hoisoserious/formal-grammar-llm-benchmark

A formal grammar benchmark to study learning and memorization of large language models

Usage

Load a specific grammar (config) and split:

from datasets import load_dataset

ds = load_dataset(
    "<username>/formal-grammar-llm-benchmark",
    name="pcfg_cfg3b_eq_len_skewed_prob",
)
# available splits per grammar:
# train_sequences, test_sequences, non_grammatical_sequences,
# non_grammatical_*_grammar_edit_*, non_grammatical_*_edit_distance_*
print(ds["train_sequences"][0])

Load the full grammar rules for a config:

import json
from huggingface_hub import hf_hub_download

path = hf_hub_download(
    repo_id="<username>/formal-grammar-llm-benchmark",
    filename="<grammar_name>/grammar_meta.json",
    repo_type="dataset",
)
grammar_string = json.load(open(path))["grammar_string"]
print(grammar_string)

Columns

Column	Splits	Description
sequence	all	Space-separated token string, e.g. 6 5 4 9 8 7 3 1 2
non_terminal_positions	train, test	JSON list of parse dicts [{"A8": [[start, end, [rule_idx, parent_NT, child_idx]], ...], ...}, ...] — one entry per parse tree (context is null for the root S node)
sequence_freq	train, test	How many times this sequence appears in the training corpus
sequence_prob	train, test	Probability of this sequence under the grammar

---

pcfg_4_3_1_2_3_4_5_6_7_8_9

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> '2' '9' '3' [0.3333]
B_1 -> '9' '6' '1' [0.3333]
B_1 -> '1' '8' '6' '2' [0.3333]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]

Show all 38 rules

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> '2' '9' '3' [0.3333]
B_1 -> '9' '6' '1' [0.3333]
B_1 -> '1' '8' '6' '2' [0.3333]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]
E_3 -> E_2 [0.3333]
E_3 -> E_2 E_2 [0.3333]
E_3 -> E_2 [0.3333]
E_2 -> E_1 E_1 [0.3333]
E_2 -> E_1 [0.3333]
E_2 -> E_1 E_1 E_1 [0.3333]
E_1 -> '5' '6' [0.3333]
E_1 -> '1' '8' '6' '6' [0.3333]
E_1 -> '1' '5' '1' '5' '5' '9' [0.3333]
T_1_1 -> '1' [1]
T_1_2 -> '2' [1]
T_1_3 -> '3' [1]
T_1_4 -> '4' [1]
C_1_1 -> '5' [1]
C_1_2 -> '6' [1]
C_1_3 -> '7' [1]
C_1_4 -> '8' [1]
C_1_5 -> '9' [1]

pcfg_4_3_1_2_3_4_5_6_7_8_9_eq_len_skewed_prob

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> '2' '9' '3' [0.95]
B_1 -> '9' '6' '1' [0.025]
B_1 -> '1' '8' '6' [0.025]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]

Show all 38 rules

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> '2' '9' '3' [0.95]
B_1 -> '9' '6' '1' [0.025]
B_1 -> '1' '8' '6' [0.025]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]
E_3 -> E_2 [0.3333]
E_3 -> E_2 E_2 [0.3333]
E_3 -> E_2 [0.3333]
E_2 -> E_1 E_1 [0.3333]
E_2 -> E_1 [0.3333]
E_2 -> E_1 E_1 E_1 [0.3333]
E_1 -> '5' '6' '5' '9' [0.95]
E_1 -> '1' '8' '6' '6' [0.025]
E_1 -> '1' '5' '1' '5' [0.025]
T_1_1 -> '1' [1]
T_1_2 -> '2' [1]
T_1_3 -> '3' [1]
T_1_4 -> '4' [1]
C_1_1 -> '5' [1]
C_1_2 -> '6' [1]
C_1_3 -> '7' [1]
C_1_4 -> '8' [1]
C_1_5 -> '9' [1]

pcfg_4_3_1_2_3_4_5_6_7_8_9_eq_len_uniform_prob

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> '2' '9' '3' [0.3333]
B_1 -> '9' '6' '1' [0.3333]
B_1 -> '1' '8' '6' [0.3333]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]

