Wael Khreich

29 papers A 1B 1C 2Journal 17Unranked 8
YearRankTypeTitle / Venue / Authors
2025 J jnl
Complex Intell. Syst.
Wael Khreich, Jad Doughman
2025 J jnl
Neural Comput. Appl.
Baraa Abou Ghouch, Wael Khreich
2024 J jnl
J. Syst. Softw.
Mohammed A. Shehab, Wael Khreich, Abdelwahab Hamou-Lhadj, Issam Sedki
2024 J jnl
Array
Ahmad Mustapha, Wael Khreich, Wes Masri
2022 J jnl
CoRR
Ahmad Mustapha, Wael Khreich, Wasim Masr
2022 J jnl
CoRR
Jad Doughman, Wael Khreich
2022 J jnl
CoRR
Ahmad Mustapha, Wael Khreich, Wassim Masri
2018 J jnl
IEEE Trans. Reliab.
Md. Shariful Islam, Wael Khreich, Abdelwahab Hamou-Lhadj
2018 J jnl
J. Syst. Softw.
Wael Khreich, Syed Shariyar Murtaza, Abdelwahab Hamou-Lhadj, Chamseddine Talhi
2017 J jnl
Inf. Softw. Technol.
Wael Khreich, Babak Khosravifar, Abdelwahab Hamou-Lhadj, Chamseddine Talhi
2016 conf
CCECE
Assad Sahebalam, Soosan Beheshti, Wael Khreich, Edward W. Nidoy
2016 J jnl
J. Syst. Softw.
Syed Shariyar Murtaza, Wael Khreich, Abdelwahab Hamou-Lhadj, Ayse Basar Bener
2015 J jnl
Comput. Intell.
Atefeh Farzindar, Wael Khreich
2015 conf
CISDA
Syed Shariyar Murtaza, Wael Khreich, Abdelwahab Hamou-Lhadj, Stéphane Gagnon
2015 C conf
QRS
Amirreza Soudi, Wael Khreich, Abdelwahab Hamou-Lhadj
2014 C conf
SCAM
Syed Shariyar Murtaza, Abdelwahab Hamou-Lhadj, Wael Khreich, Mario Couture
2013 A conf
ISSRE
Syed Shariyar Murtaza, Wael Khreich, Abdelwahab Hamou-Lhadj, Mario Couture
2013 conf
ISSRE (Supplemental Proceedings)
Shayan Eskandari, Wael Khreich, Syed Shariyar Murtaza, Abdelwahab Hamou-Lhadj, Mario Couture
2012 J jnl
Inf. Sci.
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2012 J jnl
Pattern Recognit.
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2012 conf
Canadian AI
Baskaran Sankaran, Majid Razmara, Atefeh Farzindar, Wael Khreich, Fred Popowich, Anoop Sarkar
2012 J jnl
Int. J. Biom.
Eric Granger, Wael Khreich, Robert Sabourin, Dmitry O. Gorodnichy
2011 conf
CIBIM
Dmitry O. Gorodnichy, Elan Dubrofsky, Richard Hoshino, Wael Khreich, Eric Granger, Robert Sabourin
2011 conf
MCS
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2010 B conf
ICPR
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2010 J jnl
Pattern Recognit.
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2010 J jnl
Pattern Recognit. Lett.
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2009 conf
CISDA
Wael Khreich, Eric Granger, Ali Miri, Robert Sabourin
2009 conf
ICC
Wael Khreich, Eric Granger, Robert Sabourin, Ali Miri
redb/extractors/decompiler/apk/smali_cfg.py
← Index redb/extractors/decompiler/apk/smali_cfg.py python
"""Build a basic-block CFG from smali method bodies and compute graph metrics.

Handles both apktool smali (label-based branches like :cond_0) and
androguard fallback smali (offset-based branches like +005h).

