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praca_magisterska/pytania/generate_automata_diagrams.py

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#!/usr/bin/env python3
"""
Generate diagrams for PYTANIE 1: Automata and language classes.
1. FA recognition example — DFA for strings ending in "ab"
2. PDA recognition example — PDA for aⁿbⁿ
3. LBA recognition example — LBA for aⁿbⁿcⁿ
4. TM recognition example — TM for 0ⁿ1ⁿ
All: A4-compatible, B&W, 300 DPI, laser-printer-friendly.
"""
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from matplotlib.patches import FancyBboxPatch, FancyArrowPatch, Circle
import numpy as np
import os
DPI = 300
BG = 'white'
LN = 'black'
FS = 8
FS_TITLE = 11
FS_SMALL = 6.5
OUTPUT_DIR = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'img')
os.makedirs(OUTPUT_DIR, exist_ok=True)
GRAY1 = '#E8E8E8'
GRAY2 = '#D0D0D0'
GRAY3 = '#B8B8B8'
GRAY4 = '#F5F5F5'
GRAY5 = '#C0C0C0'
LIGHT_GREEN = '#D5E8D4'
LIGHT_RED = '#F8D7DA'
LIGHT_BLUE = '#D6EAF8'
LIGHT_YELLOW = '#FFF9C4'
def draw_state_circle(ax, x, y, r, label, accepting=False, initial=False,
fillcolor='white', fontsize=FS):
"""Draw an automaton state circle."""
circle = plt.Circle((x, y), r, fill=True, facecolor=fillcolor,
edgecolor=LN, linewidth=1.5, zorder=3)
ax.add_patch(circle)
if accepting:
inner = plt.Circle((x, y), r * 0.82, fill=False,
edgecolor=LN, linewidth=1.2, zorder=3)
ax.add_patch(inner)
if initial:
ax.annotate("", xy=(x - r, y), xytext=(x - r - 0.4, y),
arrowprops=dict(arrowstyle='->', color=LN, lw=1.5),
zorder=4)
ax.text(x, y, label, ha='center', va='center', fontsize=fontsize,
fontweight='bold', zorder=5)
def draw_curved_arrow(ax, x1, y1, x2, y2, label, r=0.25,
connectionstyle="arc3,rad=0.3", fontsize=FS_SMALL,
label_offset=(0, 0)):
"""Draw a curved arrow between points with label."""
ax.annotate("", xy=(x2, y2), xytext=(x1, y1),
arrowprops=dict(arrowstyle='->', color=LN, lw=1.2,
connectionstyle=connectionstyle),
zorder=2)
mx = (x1 + x2) / 2 + label_offset[0]
my = (y1 + y2) / 2 + label_offset[1]
ax.text(mx, my, label, ha='center', va='center', fontsize=fontsize,
fontstyle='italic', zorder=5,
bbox=dict(boxstyle='round,pad=0.15', facecolor='white',
edgecolor='none', alpha=0.9))
def draw_self_loop(ax, x, y, r, label, direction='top', fontsize=FS_SMALL):
"""Draw a self-loop on a state."""
if direction == 'top':
loop = mpatches.FancyArrowPatch(
(x - 0.12, y + r), (x + 0.12, y + r),
connectionstyle="arc3,rad=-1.8",
arrowstyle='->', mutation_scale=12, lw=1.2, color=LN, zorder=2)
ax.add_patch(loop)
ax.text(x, y + r + 0.35, label, ha='center', va='center',
fontsize=fontsize, fontstyle='italic', zorder=5)
elif direction == 'bottom':
loop = mpatches.FancyArrowPatch(
(x - 0.12, y - r), (x + 0.12, y - r),
connectionstyle="arc3,rad=1.8",
arrowstyle='->', mutation_scale=12, lw=1.2, color=LN, zorder=2)
ax.add_patch(loop)
ax.text(x, y - r - 0.35, label, ha='center', va='center',
fontsize=fontsize, fontstyle='italic', zorder=5)
# ============================================================
# 1. FA Recognition Example — DFA for strings ending in "ab"
# ============================================================
def draw_fa_recognition():
"""FA state diagram + step-by-step trace for 'baab'."""
