2nd/10_Wiki/Topics/Other/Search-Space.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-search-space	Search Space	10_Wiki/Topics	verified	self	State Space Solution Space Hypothesis Space	none	A	0.9	applied	algorithms search optimization ai planning		2026-05-10	pending	language framework python algorithms

Search Space

매 한 줄

"매 search space = 매 algorithm 의 매 explore-able 모든 candidate 의 set". 매 problem 을 매 (state, transition, goal) tuple 로 modeling 시 의 전체 reachable state set. 매 search 의 효율 = 매 1) space 의 size 줄이기 + 2) 매 promising region 의 priorit ize.

매 핵심

매 정의 components

• State: 매 partial / full solution candidate.
• Initial state: 매 search 시작 점.
• Successor function: 매 state → 매 reachable next states.
• Goal test: 매 state 가 매 valid solution 인지.
• Path cost: 매 path 의 매 quality metric.

매 size scaling

• Combinatorial explosion: 매 N-queens 의 N=8 → 매 16M state. N=20 → 매 effectively infinite.
• Branching factor (b) × depth (d) → b^d.
• Pruning (alpha-beta, constraint propagation, branch-and-bound) → 매 effective space ↓.

매 응용

1. Pathfinding: 매 grid/graph 의 매 cell/node space.
2. Game AI: 매 chess/go 의 매 game tree.
3. Planning: 매 STRIPS, PDDL 의 매 action sequence space.
4. NAS: 매 neural architecture 의 매 hyperparameter space.
5. LLM reasoning: 매 chain-of-thought / tree-of-thought 의 매 reasoning tree.

💻 패턴

Pattern 1: Generic search space (BFS)

from collections import deque

def bfs(initial, successors, is_goal):
    frontier = deque([(initial, [])])
    visited = {initial}
    while frontier:
        state, path = frontier.popleft()
        if is_goal(state):
            return path + [state]
        for nxt in successors(state):
            if nxt not in visited:
                visited.add(nxt)
                frontier.append((nxt, path + [state]))
    return None

Pattern 2: A* with admissible heuristic (search space reduction)

import heapq

def astar(initial, successors, is_goal, heuristic, cost):
    pq = [(heuristic(initial), 0, initial, [])]
    seen = {}
    while pq:
        _, g, s, path = heapq.heappop(pq)
        if is_goal(s):
            return path + [s]
        if s in seen and seen[s] <= g:
            continue
        seen[s] = g
        for nxt in successors(s):
            new_g = g + cost(s, nxt)
            f = new_g + heuristic(nxt)
            heapq.heappush(pq, (f, new_g, nxt, path + [s]))

Pattern 3: Constraint propagation (CSP)

# 매 search space 의 매 prune via 매 arc-consistency.
def ac3(domains, constraints):
    queue = [(x, y) for x in domains for y in constraints.get(x, [])]
    while queue:
        x, y = queue.pop(0)
        if revise(domains, x, y, constraints):
            if not domains[x]:
                return False  # 매 inconsistent
            for z in constraints.get(x, []) - {y}:
                queue.append((z, x))
    return True

Pattern 4: Tree-of-Thoughts (LLM reasoning space)

# 매 LLM 의 매 reasoning step 을 매 search node 로.
async def tot_search(problem, max_depth=5, beam=3):
    frontier = [{"state": problem, "trace": []}]
    for d in range(max_depth):
        cands = []
        for node in frontier:
            thoughts = await llm.expand(node["state"], k=beam)
            for t in thoughts:
                cands.append({"state": t, "trace": node["trace"] + [t]})
        # 매 evaluator (LLM-as-judge) 가 매 top-beam pick.
        scored = await llm.evaluate(cands)
        frontier = sorted(scored, key=lambda x: -x["score"])[:beam]
        if any(is_goal(n["state"]) for n in frontier):
            break
    return frontier[0]["trace"]

매 결정 기준

상황	Approach
매 small finite space	BFS / DFS — 매 complete
매 large but heuristic-able	A* / IDA*
매 huge stochastic	MCTS (UCT)
매 continuous space	gradient-based / Bayesian opt
매 LLM reasoning	Tree-of-Thoughts / Graph-of-Thoughts
매 constraint-rich	CSP solver (Z3, OR-Tools)

기본값: 매 first 매 reformulate problem 으로 매 space 의 size ↓ — 매 algorithm choice 보다 효과 큼.

🔗 Graph

• 부모: Combinatorial Optimization
• 변형: State Space · Hypothesis Space
• 응용: MCTS

🤖 LLM 활용

언제: 매 problem 의 매 search space modeling 의 매 design 도움. 언제 X: 매 매우 narrow domain (chess engine 등) — specialized solver 가 우위.

❌ 안티패턴

• No pruning: 매 brute-force on b^d=10^15 — 매 wall-clock 의 절망.
• Wrong representation: 매 redundant states (symmetry 의 explode) — canonicalize 필요.
• Heuristic over-engineering: 매 inadmissible heuristic 의 매 optimality 깨짐.

🧪 검증 / 중복

• Verified (Russell & Norvig AIMA 4th ed; Yao et al. ToT 2023).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — Search Space components/scaling/BFS/A*/CSP/ToT 정리