Graph metrics match the Binary Ninja CFG pipeline for cross-platform
consistency: cyclomatic complexity (E - N + 2), loop count (back edges),
max BFS depth, max fan-out. Advanced features (topology hash, MD-index,
WL-MinHash, packed adjacency) reuse the generic cfg_features module.
"""

import logging
import re
from collections import deque
from dataclasses import dataclass, field
from typing import Dict, List, Optional, Tuple

from redb.extractors.decompiler.apk.smali_normalization import (
    categorize_opcode,
    CATEGORY_TO_ACFG_INDEX,
)
from redb.extractors.decompiler.bninja.analysis import cfg_features

logger = logging.getLogger(__name__)


# Instruction classification patterns
_IF_RE = re.compile(r"^if-\w+")
_GOTO_RE = re.compile(r"^goto(?:/\d+)?(?:\s|$)")
_RETURN_RE = re.compile(r"^return")
_THROW_RE = re.compile(r"^throw(?:\s|$)")
_SWITCH_RE = re.compile(r"^(?:packed|sparse)-switch\s")

# Label reference in apktool format: :cond_0, :goto_1, etc.
_LABEL_TARGET_RE = re.compile(r":[\w]+")

# Offset reference in androguard format: +005h, -003h
_OFFSET_TARGET_RE = re.compile(r"[+-]\w+h\b")

# Directives and labels
_SKIP_RE = re.compile(r"^\s*(?:\.|#|$)")
_LABEL_DEF_RE = re.compile(r"^\s*:([\w]+)")


@dataclass
class SmaliCFGMetrics:
    """CFG-derived metrics for a smali method."""
    block_count: int = 0
    edge_count: int = 0
    cyclomatic_complexity: int = 1
    loop_count: int = 0
    max_depth: int = 0
    max_fan_out: int = 0
    # Obfuscation scores (parity with code_binja_decompiled_functions_content)
    flattened_score: float = 0.0
    mba_score: float = 0.0
    # Per-block ACFG feature vectors (Gemini-style, same format as BNinja).
    # Each entry: [instr_count, arithmetic, logic, transfer, call,
    #              comparison, memory, successor_count]
    # Empty list if block features were not computed.
    block_features: List[List[int]] = field(default_factory=list)
    # Advanced CFG features (Phase 5 — parity with code_binja_cfg_functions)
    cfg_topology_hash: bytes = field(default_factory=lambda: b'\x00' * 16)
    md_index_topdown: int = 0
    md_index_bottomup: int = 0
    cfg_feature_tlsh: Optional[str] = None
    wl_minhash: List[int] = field(default_factory=lambda: [255] * 128)
    cfg_adjacency: List[int] = field(default_factory=list)


def compute_cfg_metrics(smali_body: str) -> SmaliCFGMetrics:
    """Compute CFG metrics from a smali method body.

    Works with both apktool label-based smali and androguard offset-based
    smali. Falls back to instruction-counting heuristic if CFG construction
    fails.
    """
    if not smali_body or not smali_body.strip():
        return SmaliCFGMetrics()

    lines = smali_body.split("\n")

    # Determine format: apktool (has labels) vs androguard (no labels)
    has_labels = any(_LABEL_DEF_RE.match(line) for line in lines)

    if has_labels:
        return _build_cfg_with_labels(lines)
    else:
        return _build_cfg_from_instructions(lines)


def _parse_instructions(lines: List[str]) -> List[Tuple[int, str]]:
    """Extract instruction lines, skipping directives, labels, blanks, comments.

    Returns list of (original_line_index, stripped_instruction).
    """
    instructions = []
    for i, line in enumerate(lines):
        stripped = line.strip()
        if not stripped or stripped.startswith(".") or stripped.startswith("#"):
            continue
        if stripped.startswith(":"):
            continue
        instructions.append((i, stripped))
    return instructions


def _build_cfg_with_labels(lines: List[str]) -> SmaliCFGMetrics:
    """Build CFG using apktool label-based format.