fig, axes = plt.subplots(1, 2, figsize=(11.69, 4),
gridspec_kw={'width_ratios': [1, 1.3]})
# --- Left: State diagram ---
ax = axes[0]
ax.set_xlim(-1, 5.5)
ax.set_ylim(-1.5, 2.5)
ax.set_aspect('equal')
ax.axis('off')
ax.set_title('DFA — diagram stanów\nL = {słowa nad {a,b} kończące się na "ab"}',
fontsize=FS_TITLE, fontweight='bold', pad=10)
R = 0.35
# States positions
states = {'q₀': (0.8, 0.5), 'q₁': (2.8, 0.5), 'q₂': (4.8, 0.5)}
draw_state_circle(ax, *states['q₀'], R, 'q₀', initial=True)
draw_state_circle(ax, *states['q₁'], R, 'q₁')
draw_state_circle(ax, *states['q₂'], R, 'q₂', accepting=True,
fillcolor=LIGHT_GREEN)
# Transitions
# q₀ --a--> q₁
draw_curved_arrow(ax, states['q₀'][0] + R, states['q₀'][1] + 0.05,
states['q₁'][0] - R, states['q₁'][1] + 0.05,
'a', connectionstyle="arc3,rad=0.15",
label_offset=(0, 0.25))
# q₁ --b--> q₂
draw_curved_arrow(ax, states['q₁'][0] + R, states['q₁'][1] + 0.05,
states['q₂'][0] - R, states['q₂'][1] + 0.05,
'b', connectionstyle="arc3,rad=0.15",
label_offset=(0, 0.25))
# q₂ --a--> q₁
draw_curved_arrow(ax, states['q₂'][0] - R, states['q₂'][1] - 0.05,
states['q₁'][0] + R, states['q₁'][1] - 0.05,
'a', connectionstyle="arc3,rad=0.15",
label_offset=(0, -0.3))
# q₂ --b--> q₀
draw_curved_arrow(ax, states['q₂'][0] - 0.2, states['q₂'][1] - R,
states['q₀'][0] + 0.2, states['q₀'][1] - R,
'b', connectionstyle="arc3,rad=0.4",
label_offset=(0, -0.4))
# q₀ --b--> q₀ (self-loop)
draw_self_loop(ax, *states['q₀'], R, 'b', direction='top')
# q₁ --a--> q₁ (self-loop)
draw_self_loop(ax, *states['q₁'], R, 'a', direction='top')
# Legend
ax.text(0.3, -1.0, '→ = start ◎ = akceptujący',
fontsize=FS_SMALL, ha='left', va='center',
bbox=dict(boxstyle='round,pad=0.3', facecolor=GRAY4, edgecolor=GRAY3))
# --- Right: Step-by-step trace ---
ax2 = axes[1]
ax2.axis('off')
ax2.set_title('Ślad wykonania — wejście: "baab"',
fontsize=FS_TITLE, fontweight='bold', pad=10)
trace_data = [
['Krok', 'Czytam', 'Stan przed', 'Przejście', 'Stan po'],
['—', '—', 'q₀ (start)', '—', 'q₀'],
['1', 'b', 'q₀', 'δ(q₀, b) = q₀', 'q₀'],
['2', 'a', 'q₀', 'δ(q₀, a) = q₁', 'q₁'],
['3', 'a', 'q₁', 'δ(q₁, a) = q₁', 'q₁'],
['4', 'b', 'q₁', 'δ(q₁, b) = q₂', 'q₂ ✓'],
]
colors = [GRAY2] + ['white'] * 4 + [LIGHT_GREEN]
table = ax2.table(cellText=trace_data, cellLoc='center',
loc='center', bbox=[0.05, 0.15, 0.9, 0.75])
table.auto_set_font_size(False)
table.set_fontsize(FS)
for (row, col), cell in table.get_celld().items():
cell.set_edgecolor(GRAY3)
if row == 0:
cell.set_facecolor(GRAY2)
cell.set_text_props(fontweight='bold')
else:
cell.set_facecolor(colors[row])
cell.set_height(0.12)
ax2.text(0.5, 0.05, 'Wynik: q₂ ∈ F → "baab" AKCEPTOWANE ✓',
ha='center', va='center', fontsize=FS + 1, fontweight='bold',
transform=ax2.transAxes,
bbox=dict(boxstyle='round,pad=0.4', facecolor=LIGHT_GREEN,
edgecolor=LN))
plt.tight_layout()
plt.savefig(os.path.join(OUTPUT_DIR, 'fa_recognition_example.png'),
dpi=DPI, bbox_inches='tight', facecolor=BG)
plt.close()
print(" ✓ fa_recognition_example.png")
# ============================================================
# 2. PDA Recognition Example — PDA for aⁿbⁿ
# ============================================================
def draw_pda_recognition():
"""PDA state diagram + step-by-step trace with stack visualization for 'aabb'."""
