
AutoToS prompt:

The task is a 5x5 mini crosswords. A state is a 2D array representing the current puzzle state, where the initial grid is all "None". Note that some of the possible answers are not exactly 5 character long. Given an input of possible answers to horizontal clues and vertical clues, how is the successor state function defined? Please first think step by step. Then provide the successor state function in Python code. 

The possible clues for each row and each column are given separately. Here is an example of possible horizontal and vertical clues:

horizontal_answers = [
        ["tasks", "goals", "plans", "agend", "chores", "works", "deeds", "items", "lists", "brief"],
        ["motor", "power", "drive", "diesel", "steam", "pumps", "crank", "gears", "turbn", "motor"],
        ["grand", "artsy", "showy", "ornate", "fancy", "vain", "proud", "vogue", "swank", "luxus"], 
        ["venue", "salle", "forum", "atria", "lobby", "parls", "court", "malls", "mall", "lobby"], 
        ["jeer", "scoff", "sleer", "deris", "sneer", "scorn", "derid", "gibes", "gibed", "flout"] 
]
vertical_answers = [
        ["amass", "stack", "hoard", "pile", "store", "heaps", "massy", "gathe", "lumps", "mound"],
        ["nilga", "goral", "eland", "lepus", "gazal", "kudu", "oryx", "gnu", "imps", "carb"],
        ["scheme", "design", "ettle", "nettle", "sting", "wiles", "plans", "ideas", "plots", "cocks"], 
        ["spout", "nosle", "snout", "mouth", "nostr", "ports", "inlet", "vents", "outlt", "beaks"], 
        ["drier", "arid", "sere", "parch", "dryer", "wring", "drear", "sear", "pall", "lack"]
]

where horizontal_answers is a list where element i is a list of possible answers to clue in row i, and vertical_answers is a list where element i is a list of possible answers to clue in column i.

Model response:
```python
def successor_state(state, horizontal_answers, vertical_answers):
    from itertools import product

    def is_valid(state, row, col, word, horizontal=True):
        if horizontal:
            for idx in range(len(word)):
                if state[row][col + idx] is not None and state[row][col + idx] != word[idx]:
                    return False
            return True
        else:
            for idx in range(len(word)):
                if state[row + idx][col] is not None and state[row + idx][col] != word[idx]:
                    return False
            return True

    def place_word(state, row, col, word, horizontal=True):
        new_state = [row[:] for row in state]
        if horizontal:
            for idx in range(len(word)):
                new_state[row][col + idx] = word[idx]
        else:
            for idx in range(len(word)):
                new_state[row + idx][col] = word[idx]
        return new_state

    successors = []
    for row, col in product(range(5), range(5)):
        if state[row][col] is None:  # Only try to place a word if the cell is empty
            for word in horizontal_answers[row]:
                if is_valid(state, row, col, word, horizontal=True):
                    new_state = place_word(state, row, col, word, horizontal=True)
                    successors.append(new_state)
            for word in vertical_answers[col]:
                if is_valid(state, row, col, word, horizontal=False):
                    new_state = place_word(state, row, col, word, horizontal=False)
                    successors.append(new_state)
    
    return successors
```

AutoToS prompt:

Please provide a goal test function in Python ensuring that all cells are not None, all words horizontally are matching at least one of the horizontal answers, and all words vertically match at least one of the vertical answers. The function should receive a state, horizontal_answers, and vertical_answers as before and return True for a goal state and False otherwise.

Model response:
```python
def is_goal_state(state, horizontal_answers, vertical_answers):
    def word_in_list(word, word_list):
        return word in word_list

    def check_horizontal(state, row):
        word = ''.join(state[row])
        return any(word_in_list(word, answers) for answers in horizontal_answers[row])

    def check_vertical(state, col):
        word = ''.join(state[row][col] for row in range(5))
        return any(word_in_list(word, answers) for answers in vertical_answers[col])

    # Check if all cells are not None
    for row in state:
        if any(cell is None for cell in row):
            return False

    # Check horizontal words
    for row in range(5):
        if not check_horizontal(state, row):
            return False

    # Check vertical words
    for col in range(5):
        if not check_vertical(state, col):
            return False

    return True
```

System message:
Goal Soundness Test Passed
Soundness test
Successor Iteration 1

AutoToS prompt:
The following exception was produced when testing the successor function: 
  File "<string>", line 7, in is_valid

list index out of range. Please fix this exception in the successor function.
Model response:
```python
def successor_state(state, horizontal_answers, vertical_answers):
    from itertools import product

    def is_valid(state, row, col, word, horizontal=True):
        if horizontal:
            if col + len(word) > 5:  # Check if the word can fit horizontally
                return False
            for idx in range(len(word)):
                if state[row][col + idx] is not None and state[row][col + idx] != word[idx]:
                    return False
            return True
        else:
            if row + len(word) > 5:  # Check if the word can fit vertically
                return False
            for idx in range(len(word)):
                if state[row + idx][col] is not None and state[row + idx][col] != word[idx]:
                    return False
            return True

    def place_word(state, row, col, word, horizontal=True):
        new_state = [row[:] for row in state]
        if horizontal:
            for idx in range(len(word)):
                new_state[row][col + idx] = word[idx]
        else:
            for idx in range(len(word)):
                new_state[row + idx][col] = word[idx]
        return new_state

    successors = []
    for row, col in product(range(5), range(5)):
        if state[row][col] is None:  # Only try to place a word if the cell is empty
            for word in horizontal_answers[row]:  # Try to place horizontal words
                if is_valid(state, row, col, word, horizontal=True):
                    new_state = place_word(state, row, col, word, horizontal=True)
                    successors.append(new_state)
            for word in vertical_answers[col]:  # Try to place vertical words
                if is_valid(state, row, col, word, horizontal=False):
                    new_state = place_word(state, row, col, word, horizontal=False)
                    successors.append(new_state)

    return successors
```

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Evaluating the final outcome
Success: 20, failure: 0, total expansions 4514757, total generated 16830232