    Labels (e.g., :cond_0, :goto_1) define branch targets.
    Branch instructions reference labels directly.
    """
    # First pass: collect label positions and instructions
    # We track everything by instruction index (position in instruction list)
    labels: Dict[str, int] = {}  # label_name -> instruction_index
    instructions: List[str] = []
    # Map: line_index -> instruction_index (for label resolution)
    line_to_instr: Dict[int, int] = {}

    instr_idx = 0
    for i, line in enumerate(lines):
        stripped = line.strip()
        if not stripped or stripped.startswith(".") or stripped.startswith("#"):
            continue
        m = _LABEL_DEF_RE.match(stripped)
        if m:
            label_name = ":" + m.group(1)
            labels[label_name] = instr_idx  # next instruction after this label
            continue
        line_to_instr[i] = instr_idx
        instructions.append(stripped)
        instr_idx += 1

    n_instr = len(instructions)
    if n_instr == 0:
        return SmaliCFGMetrics()

    # Identify basic block start points
    block_starts = {0}

    for idx, instr in enumerate(instructions):
        next_idx = idx + 1

        if _IF_RE.match(instr):
            # Conditional branch: fall-through + branch target
            if next_idx < n_instr:
                block_starts.add(next_idx)
            target_label = _extract_label_target(instr)
            if target_label and target_label in labels:
                block_starts.add(labels[target_label])

        elif _GOTO_RE.match(instr):
            # Unconditional jump
            if next_idx < n_instr:
                block_starts.add(next_idx)
            target_label = _extract_label_target(instr)
            if target_label and target_label in labels:
                block_starts.add(labels[target_label])

        elif _RETURN_RE.match(instr) or _THROW_RE.match(instr):
            if next_idx < n_instr:
                block_starts.add(next_idx)

        elif _SWITCH_RE.match(instr):
            if next_idx < n_instr:
                block_starts.add(next_idx)

    # Also add all label targets as block starts
    for label, target_idx in labels.items():
        if target_idx < n_instr:
            block_starts.add(target_idx)

    # Build blocks: sorted list of start indices
    sorted_starts = sorted(block_starts)
    n_blocks = len(sorted_starts)

    # Map instruction index -> block index
    instr_to_block = {}
    for block_idx, start in enumerate(sorted_starts):
        end = sorted_starts[block_idx + 1] if block_idx + 1 < n_blocks else n_instr
        for i in range(start, end):
            instr_to_block[i] = block_idx

    # Collect per-block instruction lists for ACFG feature extraction
    block_instructions: List[List[str]] = []
    for block_idx in range(n_blocks):
        start = sorted_starts[block_idx]
        end = sorted_starts[block_idx + 1] if block_idx + 1 < n_blocks else n_instr
        block_instructions.append(instructions[start:end])

    # Build adjacency lists
    successors: List[List[int]] = [[] for _ in range(n_blocks)]

    for block_idx in range(n_blocks):
        start = sorted_starts[block_idx]
        end = sorted_starts[block_idx + 1] if block_idx + 1 < n_blocks else n_instr
        last_instr_idx = end - 1
        last_instr = instructions[last_instr_idx]

        if _IF_RE.match(last_instr):
            # Fall-through
            if block_idx + 1 < n_blocks:
                _add_edge(successors, block_idx, block_idx + 1)
            # Branch target
            target_label = _extract_label_target(last_instr)
            if target_label and target_label in labels:
                target_block = instr_to_block.get(labels[target_label])
                if target_block is not None:
                    _add_edge(successors, block_idx, target_block)

        elif _GOTO_RE.match(last_instr):
            # Only branch target, no fall-through
            target_label = _extract_label_target(last_instr)
            if target_label and target_label in labels:
                target_block = instr_to_block.get(labels[target_label])
                if target_block is not None:
                    _add_edge(successors, block_idx, target_block)

        elif _RETURN_RE.match(last_instr) or _THROW_RE.match(last_instr):
            # No successors
            pass

        elif _SWITCH_RE.match(last_instr):
            # Fall-through (default case)
            if block_idx + 1 < n_blocks:
                _add_edge(successors, block_idx, block_idx + 1)
            # Switch targets are defined in switch payload (.packed-switch/.sparse-switch)
            # which we can't easily parse from the body alone. The targets are labels
            # referenced in the switch data section. We handle them via label targets.
            _add_switch_targets(
                lines, last_instr, labels, instr_to_block,
                successors, block_idx
            )

        else:
            # Normal instruction at end of block — fall through
            if block_idx + 1 < n_blocks:
                _add_edge(successors, block_idx, block_idx + 1)

    return _compute_metrics_from_cfg(successors, n_blocks, block_instructions)


def _build_cfg_from_instructions(lines: List[str]) -> SmaliCFGMetrics:
    """Build CFG from androguard offset-based format.