fig, axes = plt.subplots(1, 2, figsize=(11.69, 5.5),
gridspec_kw={'width_ratios': [1, 1.4]})
# --- Left: State diagram ---
ax = axes[0]
ax.set_xlim(-1, 5.5)
ax.set_ylim(-2, 3)
ax.set_aspect('equal')
ax.axis('off')
ax.set_title('PDA — diagram stanów\nL = {aⁿbⁿ | n ≥ 1}',
fontsize=FS_TITLE, fontweight='bold', pad=10)
R = 0.38
states = {'q₀': (0.8, 0.5), 'q₁': (2.8, 0.5), 'q₂': (4.8, 0.5)}
draw_state_circle(ax, *states['q₀'], R, 'q₀', initial=True)
draw_state_circle(ax, *states['q₁'], R, 'q₁')
draw_state_circle(ax, *states['q₂'], R, 'q₂', accepting=True,
fillcolor=LIGHT_GREEN)
# q₀ --b,A/ε--> q₁
draw_curved_arrow(ax, states['q₀'][0] + R, states['q₀'][1],
states['q₁'][0] - R, states['q₁'][1],
'b, A → ε\n(pop A)', connectionstyle="arc3,rad=0.0",
label_offset=(0, 0.4))
# q₁ --ε,Z₀/Z₀--> q₂
draw_curved_arrow(ax, states['q₁'][0] + R, states['q₁'][1],
states['q₂'][0] - R, states['q₂'][1],
'ε, Z₀ → Z₀\n(akceptuj)', connectionstyle="arc3,rad=0.0",
label_offset=(0, 0.45))
# q₀ self-loop: a, Z₀/AZ₀ and a, A/AA
draw_self_loop(ax, *states['q₀'], R, 'a, Z₀ → AZ₀\na, A → AA\n(push A)',
direction='top')
# q₁ self-loop: b, A/ε
draw_self_loop(ax, *states['q₁'], R, 'b, A → ε\n(pop A)', direction='top')
# Key explanation
ax.text(0.3, -1.3, 'Notacja: symbol_wejścia, szczyt_stosu → nowy_szczyt\n'
'ε = brak symbolu (przejście spontaniczne lub pusty stos)',
fontsize=FS_SMALL, ha='left', va='center',
bbox=dict(boxstyle='round,pad=0.3', facecolor=GRAY4, edgecolor=GRAY3))
# --- Right: Step trace with stack ---
ax2 = axes[1]
ax2.axis('off')
ax2.set_title('Ślad wykonania z wizualizacją stosu — wejście: "aabb"',
fontsize=FS_TITLE, fontweight='bold', pad=10)
trace_data = [
['Krok', 'Czytam', 'Stan', 'Stos (szczyt→)', 'Operacja'],
['start', '—', 'q₀', '[Z₀]', '—'],
['1', 'a', 'q₀', '[A, Z₀]', 'push A'],
['2', 'a', 'q₀', '[A, A, Z₀]', 'push A'],
['3', 'b', 'q₁', '[A, Z₀]', 'pop A'],
['4', 'b', 'q₁', '[Z₀]', 'pop A'],
['5', 'ε', 'q₂', '[Z₀]', 'akceptuj!'],
]
colors = [GRAY2, 'white', LIGHT_BLUE, LIGHT_BLUE, LIGHT_YELLOW, LIGHT_YELLOW, LIGHT_GREEN]
table = ax2.table(cellText=trace_data, cellLoc='center',
loc='center', bbox=[0.02, 0.08, 0.96, 0.82])
table.auto_set_font_size(False)
table.set_fontsize(FS)
for (row, col), cell in table.get_celld().items():
cell.set_edgecolor(GRAY3)
if row == 0:
cell.set_facecolor(GRAY2)
cell.set_text_props(fontweight='bold')
else:
cell.set_facecolor(colors[row])
cell.set_height(0.11)
ax2.text(0.5, 0.0, 'Wynik: q₂ ∈ F, stos=[Z₀] → "aabb" AKCEPTOWANE ✓\n'
'Intuicja: 2× push A (za "aa") + 2× pop A (za "bb") = stos pusty = OK',
ha='center', va='center', fontsize=FS, fontweight='bold',
transform=ax2.transAxes,
bbox=dict(boxstyle='round,pad=0.4', facecolor=LIGHT_GREEN,
edgecolor=LN))
plt.tight_layout()
plt.savefig(os.path.join(OUTPUT_DIR, 'pda_recognition_example.png'),
dpi=DPI, bbox_inches='tight', facecolor=BG)
plt.close()
print(" ✓ pda_recognition_example.png")
# ============================================================
# 3. LBA Recognition Example — LBA for aⁿbⁿcⁿ
# ============================================================
def draw_lba_recognition():
"""LBA tape visualization showing marking rounds for 'aabbcc'."""