Show all 38 rules

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> '2' '9' '3' [0.3333]
B_1 -> '9' '6' '1' [0.3333]
B_1 -> '1' '8' '6' [0.3333]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]
E_3 -> E_2 [0.3333]
E_3 -> E_2 E_2 [0.3333]
E_3 -> E_2 [0.3333]
E_2 -> E_1 E_1 [0.3333]
E_2 -> E_1 [0.3333]
E_2 -> E_1 E_1 E_1 [0.3333]
E_1 -> '5' '6' '5' '9' [0.3333]
E_1 -> '1' '8' '6' '6' [0.3333]
E_1 -> '1' '5' '1' '5' [0.3333]
T_1_1 -> '1' [1]
T_1_2 -> '2' [1]
T_1_3 -> '3' [1]
T_1_4 -> '4' [1]
C_1_1 -> '5' [1]
C_1_2 -> '6' [1]
C_1_3 -> '7' [1]
C_1_4 -> '8' [1]
C_1_5 -> '9' [1]

pcfg_4_3_1_2_3_4_5_6_7_8_9_latin

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> 'b' 'i' 'c' [0.3333]
B_1 -> 'i' 'f' 'a' [0.3333]
B_1 -> 'a' 'h' 'f' 'b' [0.3333]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]

Show all 38 rules

S -> S_5 [1]
S_5 -> B_4 C_1_1 E_4 T_1_1 [0.25]
S_5 -> B_4 C_1_2 E_4 T_1_2 [0.25]
S_5 -> B_4 C_1_3 E_4 T_1_3 [0.25]
S_5 -> B_4 C_1_4 E_4 T_1_4 [0.25]
B_4 -> B_3 [0.3333]
B_4 -> B_3 B_3 B_3 [0.3333]
B_4 -> B_3 B_3 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 [0.3333]
B_3 -> B_2 B_2 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 [0.3333]
B_2 -> B_1 B_1 B_1 [0.3333]
B_1 -> 'b' 'i' 'c' [0.3333]
B_1 -> 'i' 'f' 'a' [0.3333]
B_1 -> 'a' 'h' 'f' 'b' [0.3333]
E_4 -> E_3 [0.3333]
E_4 -> E_3 E_3 [0.3333]
E_4 -> E_3 E_3 E_3 [0.3333]
E_3 -> E_2 [0.3333]
E_3 -> E_2 E_2 [0.3333]
E_3 -> E_2 [0.3333]
E_2 -> E_1 E_1 [0.3333]
E_2 -> E_1 [0.3333]
E_2 -> E_1 E_1 E_1 [0.3333]
E_1 -> 'e' 'f' [0.3333]
E_1 -> 'a' 'h' 'f' 'f' [0.3333]
E_1 -> 'a' 'e' 'a' 'e' 'e' 'i' [0.3333]
T_1_1 -> 'a' [1]
T_1_2 -> 'b' [1]
T_1_3 -> 'c' [1]
T_1_4 -> 'd' [1]
C_1_1 -> 'e' [1]
C_1_2 -> 'f' [1]
C_1_3 -> 'g' [1]
C_1_4 -> 'h' [1]
C_1_5 -> 'i' [1]

pcfg_cfg3b_disjoint_terminals

S -> A16 [1]
A16 -> A15 A13 [0.50]
A16 -> A13 A15 A14 [0.50]
A13 -> A11 A12 [0.50]
A13 -> A12 A11 [0.50]
A14 -> A11 A10 A12 [0.50]
A14 -> A10 A11 A12 [0.50]
A15 -> A12 A11 A10 [0.50]
A15 -> A11 A12 A10 [0.50]
A10 -> A7 A9 A8 [0.50]
A10 -> A9 A8 A7 [0.50]
A11 -> A8 A7 A9 [0.50]
A11 -> A7 A8 A9 [0.50]
A12 -> A8 A9 A7 [0.50]
A12 -> A9 A7 A8 [0.50]
A7 -> '3' '1' [0.50]
A7 -> '1' '2' '3' [0.50]
A8 -> '6' '5' [0.50]
A8 -> '6' '4' '5' [0.50]
A9 -> '9' '8' '7' [0.50]