    Without labels, we use instruction counting to build a basic CFG.
    Branch targets are hex offsets (e.g., +005h) which we resolve by
    tracking instruction positions.
    """
    instructions = _parse_instructions(lines)
    n_instr = len(instructions)
    if n_instr == 0:
        return SmaliCFGMetrics()

    # Identify basic block starts
    block_starts = {0}

    for idx, (_, instr) in enumerate(instructions):
        next_idx = idx + 1

        if _IF_RE.match(instr):
            if next_idx < n_instr:
                block_starts.add(next_idx)
            # Try to resolve offset target to instruction index
            target = _resolve_offset_target(instr, idx, n_instr)
            if target is not None:
                block_starts.add(target)

        elif _GOTO_RE.match(instr):
            if next_idx < n_instr:
                block_starts.add(next_idx)
            target = _resolve_offset_target(instr, idx, n_instr)
            if target is not None:
                block_starts.add(target)

        elif _RETURN_RE.match(instr) or _THROW_RE.match(instr):
            if next_idx < n_instr:
                block_starts.add(next_idx)

    sorted_starts = sorted(block_starts)
    n_blocks = len(sorted_starts)

    # Map instruction index -> block index
    instr_to_block = {}
    for block_idx, start in enumerate(sorted_starts):
        end = sorted_starts[block_idx + 1] if block_idx + 1 < n_blocks else n_instr
        for i in range(start, end):
            instr_to_block[i] = block_idx

    # Collect per-block instruction lists for ACFG features
    block_instructions: List[List[str]] = []
    for block_idx in range(n_blocks):
        start = sorted_starts[block_idx]
        end = sorted_starts[block_idx + 1] if block_idx + 1 < n_blocks else n_instr
        block_instructions.append(
            [instructions[i][1] for i in range(start, end)]
        )

    # Build adjacency
    successors: List[List[int]] = [[] for _ in range(n_blocks)]

    for block_idx in range(n_blocks):
        start = sorted_starts[block_idx]
        end = sorted_starts[block_idx + 1] if block_idx + 1 < n_blocks else n_instr
        last_idx = end - 1
        _, last_instr = instructions[last_idx]

        if _IF_RE.match(last_instr):
            if block_idx + 1 < n_blocks:
                _add_edge(successors, block_idx, block_idx + 1)
            target = _resolve_offset_target(last_instr, last_idx, n_instr)
            if target is not None:
                target_block = instr_to_block.get(target)
                if target_block is not None:
                    _add_edge(successors, block_idx, target_block)

        elif _GOTO_RE.match(last_instr):
            target = _resolve_offset_target(last_instr, last_idx, n_instr)
            if target is not None:
                target_block = instr_to_block.get(target)
                if target_block is not None:
                    _add_edge(successors, block_idx, target_block)

        elif _RETURN_RE.match(last_instr) or _THROW_RE.match(last_instr):
            pass

        else:
            if block_idx + 1 < n_blocks:
                _add_edge(successors, block_idx, block_idx + 1)

    return _compute_metrics_from_cfg(successors, n_blocks, block_instructions)


def _resolve_offset_target(instr: str, current_idx: int, n_instr: int) -> Optional[int]:
    """Resolve androguard hex offset to an instruction index.

    Androguard offsets (e.g., +005h, -003h) are in 16-bit code units relative
    to the branch instruction. Since most Dalvik instructions are 1-3 code
    units, we approximate: each instruction ≈ 1 code unit for offset
    resolution. This gives an approximate but usable CFG.

    For better accuracy, we treat the offset as an instruction count
    (which is correct for 1-unit instructions and approximate for larger ones).
    """
    m = _OFFSET_TARGET_RE.search(instr)
    if not m:
        return None

    offset_str = m.group(0)
    try:
        # Parse hex offset: +005h -> 5, -003h -> -3
        offset_val = int(offset_str.rstrip("h"), 16)
    except ValueError:
        return None

    target = current_idx + offset_val
    if 0 <= target < n_instr:
        return target
    return None


def _extract_label_target(instr: str) -> Optional[str]:
    """Extract the label target from a branch/goto instruction.