fig, ax = plt.subplots(1, 1, figsize=(11.69, 6.5))
ax.set_xlim(-0.5, 12)
ax.set_ylim(-1, 10.5)
ax.axis('off')
ax.set_title('LBA — rozpoznawanie aⁿbⁿcⁿ (n=2)\n'
'Strategia: w każdej rundzie zaznacz jedno a, b, c',
fontsize=FS_TITLE, fontweight='bold', pad=10)
CELL_W = 0.9
CELL_H = 0.7
TAPE_X0 = 1.5
HEAD_COLOR = '#FFD700'
def draw_tape(y, cells, head_pos, label, step_label=""):
"""Draw a tape row with cells, head position highlighted."""
ax.text(0.2, y + CELL_H/2, label, ha='right', va='center',
fontsize=FS, fontweight='bold')
for i, (sym, color) in enumerate(cells):
x = TAPE_X0 + i * CELL_W
fc = HEAD_COLOR if i == head_pos else color
rect = mpatches.FancyBboxPatch((x, y), CELL_W, CELL_H,
boxstyle="round,pad=0.03",
lw=1.2, edgecolor=LN, facecolor=fc)
ax.add_patch(rect)
ax.text(x + CELL_W/2, y + CELL_H/2, sym,
ha='center', va='center', fontsize=FS + 2,
fontweight='bold' if sym in ('X', 'Y', 'Z') else 'normal',
family='monospace')
if head_pos is not None:
hx = TAPE_X0 + head_pos * CELL_W + CELL_W/2
ax.annotate('▼', xy=(hx, y + CELL_H), xytext=(hx, y + CELL_H + 0.25),
ha='center', va='bottom', fontsize=8, color='black')
if step_label:
sx = TAPE_X0 + 6 * CELL_W + 0.5
ax.text(sx, y + CELL_H/2, step_label, ha='left', va='center',
fontsize=FS_SMALL,
bbox=dict(boxstyle='round,pad=0.2', facecolor=GRAY4,
edgecolor=GRAY3))
W = 'white'
MK = GRAY1 # marked cell color
# Row 1: Initial tape
y = 9.0
draw_tape(y, [('a', W), ('a', W), ('b', W), ('b', W), ('c', W), ('c', W)],
0, 'Początek', 'taśma = [a, a, b, b, c, c], głowica na 0')
# Row 2: After marking first 'a'
y = 7.8
draw_tape(y, [('X', MK), ('a', W), ('b', W), ('b', W), ('c', W), ('c', W)],
1, 'R1, krok 1', 'zaznacz a→X, szukaj b')
# Row 3: After marking first 'b'
y = 6.6
draw_tape(y, [('X', MK), ('a', W), ('Y', MK), ('b', W), ('c', W), ('c', W)],
3, 'R1, krok 2', 'zaznacz b→Y, szukaj c')
# Row 4: After marking first 'c'
y = 5.4
draw_tape(y, [('X', MK), ('a', W), ('Y', MK), ('b', W), ('Z', MK), ('c', W)],
0, 'R1, krok 3', 'zaznacz c→Z, wróć na początek')
# Runda 2 header
y = 4.5
ax.text(TAPE_X0 + 3 * CELL_W, y + 0.3, '═══ RUNDA 2 ═══',
ha='center', va='center', fontsize=FS, fontweight='bold',
color=LN)
# Row 5: After marking second 'a'
y = 3.6
draw_tape(y, [('X', MK), ('X', MK), ('Y', MK), ('b', W), ('Z', MK), ('c', W)],
2, 'R2, krok 1', 'pomiń X, zaznacz a→X, szukaj b')
# Row 6: After marking second 'b'
y = 2.4
draw_tape(y, [('X', MK), ('X', MK), ('Y', MK), ('Y', MK), ('Z', MK), ('c', W)],
4, 'R2, krok 2', 'pomiń Y, zaznacz b→Y, szukaj c')