Show all 21 rules

S -> A16 [1]
A16 -> A15 A13 [0.50]
A16 -> A13 A15 A14 [0.50]
A13 -> A11 A12 [0.50]
A13 -> A12 A11 [0.50]
A14 -> A11 A10 A12 [0.50]
A14 -> A10 A11 A12 [0.50]
A15 -> A12 A11 A10 [0.50]
A15 -> A11 A12 A10 [0.50]
A10 -> A7 A9 A8 [0.50]
A10 -> A9 A8 A7 [0.50]
A11 -> A8 A7 A9 [0.50]
A11 -> A7 A8 A9 [0.50]
A12 -> A8 A9 A7 [0.50]
A12 -> A9 A7 A8 [0.50]
A7 -> '3' '1' [0.50]
A7 -> '1' '2' '3' [0.50]
A8 -> '6' '5' [0.50]
A8 -> '6' '4' '5' [0.50]
A9 -> '9' '8' '7' [0.50]
A9 -> '8' '7' [0.50]

pcfg_cfg3b_disjoint_terminals_latin

S -> A16 [1]
A16 -> A15 A13 [0.50]
A16 -> A13 A15 A14 [0.50]
A13 -> A11 A12 [0.50]
A13 -> A12 A11 [0.50]
A14 -> A11 A10 A12 [0.50]
A14 -> A10 A11 A12 [0.50]
A15 -> A12 A11 A10 [0.50]
A15 -> A11 A12 A10 [0.50]
A10 -> A7 A9 A8 [0.50]
A10 -> A9 A8 A7 [0.50]
A11 -> A8 A7 A9 [0.50]
A11 -> A7 A8 A9 [0.50]
A12 -> A8 A9 A7 [0.50]
A12 -> A9 A7 A8 [0.50]
A7 -> 'c' 'a' [0.50]
A7 -> 'a' 'b' 'c' [0.50]
A8 -> 'f' 'e' [0.50]
A8 -> 'f' 'd' 'e' [0.50]
A9 -> 'i' 'h' 'g' [0.50]

Show all 21 rules

S -> A16 [1]
A16 -> A15 A13 [0.50]
A16 -> A13 A15 A14 [0.50]
A13 -> A11 A12 [0.50]
A13 -> A12 A11 [0.50]
A14 -> A11 A10 A12 [0.50]
A14 -> A10 A11 A12 [0.50]
A15 -> A12 A11 A10 [0.50]
A15 -> A11 A12 A10 [0.50]
A10 -> A7 A9 A8 [0.50]
A10 -> A9 A8 A7 [0.50]
A11 -> A8 A7 A9 [0.50]
A11 -> A7 A8 A9 [0.50]
A12 -> A8 A9 A7 [0.50]
A12 -> A9 A7 A8 [0.50]
A7 -> 'c' 'a' [0.50]
A7 -> 'a' 'b' 'c' [0.50]
A8 -> 'f' 'e' [0.50]
A8 -> 'f' 'd' 'e' [0.50]
A9 -> 'i' 'h' 'g' [0.50]
A9 -> 'h' 'g' [0.50]

pcfg_cfg3b_eq_len_skewed_prob

S -> A16 [1]
A16 -> A15 A14 A13 [0.95]
A16 -> A13 A15 A14 [0.05]
A13 -> A11 A12 [0.95]
A13 -> A12 A11 [0.05]
A14 -> A11 A10 A12 [0.95]
A14 -> A10 A11 A12 [0.05]
A15 -> A12 A11 A10 [0.95]
A15 -> A11 A12 A10 [0.05]
A10 -> A7 A9 A8 [0.95]
A10 -> A9 A8 A7 [0.05]
A11 -> A8 A7 A9 [0.95]
A11 -> A7 A8 A9 [0.05]
A12 -> A8 A9 A7 [0.95]
A12 -> A9 A7 A8 [0.05]
A7 -> '3' '1' '2' [0.95]
A7 -> '1' '2' '3' [0.05]
A8 -> '6' '5' '4' [0.95]
A8 -> '6' '4' '5' [0.05]
A9 -> '9' '8' '7' [0.95]