    E.g., 'if-eqz v0, :cond_0' -> ':cond_0'
          'goto :goto_1' -> ':goto_1'
    """
    m = _LABEL_TARGET_RE.search(instr)
    return m.group(0) if m else None


def _add_edge(successors: List[List[int]], src: int, dst: int):
    """Add edge if not duplicate."""
    if dst not in successors[src]:
        successors[src].append(dst)


def _add_switch_targets(
    lines: List[str],
    switch_instr: str,
    labels: Dict[str, int],
    instr_to_block: Dict[int, int],
    successors: List[List[int]],
    block_idx: int,
):
    """Try to resolve switch case targets.

    Switch payloads in apktool smali are defined as:
      .packed-switch 0x0
        :pswitch_0
        :pswitch_1
      .end packed-switch

    We scan the body for label references in switch payload sections.
    """
    # Find the switch payload target label
    target_label = _extract_label_target(switch_instr)
    if not target_label:
        return

    # Scan for packed-switch/sparse-switch payload sections
    in_switch = False
    for line in lines:
        stripped = line.strip()
        if stripped.startswith(".packed-switch") or stripped.startswith(".sparse-switch"):
            in_switch = True
            continue
        if stripped.startswith(".end packed-switch") or stripped.startswith(".end sparse-switch"):
            in_switch = False
            continue
        if in_switch:
            # Lines in switch payload are label references
            m = _LABEL_TARGET_RE.search(stripped)
            if m:
                case_label = m.group(0)
                if case_label in labels:
                    target_block = instr_to_block.get(labels[case_label])
                    if target_block is not None:
                        _add_edge(successors, block_idx, target_block)


def _build_block_features(
    block_instructions: List[List[str]],
    successors: List[List[int]],
    n: int,
) -> List[List[int]]:
    """Build Gemini-style ACFG feature vectors per block from smali instructions.

    Same 8-element format as Binary Ninja's build_block_features:
    [instr_count, arithmetic, logic, transfer, call, comparison, memory, successor_count]

    Uses semantic opcode categorization (analogous to LLIL operation categories)
    to map each Dalvik instruction to one of 7 category bins.
    """
    features = []
    for i in range(n):
        cats = [0, 0, 0, 0, 0, 0, 0]  # 7 categories
        instrs = block_instructions[i] if i < len(block_instructions) else []
        for instr in instrs:
            opcode = instr.split(None, 1)[0] if instr else ""
            category = categorize_opcode(opcode)
            acfg_idx = CATEGORY_TO_ACFG_INDEX.get(category, 6)
            cats[acfg_idx] += 1

        features.append([
            min(len(instrs), 65535),
            min(cats[0], 65535),  # arithmetic
            min(cats[1], 65535),  # logic
            min(cats[2], 65535),  # transfer
            min(cats[3], 65535),  # call
            min(cats[4], 65535),  # comparison
            min(cats[5], 65535),  # memory
            min(len(successors[i]), 65535),
        ])
    return features


def _compute_metrics_from_cfg(
    successors: List[List[int]],
    n: int,
    block_instructions: Optional[List[List[str]]] = None,
) -> SmaliCFGMetrics:
    """Compute all graph metrics from the adjacency list."""
    if n == 0:
        return SmaliCFGMetrics()

    edge_count = sum(len(s) for s in successors)

    # Cyclomatic complexity: E - N + 2
    cc = edge_count - n + 2
    if cc < 1:
        cc = 1

    # Loop count: back edges via iterative DFS
    loop_count = _count_back_edges(successors, n)

    # Max BFS depth from entry
    max_depth = _bfs_max_depth(successors, n)

    # Max fan-out
    max_fan_out = max(len(s) for s in successors) if successors else 0

    # Per-block ACFG features
    bb_features = []
    if block_instructions is not None:
        bb_features = _build_block_features(block_instructions, successors, n)