# Row 7: After marking second 'c'
y = 1.2
draw_tape(y, [('X', MK), ('X', MK), ('Y', MK), ('Y', MK), ('Z', MK), ('Z', MK)],
None, 'R2, krok 3', 'zaznacz c→Z, wróć na początek')
# Result
y = 0.0
ax.text(TAPE_X0 + 3 * CELL_W, y + 0.3,
'Wszystko zaznaczone → q_acc → "aabbcc" AKCEPTOWANE ✓',
ha='center', va='center', fontsize=FS + 1, fontweight='bold',
bbox=dict(boxstyle='round,pad=0.4', facecolor=LIGHT_GREEN,
edgecolor=LN))
# Key
ax.text(TAPE_X0 + 6 * CELL_W + 0.5, y + 0.3,
'Ograniczenie LBA:\ngłowica ≤ 6 komórek\n(= |w| = |"aabbcc"|)',
ha='left', va='center', fontsize=FS_SMALL,
bbox=dict(boxstyle='round,pad=0.3', facecolor=LIGHT_YELLOW,
edgecolor=GRAY3))
plt.tight_layout()
plt.savefig(os.path.join(OUTPUT_DIR, 'lba_recognition_example.png'),
dpi=DPI, bbox_inches='tight', facecolor=BG)
plt.close()
print(" ✓ lba_recognition_example.png")
# ============================================================
# 4. TM Recognition Example — TM for 0ⁿ1ⁿ
# ============================================================
def draw_tm_recognition():
"""TM tape visualization for 0ⁿ1ⁿ with infinite tape shown."""
fig, ax = plt.subplots(1, 1, figsize=(11.69, 6.5))
ax.set_xlim(-0.5, 13)
ax.set_ylim(-1, 10.5)
ax.axis('off')
ax.set_title('TM — rozpoznawanie 0ⁿ1ⁿ (n=2)\n'
'Strategia: zaznacz jedno 0 i jedno 1 w każdej rundzie',
fontsize=FS_TITLE, fontweight='bold', pad=10)
CELL_W = 0.9
CELL_H = 0.7
TAPE_X0 = 1.5
HEAD_COLOR = '#FFD700'
def draw_tape(y, cells, head_pos, label, step_label=""):
ax.text(0.2, y + CELL_H/2, label, ha='right', va='center',
fontsize=FS, fontweight='bold')
for i, (sym, color) in enumerate(cells):
x = TAPE_X0 + i * CELL_W
fc = HEAD_COLOR if i == head_pos else color
lw = 1.2
ls = '-'
if sym == '⊔':
ls = '--'
rect = mpatches.FancyBboxPatch((x, y), CELL_W, CELL_H,
boxstyle="round,pad=0.03",
lw=lw, edgecolor=LN, facecolor=fc,
linestyle=ls)
ax.add_patch(rect)
ax.text(x + CELL_W/2, y + CELL_H/2, sym,
ha='center', va='center', fontsize=FS + 2,
fontweight='bold' if sym in ('X', 'Y') else 'normal',
family='monospace',
color=GRAY3 if sym == '⊔' else LN)
# ∞ arrow
last_x = TAPE_X0 + len(cells) * CELL_W
ax.annotate('→ ∞', xy=(last_x + 0.3, y + CELL_H/2),
fontsize=FS, ha='left', va='center', color=GRAY3)
if head_pos is not None:
hx = TAPE_X0 + head_pos * CELL_W + CELL_W/2
ax.annotate('▼', xy=(hx, y + CELL_H), xytext=(hx, y + CELL_H + 0.25),
ha='center', va='bottom', fontsize=8, color='black')
if step_label:
sx = TAPE_X0 + 8 * CELL_W + 0.8