Show all 21 rules

S -> A16 [1]
A16 -> A15 A14 A13 [0.95]
A16 -> A13 A15 A14 [0.05]
A13 -> A11 A12 [0.95]
A13 -> A12 A11 [0.05]
A14 -> A11 A10 A12 [0.95]
A14 -> A10 A11 A12 [0.05]
A15 -> A12 A11 A10 [0.95]
A15 -> A11 A12 A10 [0.05]
A10 -> A7 A9 A8 [0.95]
A10 -> A9 A8 A7 [0.05]
A11 -> A8 A7 A9 [0.95]
A11 -> A7 A8 A9 [0.05]
A12 -> A8 A9 A7 [0.95]
A12 -> A9 A7 A8 [0.05]
A7 -> '3' '1' '2' [0.95]
A7 -> '1' '2' '3' [0.05]
A8 -> '6' '5' '4' [0.95]
A8 -> '6' '4' '5' [0.05]
A9 -> '9' '8' '7' [0.95]
A9 -> '8' '7' '9' [0.05]

pcfg_cfg3b_eq_len_uniform_prob

S -> A16 [1]
A16 -> A15 A14 A13 [0.50]
A16 -> A13 A15 A14 [0.50]
A13 -> A11 A12 [0.50]
A13 -> A12 A11 [0.50]
A14 -> A11 A10 A12 [0.50]
A14 -> A10 A11 A12 [0.50]
A15 -> A12 A11 A10 [0.50]
A15 -> A11 A12 A10 [0.50]
A10 -> A7 A9 A8 [0.50]
A10 -> A9 A8 A7 [0.50]
A11 -> A8 A7 A9 [0.50]
A11 -> A7 A8 A9 [0.50]
A12 -> A8 A9 A7 [0.50]
A12 -> A9 A7 A8 [0.50]
A7 -> '3' '1' '2' [0.50]
A7 -> '1' '2' '3' [0.50]
A8 -> '6' '5' '4' [0.50]
A8 -> '6' '4' '5' [0.50]
A9 -> '9' '8' '7' [0.50]

Show all 21 rules

S -> A16 [1]
A16 -> A15 A14 A13 [0.50]
A16 -> A13 A15 A14 [0.50]
A13 -> A11 A12 [0.50]
A13 -> A12 A11 [0.50]
A14 -> A11 A10 A12 [0.50]
A14 -> A10 A11 A12 [0.50]
A15 -> A12 A11 A10 [0.50]
A15 -> A11 A12 A10 [0.50]
A10 -> A7 A9 A8 [0.50]
A10 -> A9 A8 A7 [0.50]
A11 -> A8 A7 A9 [0.50]
A11 -> A7 A8 A9 [0.50]
A12 -> A8 A9 A7 [0.50]
A12 -> A9 A7 A8 [0.50]
A7 -> '3' '1' '2' [0.50]
A7 -> '1' '2' '3' [0.50]
A8 -> '6' '5' '4' [0.50]
A8 -> '6' '4' '5' [0.50]
A9 -> '9' '8' '7' [0.50]
A9 -> '8' '7' '9' [0.50]

pcfg_max-depth_3_max-breadth_9_rules_9_skewness_10_alphabet-size_20_large

S -> A_19 [1]
A_19 -> A_12 A_18 A_14 A_17 A_11 A_17 A_15 A_10 [0.1633488445]
A_19 -> A_15 A_13 [0.2032909216]
A_19 -> A_10 A_12 [0.2376710982]
A_19 -> A_18 [0.2594097969]
A_19 -> A_16 A_15 A_15 [0.1346583572]
A_19 -> A_11 A_18 A_13 A_10 [0.0016209134]
A_19 -> A_12 A_16 A_18 A_17 A_12 [0.0000000681]
A_19 -> A_13 A_18 A_14 A_12 A_14 [0.0000000000]
A_19 -> A_13 A_13 A_15 A_14 [0.0000000000]
A_18 -> A_6 A_5 A_3 A_1 A_8 A_2 A_9 [0.1633488445]
A_18 -> A_5 A_8 A_4 A_6 A_5 [0.2032909216]
A_18 -> A_1 A_6 A_8 A_1 A_3 A_5 [0.2376710982]
A_18 -> A_9 A_7 A_9 A_3 A_7 [0.2594097969]
A_18 -> A_2 A_4 A_5 A_7 A_2 A_1 [0.1346583572]
A_18 -> A_1 A_8 A_7 A_8 A_7 A_1 A_3 A_8 A_5 [0.0016209134]
A_18 -> A_4 A_9 A_1 A_5 A_5 [0.0000000681]
A_18 -> A_8 A_9 A_4 A_4 A_9 [0.0000000000]
A_18 -> A_1 [0.0000000000]
A_17 -> A_2 A_8 A_7 [0.1633488445]

