可判定性与可识别性

LEFT SIDE - 必要性(⇒):

• L可判定 → 存在判定器D
• M₁ = D 识别L，M₂识别¬L
• L和¬L都可识别

RIGHT SIDE - 充分性(⇐):

• L和¬L都可识别 → 存在M₁和M₂
• 并行运行M₁和M₂
• 构造判定器D：谁接受就接受
• D总是给出正确答案

DIVIDER: “判定器 ⇔ L和¬L都可识别”

KEY INSIGHTS:

• 递归语言 = 可判定语言
• 递归可枚举语言 = 可识别语言
• 补集性质连接了可判定性与可识别性

PALETTE: macaron — soft pastel color blocks COLORS: Left side in Macaron Blue (#A8D8EA), right side in Mint (#B5E5CF), Lavender (#D5C6E0) for machines, arrows in Coral Red (#E8655A), Warm Cream background (#F5F0E8), Black (#1A1A1A) for outlines ELEMENTS: Hand-drawn comparison with vertical divider. Left side: “⇒” with box showing D → {M₁, M₂}. Right side: “⇐” with box showing {M₁, M₂} → D. Wavy border separating sides. Hand-lettered labels “必要性” and “充分性”.

STYLE: Hand-drawn educational comparison on warm cream paper. Slight wobble on all lines. Hand-lettered machine labels. Generous white space.

Color values (#hex) and color names are rendering guidance only — do not display color names, hex codes, or palette labels as visible text in the image.

Clean composition with generous white space. Simple or no background. Main elements centered or positioned by content needs.

Text should be large and prominent with handwritten-style fonts. Keep minimal, focus on keywords.

ASPECT: 16:9