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

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

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

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

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

# 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)

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