Show all 172 rules

S -> A_19 [1]
A_19 -> A_12 A_18 A_14 A_17 A_11 A_17 A_15 A_10 [0.1633488445]
A_19 -> A_15 A_13 [0.2032909216]
A_19 -> A_10 A_12 [0.2376710982]
A_19 -> A_18 [0.2594097969]
A_19 -> A_16 A_15 A_15 [0.1346583572]
A_19 -> A_11 A_18 A_13 A_10 [0.0016209134]
A_19 -> A_12 A_16 A_18 A_17 A_12 [0.0000000681]
A_19 -> A_13 A_18 A_14 A_12 A_14 [0.0000000000]
A_19 -> A_13 A_13 A_15 A_14 [0.0000000000]
A_18 -> A_6 A_5 A_3 A_1 A_8 A_2 A_9 [0.1633488445]
A_18 -> A_5 A_8 A_4 A_6 A_5 [0.2032909216]
A_18 -> A_1 A_6 A_8 A_1 A_3 A_5 [0.2376710982]
A_18 -> A_9 A_7 A_9 A_3 A_7 [0.2594097969]
A_18 -> A_2 A_4 A_5 A_7 A_2 A_1 [0.1346583572]
A_18 -> A_1 A_8 A_7 A_8 A_7 A_1 A_3 A_8 A_5 [0.0016209134]
A_18 -> A_4 A_9 A_1 A_5 A_5 [0.0000000681]
A_18 -> A_8 A_9 A_4 A_4 A_9 [0.0000000000]
A_18 -> A_1 [0.0000000000]
A_17 -> A_2 A_8 A_7 [0.1633488445]
A_17 -> A_9 A_7 [0.2032909216]
A_17 -> A_4 A_4 [0.2376710982]
A_17 -> A_4 [0.2594097969]
A_17 -> A_5 [0.1346583572]
A_17 -> A_4 A_8 A_5 A_3 A_9 A_5 A_7 A_3 [0.0016209134]
A_17 -> A_8 A_8 A_9 [0.0000000681]
A_17 -> A_4 A_1 A_2 A_6 A_6 A_2 A_7 A_1 [0.0000000000]
A_17 -> A_5 A_7 [0.0000000000]
A_16 -> A_3 A_6 A_6 A_8 A_8 A_1 A_2 A_2 A_3 [0.1633488445]
A_16 -> A_4 A_6 A_6 A_5 A_3 [0.2032909216]
A_16 -> A_6 A_6 A_6 A_1 A_9 A_6 A_9 [0.2376710982]
A_16 -> A_5 [0.2594097969]
A_16 -> A_9 A_3 A_4 A_2 A_4 [0.1346583572]
A_16 -> A_2 A_6 [0.0016209134]
A_16 -> A_2 A_1 A_7 A_6 A_1 A_6 A_5 A_9 [0.0000000681]
A_16 -> A_2 A_1 [0.0000000000]
A_16 -> A_6 A_4 A_2 A_9 A_6 [0.0000000000]
A_15 -> A_7 A_8 A_5 [0.1633488445]
A_15 -> A_3 A_3 A_4 A_1 A_8 A_4 A_2 [0.2032909216]
A_15 -> A_5 A_1 A_3 A_6 A_6 A_9 A_8 A_8 A_3 [0.2376710982]
A_15 -> A_7 A_1 A_5 A_6 A_4 A_6 A_1 A_4 A_5 [0.2594097969]
A_15 -> A_4 A_5 A_3 A_6 [0.1346583572]
A_15 -> A_6 A_8 A_8 A_6 [0.0016209134]
A_15 -> A_4 A_5 A_4 A_8 A_3 [0.0000000681]
A_15 -> A_6 A_9 A_2 [0.0000000000]
A_15 -> A_7 [0.0000000000]
A_14 -> A_4 A_3 A_3 A_2 A_6 A_2 [0.1633488445]
A_14 -> A_4 [0.2032909216]
A_14 -> A_5 A_4 A_3 A_2 A_5 A_2 [0.2376710982]
A_14 -> A_6 A_7 A_6 A_9 A_6 [0.2594097969]
A_14 -> A_3 A_2 A_7 A_4 A_8 A_7 [0.1346583572]
A_14 -> A_9 A_6 A_1 A_4 A_8 A_4 A_5 A_7 A_6 [0.0016209134]
A_14 -> A_6 A_8 A_4 [0.0000000681]
A_14 -> A_1 A_6 A_3 [0.0000000000]
A_14 -> A_6 A_9 A_9 A_6 A_2 A_2 A_3 A_5 [0.0000000000]
A_13 -> A_7 A_9 A_7 [0.1633488445]
A_13 -> A_4 A_9 A_6 [0.2032909216]
A_13 -> A_3 A_7 A_4 A_3 A_4 [0.2376710982]
A_13 -> A_3 A_4 A_5 A_4 A_5 A_1 A_1 A_7 [0.2594097969]
