proof_systems.py

# proof_systems.py

class PropositionalProofSystem:
    """
    A class representing a generic propositional proof system.
    Includes methods to check proof validity, estimate proof size, and
    explore the relationship between proof length and complexity.
    """
    def __init__(self, proof_structure):
        self.proof_structure = proof_structure
    
    def is_valid_proof(self, formula):
        """
        Verifies whether the given proof proves the formula.

        Parameters:
        formula (str): A propositional formula in CNF.

        Returns:
        bool: True if the proof is valid, False otherwise.
        """
        # Placeholder logic
        return "PROOF_OF(" + formula + ")" in self.proof_structure
    
    def proof_size(self):
        """
        Calculates the size of the proof in some normalized units.

        Returns:
        int: The size of the proof.
        """
        return len(self.proof_structure)
    
    def check_efficiency(self):
        """
        Determines if the proof is considered efficient by comparing its size
        against known lower bounds for propositional tautologies.

        Returns:
        bool: True if the proof is efficient, False otherwise.
        """
        # For demonstration purposes, assume 1000 is the threshold
        return self.proof_size() < 1000