    # Obfuscation scores
    flattened = _compute_flattened_score(successors, n)
    mba = (
        _compute_mba_score(block_instructions, n)
        if block_instructions is not None
        else 0.0
    )

    # Advanced CFG features — reuse generic cfg_features module
    # Build predecessors from successors
    predecessors = [[] for _ in range(n)]
    for src, targets in enumerate(successors):
        for tgt in targets:
            predecessors[tgt].append(src)

    try:
        bfs = cfg_features.bfs_order(successors, n)
        topology_hash = cfg_features.compute_topology_hash(successors, bfs, n)
        md_topdown = cfg_features.compute_md_index_topdown(
            successors, predecessors, bfs
        )
        md_bottomup = cfg_features.compute_md_index_bottomup(
            successors, predecessors, n
        )
        cfg_tlsh = (
            cfg_features.compute_cfg_feature_tlsh(bb_features, bfs)
            if bb_features
            else None
        )
        wl_minhash = (
            cfg_features.compute_wl_minhash(
                successors, predecessors, bb_features, n
            )
            if bb_features
            else [255] * 128
        )
        adjacency = cfg_features.pack_adjacency(successors)
    except Exception as e:
        logger.debug("Advanced CFG features failed: %s", e)
        topology_hash = b'\x00' * 16
        md_topdown = 0
        md_bottomup = 0
        cfg_tlsh = None
        wl_minhash = [255] * 128
        adjacency = []

    return SmaliCFGMetrics(
        block_count=n,
        edge_count=edge_count,
        cyclomatic_complexity=cc,
        loop_count=loop_count,
        max_depth=max_depth,
        max_fan_out=max_fan_out,
        flattened_score=flattened,
        mba_score=mba,
        block_features=bb_features,
        cfg_topology_hash=topology_hash,
        md_index_topdown=md_topdown,
        md_index_bottomup=md_bottomup,
        cfg_feature_tlsh=cfg_tlsh,
        wl_minhash=wl_minhash,
        cfg_adjacency=adjacency,
    )


def _compute_dominators(successors: List[List[int]], n: int) -> List[int]:
    """Compute immediate dominators using iterative dataflow algorithm.

    Returns idom[i] = immediate dominator of block i.  idom[0] = -1 (entry).
    """
    if n == 0:
        return []

    # Build predecessors
    preds: List[List[int]] = [[] for _ in range(n)]
    for src, targets in enumerate(successors):
        for tgt in targets:
            preds[tgt].append(src)

    # Initialize: dom[0] = {0}, dom[i] = all blocks
    all_blocks = set(range(n))
    dom = [all_blocks.copy() for _ in range(n)]
    dom[0] = {0}

    changed = True
    while changed:
        changed = False
        for i in range(1, n):
            if not preds[i]:
                new_dom = {i}
            else:
                new_dom = all_blocks.copy()
                for p in preds[i]:
                    new_dom &= dom[p]
                new_dom.add(i)
            if new_dom != dom[i]:
                dom[i] = new_dom
                changed = True

    # Extract immediate dominators from dominator sets
    idom = [-1] * n
    for i in range(1, n):
        # idom[i] = the dominator of i (other than i itself) that is
        # dominated by all other dominators of i
        doms_of_i = dom[i] - {i}
        if not doms_of_i:
            continue
        for candidate in doms_of_i:
            # candidate is idom if it is dominated by all other dominators
            if all(candidate in dom[other] for other in doms_of_i):
                # candidate dominates no other dominator besides itself
                # (i.e., it's the closest dominator)
                if all(
                    other == candidate or candidate not in dom[other]
                    for other in doms_of_i
                ):
                    pass  # not the closest
                else:
                    continue
            else:
                continue
        # Simpler approach: idom is the element in doms_of_i with the
        # largest dominator set (closest to i in the dominator tree)
        idom[i] = max(doms_of_i, key=lambda d: len(dom[d]))

    return idom


def _compute_flattened_score(
    successors: List[List[int]], n: int
) -> float:
    """Detect control flow flattening — same heuristic as Binary Ninja's
    ObfuscationScores.flattened_score (Tim Blazytko).