A_13 -> A_3 A_5 A_9 A_9 A_6 A_8 [0.1346583572]
A_13 -> A_7 A_2 A_1 A_4 A_7 A_1 A_5 A_3 A_9 [0.0016209134]
A_13 -> A_7 [0.0000000681]
A_13 -> A_7 A_8 A_8 [0.0000000000]
A_13 -> A_7 A_4 A_2 A_7 A_8 A_4 A_8 [0.0000000000]
A_12 -> A_5 A_9 A_6 [0.1633488445]
A_12 -> A_3 A_6 [0.2032909216]
A_12 -> A_5 A_9 A_7 A_6 A_9 [0.2376710982]
A_12 -> A_5 [0.2594097969]
A_12 -> A_9 A_6 A_1 A_8 [0.1346583572]
A_12 -> A_7 A_1 A_7 A_2 A_5 A_4 A_4 [0.0016209134]
A_12 -> A_5 A_1 A_6 A_5 A_3 A_2 A_9 [0.0000000681]
A_12 -> A_4 A_1 A_6 A_7 A_5 [0.0000000000]
A_12 -> A_4 A_5 A_8 A_7 A_6 [0.0000000000]
A_11 -> A_2 A_7 A_9 A_7 [0.1633488445]
A_11 -> A_5 A_4 A_4 A_7 A_3 A_2 A_1 A_6 [0.2032909216]
A_11 -> A_2 [0.2376710982]
A_11 -> A_9 A_3 A_7 A_1 A_5 A_1 A_3 [0.2594097969]
A_11 -> A_1 [0.1346583572]
A_11 -> A_3 A_3 A_4 A_2 A_8 A_1 A_6 A_8 [0.0016209134]
A_11 -> A_6 A_4 A_9 A_5 A_5 A_7 A_5 A_4 [0.0000000681]
A_11 -> A_9 A_6 A_7 A_7 A_3 A_6 A_5 A_3 [0.0000000000]
A_11 -> A_3 A_5 A_8 A_4 A_2 A_4 A_5 A_2 A_9 [0.0000000000]
A_10 -> A_5 [0.1633488445]
A_10 -> A_8 A_5 [0.2032909216]
A_10 -> A_2 A_2 [0.2376710982]
A_10 -> A_5 A_8 A_2 A_8 A_4 [0.2594097969]
A_10 -> A_4 A_1 A_7 A_5 A_7 A_8 A_1 [0.1346583572]
A_10 -> A_3 A_3 A_3 A_1 [0.0016209134]
A_10 -> A_2 A_6 A_5 A_8 A_2 A_1 A_2 A_2 A_4 [0.0000000681]
A_10 -> A_7 A_8 A_4 A_9 A_9 A_5 A_7 A_8 [0.0000000000]
A_10 -> A_8 A_2 A_5 [0.0000000000]
A_9 -> '8' '3' '2' '12' '10' '10' '13' '14' [0.1633488445]
A_9 -> '2' '19' [0.2032909216]
A_9 -> '13' '16' '18' '14' [0.2376710982]
A_9 -> '0' '0' '7' [0.2594097969]
A_9 -> '18' '14' [0.1346583572]
A_9 -> '7' [0.0016209134]
A_9 -> '7' '17' '19' '14' '6' '1' '1' '6' '10' [0.0000000681]
A_9 -> '11' '3' '14' '19' '9' '7' '19' '15' [0.0000000000]
A_9 -> '6' '13' '3' [0.0000000000]
A_8 -> '0' '12' '9' [0.1633488445]
A_8 -> '3' '0' '10' '14' '9' '9' '9' [0.2032909216]
A_8 -> '8' '10' '14' '12' '12' '12' '10' '4' '6' [0.2376710982]
A_8 -> '6' '15' '10' '5' '12' '6' '0' '5' '18' [0.2594097969]
A_8 -> '1' '0' '5' [0.1346583572]
A_8 -> '6' '0' '12' '9' '14' '7' '1' '5' [0.0016209134]
A_8 -> '14' '3' '8' '0' '3' '14' '11' [0.0000000681]
A_8 -> '2' '7' '0' [0.0000000000]
A_8 -> '13' [0.0000000000]
A_7 -> '12' '11' '8' '11' '0' '0' '0' [0.1633488445]
A_7 -> '2' '19' '4' '18' [0.2032909216]
A_7 -> '6' '18' '14' '7' '12' '19' '3' [0.2376710982]
A_7 -> '0' [0.2594097969]
A_7 -> '1' '17' '12' '11' '0' '8' [0.1346583572]
A_7 -> '13' '1' '12' '9' '11' '7' '4' [0.0016209134]
