.targets:
            if isinstance(tgt, ast.Name):
                self.defs[tgt.id].append(sid)
        self.generic_visit(node)

    def visit_If(self, node):
        sid = id(node)
        for s in node.body + node.orelse:
            self.ctrl_edges.append((sid, id(s)))
        self.generic_visit(node)
```

### Backward slicing
```python
def backward_slice(pdg, criterion: int) -> set[int]:
    # criterion = stmt_id; 매 reachable predecessors via data + ctrl edges
    reverse = defaultdict(list)
    for u, v in pdg.data_edges + pdg.ctrl_edges:
        reverse[v].append(u)
    seen, stack = set(), [criterion]
    while stack:
        n = stack.pop()
        if n in seen: continue
        seen.add(n)
        stack.extend(reverse[n])
    return seen
```

### Loop parallelization check
```python
def is_parallelizable(loop_pdg) -> bool:
    # 매 No loop-carried data dependence
    for u, v in loop_pdg.data_edges:
        if loop_pdg.iter_distance(u, v) > 0:
            return False
    return True
```

### LLVM via opt pass
```bash
# LLVM 18+ — print PDG of a function
opt -passes='print<dependence-analysis>' -disable-output input.ll
opt -passes='print<scalar-evolution>'    -disable-output input.ll
```

### Tree-sitter + custom analyzer (modern stack)
```python
import tree_sitter_python as tsp
from tree_sitter import Language, Parser
LANG = Language(tsp.language())
parser = Parser(LANG)
tree = parser.parse(b"x = 1\ny = x + 2")
# 매 walk tree, 매 build PDG with same edges as above
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Slicing / debugging aid | PDG (data + control) |
| Loop opt only | DDG (loop-carried 매 충분) |
| Cross-function impact | SDG (PDG + summary edges) |
| Code clone detection | PDG subgraph isomorphism |

**기본값**: 매 PDG 시작, 매 cross-function 필요 시 매 SDG로 확장.

## 🔗 Graph
- 부모: [[Static-Analysis]]

## 🤖 LLM 활용
**언제**: 매 code understanding tool, 매 refactoring impact, 매 LLM-assisted slicing.
**언제 X**: 매 trivial single-function script.

## ❌ 안티패턴
- **매 Pointer aliasing 무시**: 매 may-alias 매 conservative 처리 안 하면 매 unsound.
- **매 Interprocedural skip**: 매 cross-function dep 매 결측 → 매 false negative.
- **매 매 edge 폭주**: 매 every var 매 every stmt → 매 PDG 매 dense 매 unreadable.

## 🧪 검증 / 중복
- Verified (Ferrante/Ottenstein/Warren TOPLAS 1987, Horwitz et al. TOPLAS 1990).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — PDG/CDG/DDG/SDG taxonomy + slicing impl |