ax.text(sx, y + CELL_H/2, step_label, ha='left', va='center',
fontsize=FS_SMALL,
bbox=dict(boxstyle='round,pad=0.2', facecolor=GRAY4,
edgecolor=GRAY3))
W = 'white'
MK = GRAY1
BL = '#F0F0F0' # blank cell
# Row 1: Initial
y = 9.0
draw_tape(y, [('0', W), ('0', W), ('1', W), ('1', W), ('⊔', BL), ('⊔', BL), ('⊔', BL)],
0, 'Początek', 'taśma = [0,0,1,1,⊔,⊔,...∞]')
# Row 2: Mark first 0
y = 7.8
draw_tape(y, [('X', MK), ('0', W), ('1', W), ('1', W), ('⊔', BL), ('⊔', BL), ('⊔', BL)],
1, 'R1, krok 1', 'zaznacz 0→X, idź w prawo')
# Row 3: Skip to first 1, mark it
y = 6.6
draw_tape(y, [('X', MK), ('0', W), ('Y', MK), ('1', W), ('⊔', BL), ('⊔', BL), ('⊔', BL)],
0, 'R1, krok 2', 'zaznacz 1→Y, wróć na początek')
# Runda 2 header
y = 5.8
ax.text(TAPE_X0 + 3.5 * CELL_W, y + 0.3, '═══ RUNDA 2 ═══',
ha='center', va='center', fontsize=FS, fontweight='bold')
# Row 4: Mark second 0
y = 4.8
draw_tape(y, [('X', MK), ('X', MK), ('Y', MK), ('1', W), ('⊔', BL), ('⊔', BL), ('⊔', BL)],
2, 'R2, krok 1', 'pomiń X, zaznacz 0→X')
# Row 5: Mark second 1
y = 3.6
draw_tape(y, [('X', MK), ('X', MK), ('Y', MK), ('Y', MK), ('⊔', BL), ('⊔', BL), ('⊔', BL)],
0, 'R2, krok 2', 'pomiń Y, zaznacz 1→Y, wróć')
# Row 6: Check — all marked
y = 2.4
draw_tape(y, [('X', MK), ('X', MK), ('Y', MK), ('Y', MK), ('⊔', BL), ('⊔', BL), ('⊔', BL)],
None, 'Sprawdzenie', 'brak niezaznaczonych → q_acc')
# Result + TM vs LBA comparison
y = 0.8
ax.text(TAPE_X0 + 3.5 * CELL_W, y + 0.3,
'"0011" AKCEPTOWANE ✓',
ha='center', va='center', fontsize=FS + 1, fontweight='bold',
bbox=dict(boxstyle='round,pad=0.4', facecolor=LIGHT_GREEN,
edgecolor=LN))
y = -0.3
ax.text(TAPE_X0 + 3.5 * CELL_W, y + 0.3,
'Różnica TM vs LBA: taśma TM jest nieskończona (⊔ → ∞)\n'
'LBA: głowica ograniczona do |w| komórek\n'
'TM: głowica może wyjść POZA wejście i pisać na pustych ⊔',
ha='center', va='center', fontsize=FS_SMALL,
bbox=dict(boxstyle='round,pad=0.4', facecolor=LIGHT_YELLOW,
edgecolor=GRAY3))
plt.tight_layout()
plt.savefig(os.path.join(OUTPUT_DIR, 'tm_recognition_example.png'),
dpi=DPI, bbox_inches='tight', facecolor=BG)
plt.close()
print(" ✓ tm_recognition_example.png")
# ============================================================
# Main
# ============================================================
if __name__ == '__main__':
print("Generating automata diagrams for PYTANIE 1...")
draw_fa_recognition()
draw_pda_recognition()
draw_lba_recognition()
draw_tm_recognition()
print(f"\nAll diagrams saved to {OUTPUT_DIR}/")
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