A_7 -> '12' '17' '6' '18' '12' '12' '10' '0' '3' [0.0000000681]
A_7 -> '19' '7' '16' '4' '8' '12' '14' [0.0000000000]
A_7 -> '17' '3' '17' '11' '8' '10' [0.0000000000]
A_6 -> '9' '3' '16' '19' [0.1633488445]
A_6 -> '18' '0' '11' '8' '6' [0.2032909216]
A_6 -> '1' '11' '16' [0.2376710982]
A_6 -> '11' '19' '12' '3' '19' '4' [0.2594097969]
A_6 -> '12' '0' '17' '12' '3' '8' '18' [0.1346583572]
A_6 -> '19' '3' '16' '16' '6' '11' '9' '3' [0.0016209134]
A_6 -> '10' '6' '7' '11' '6' '2' '17' '14' '12' [0.0000000681]
A_6 -> '14' [0.0000000000]
A_6 -> '12' '3' '3' '12' '17' '19' [0.0000000000]
A_5 -> '17' '13' '11' '0' '7' '18' [0.1633488445]
A_5 -> '18' '16' '11' '7' '6' '17' '3' '18' [0.2032909216]
A_5 -> '19' '3' [0.2376710982]
A_5 -> '4' [0.2594097969]
A_5 -> '12' '4' '6' '11' '16' [0.1346583572]
A_5 -> '0' '6' '6' '14' '12' [0.0016209134]
A_5 -> '11' '14' [0.0000000681]
A_5 -> '16' '8' '15' '19' '19' '14' [0.0000000000]
A_5 -> '9' '8' '9' '9' '13' [0.0000000000]
A_4 -> '10' '10' '5' '8' '6' [0.1633488445]
A_4 -> '7' '8' '3' '14' '9' [0.2032909216]
A_4 -> '1' '8' '1' '1' [0.2376710982]
A_4 -> '8' '8' '7' '16' [0.2594097969]
A_4 -> '12' '12' [0.1346583572]
A_4 -> '17' '15' '16' '14' '8' '14' '4' '11' [0.0016209134]
A_4 -> '13' '6' [0.0000000681]
A_4 -> '2' '11' '18' '3' '6' '1' '3' '4' [0.0000000000]
A_4 -> '19' '5' [0.0000000000]
A_3 -> '14' '17' '0' '18' [0.1633488445]
A_3 -> '19' '8' [0.2032909216]
A_3 -> '18' '3' '4' '12' '13' '12' '11' '16' '9' [0.2376710982]
A_3 -> '15' '18' '6' '5' '15' '9' '6' [0.2594097969]
A_3 -> '10' '1' '1' '2' '9' '19' '9' '9' [0.1346583572]
A_3 -> '17' [0.0016209134]
A_3 -> '11' '1' '19' [0.0000000681]
A_3 -> '1' '9' '9' '8' '8' '11' '10' '9' [0.0000000000]
A_3 -> '14' '19' '5' '9' [0.0000000000]
A_2 -> '7' '17' '13' [0.1633488445]
A_2 -> '4' '10' '0' '17' '4' '5' '8' [0.2032909216]
A_2 -> '15' '9' '6' [0.2376710982]
A_2 -> '8' '13' '2' '10' '17' '5' '6' [0.2594097969]
A_2 -> '19' '3' '6' [0.1346583572]
A_2 -> '2' '15' '1' [0.0016209134]
A_2 -> '7' '18' '18' [0.0000000681]
A_2 -> '10' '17' [0.0000000000]
A_2 -> '16' '3' '4' '8' '0' '9' [0.0000000000]
A_1 -> '6' '10' '8' '1' [0.1633488445]
A_1 -> '3' '18' '10' [0.2032909216]
A_1 -> '19' '12' '0' '0' [0.2376710982]
A_1 -> '9' '13' '13' '2' '15' [0.2594097969]
A_1 -> '12' '7' '5' [0.1346583572]
A_1 -> '8' [0.0016209134]
A_1 -> '16' '13' '3' '10' '6' '4' '19' '19' [0.0000000681]
A_1 -> '4' [0.0000000000]
A_1 -> '8' [0.0000000000]