    Walks over all basic blocks, finds those with back edges (loop headers),
    and computes the ratio of blocks dominated by them to total blocks.
    """
    if n <= 1:
        return 0.0

    idom = _compute_dominators(successors, n)

    # Build dominator tree children from idom
    dom_children: List[List[int]] = [[] for _ in range(n)]
    for i in range(1, n):
        if idom[i] >= 0:
            dom_children[idom[i]].append(i)

    max_ratio = 0.0

    for block in range(n):
        # Get all blocks dominated by this block (reachable in dominator tree)
        dominated = set()
        worklist = [block]
        while worklist:
            b = worklist.pop()
            dominated.add(b)
            worklist.extend(dom_children[b])

        # Check for a back edge: any predecessor of block is in dominated set
        has_back_edge = False
        for src, targets in enumerate(successors):
            if block in targets and src in dominated:
                has_back_edge = True
                break

        if not has_back_edge:
            continue

        ratio = len(dominated) / n
        if ratio > max_ratio:
            max_ratio = ratio

    return max_ratio


def _compute_mba_score(block_instructions: List[List[str]], n: int) -> float:
    """Compute mixed boolean-arithmetic score for a smali method.

    Same concept as Binary Ninja's ObfuscationScores.MBA_score: ratio of
    instructions that mix arithmetic and logic operations.

    At the smali level, we check each instruction's opcode:
    - Arithmetic: add, sub, mul, div, rem, neg
    - Logic: and, or, xor, shl, shr, ushr, not

    Since Dalvik instructions are single operations (unlike x86 complex
    instructions or HLIL expression trees), we check per-instruction whether
    the method mixes both categories. The score is the fraction of
    instructions belonging to the minority category when both are present.
    """
    ARITHMETIC_OPS = {"add", "sub", "mul", "div", "rem", "neg"}
    LOGIC_OPS = {"and", "or", "xor", "shl", "shr", "ushr", "not"}

    arithmetic_count = 0
    logic_count = 0
    total_instructions = 0

    for block in block_instructions[:n]:
        for instr in block:
            opcode = instr.split(None, 1)[0] if instr else ""
            # Strip type suffix: add-int/2addr -> add
            base = opcode.split("-")[0] if "-" in opcode else opcode
            total_instructions += 1
            if base in ARITHMETIC_OPS:
                arithmetic_count += 1
            elif base in LOGIC_OPS:
                logic_count += 1

    if total_instructions == 0:
        return 0.0

    # MBA is present when both arithmetic and logic operations co-exist.
    # Score = min(arith, logic) / total — measures how much mixing occurs.
    if arithmetic_count == 0 or logic_count == 0:
        return 0.0

    return min(arithmetic_count, logic_count) / total_instructions


def _count_back_edges(successors: List[List[int]], n: int) -> int:
    """Count natural loops via iterative DFS back-edge detection.

    Same algorithm as bninja/analysis/cfg_features.py:count_back_edges.
    """
    if n == 0:
        return 0

    WHITE, GRAY, BLACK = 0, 1, 2
    color = [WHITE] * n
    back_edges = 0

    stack = [(0, iter(successors[0]))]
    color[0] = GRAY

    while stack:
        u, children = stack[-1]
        try:
            v = next(children)
            if color[v] == GRAY:
                back_edges += 1
            elif color[v] == WHITE:
                color[v] = GRAY
                stack.append((v, iter(successors[v])))
        except StopIteration:
            color[u] = BLACK
            stack.pop()

    return back_edges


def _bfs_max_depth(successors: List[List[int]], n: int) -> int:
    """Maximum BFS depth from entry block.

    Same algorithm as bninja/analysis/cfg_features.py:bfs_max_depth.
    """
    if n == 0:
        return 0

    depth = {0: 0}
    max_d = 0
    queue = deque([0])

    while queue:
        node = queue.popleft()
        for s in successors[node]:
            if s not in depth:
                depth[s] = depth[node] + 1
                if depth[s] > max_d:
                    max_d = depth[s]
                queue.append(s)

    return max_d