pcfg_max-depth_4_max-breadth_4_rules_2_skewness_1_alphabet_0-1-2-3-4

S -> A_13 [1]
A_13 -> A_10 A_12 [0.8413]
A_13 -> A_9 A_10 [0.1587]
A_12 -> A_5 A_7 A_5 A_8 [0.8413]
A_12 -> A_6 A_6 [0.1587]
A_11 -> A_5 A_7 A_8 [0.8413]
A_11 -> A_6 [0.1587]
A_10 -> A_6 A_7 A_5 A_7 [0.8413]
A_10 -> A_8 A_6 [0.1587]
A_9 -> A_6 [0.8413]
A_9 -> A_8 A_5 A_8 [0.1587]
A_8 -> A_1 [0.8413]
A_8 -> A_3 [0.1587]
A_7 -> A_1 A_2 [0.8413]
A_7 -> A_4 A_4 [0.1587]
A_6 -> A_2 A_1 A_3 A_4 [0.8413]
A_6 -> A_3 A_4 A_1 [0.1587]
A_5 -> A_1 A_4 [0.8413]
A_5 -> A_3 [0.1587]
A_4 -> '4' '3' [0.8413]

Show all 27 rules

S -> A_13 [1]
A_13 -> A_10 A_12 [0.8413]
A_13 -> A_9 A_10 [0.1587]
A_12 -> A_5 A_7 A_5 A_8 [0.8413]
A_12 -> A_6 A_6 [0.1587]
A_11 -> A_5 A_7 A_8 [0.8413]
A_11 -> A_6 [0.1587]
A_10 -> A_6 A_7 A_5 A_7 [0.8413]
A_10 -> A_8 A_6 [0.1587]
A_9 -> A_6 [0.8413]
A_9 -> A_8 A_5 A_8 [0.1587]
A_8 -> A_1 [0.8413]
A_8 -> A_3 [0.1587]
A_7 -> A_1 A_2 [0.8413]
A_7 -> A_4 A_4 [0.1587]
A_6 -> A_2 A_1 A_3 A_4 [0.8413]
A_6 -> A_3 A_4 A_1 [0.1587]
A_5 -> A_1 A_4 [0.8413]
A_5 -> A_3 [0.1587]
A_4 -> '4' '3' [0.8413]
A_4 -> '3' '0' '3' [0.1587]
A_3 -> '2' '4' '1' '0' [0.8413]
A_3 -> '0' '4' '3' [0.1587]
A_2 -> '0' '4' '3' [0.8413]
A_2 -> '4' '3' '0' '2' [0.1587]
A_1 -> '1' [0.8413]
A_1 -> '2' [0.1587]