Functional Dependency Analysis Tool

This Python script is a tool for analyzing functional dependencies in a relational database. It provides various functions to check for properties like closure, candidate keys, canonical covers, and normalization levels (2NF, 3NF, BCNF). Additionally, it can determine if a given decomposition of relations is lossless and dependency-preserving.

How to Use

1. Ensure you have Python installed on your system.

2. Copy and paste the provided code into a Python (.py) file.

3. Import the required modules and use the provided functions as needed in your Python script.

Example Usage

# Example usage:
fds = [  # Replace with your functional dependencies
    ('ABC', 'D'), 
    ('AB', 'CEA'), 
    ('A', 'EF'), 
    ('GH', 'I'), 
    ('G', 'HJ'), 
    ('ABC', 'GHE'), 
    ('KL', 'M'), 
    ('K', 'L'), 
    ('ABN', 'OPQ'), 
    ('Q', 'N'), 
    ('AE', 'K')
]
decomposition = ['ABCDG', 'GHJI', 'AEFK', 'KLM', 'ABNOPQ']  # Initial decomposition
print('Input:')
print(fds)

print_closure_list(fds, onlyCandidateKeys=True)
is_dependency_preserved(fds, decomposition, printDiff=True)
is_decomposition_lossless(fds, decomposition, printJoinOrder=True)
is_decomposition_2NF(fds, decomposition)
is_decomposition_3NF(fds, decomposition)
is_decomposition_BCNF(fds, decomposition)
all_canonical_cover(fds)

Functions that are intended for use

Here is a brief description of the functions provided in the script:

1. print_closure_list(fds, onlyCandidateKeys=False): Prints the closure of attributes based on the given functional dependencies.

2. is_dependency_preserved(fds, relation_list, printDiff=False): Checks if a given decomposition of relations preserves all functional dependencies.

3. is_decomposition_lossless(fds, relation_list, printJoinOrder=False): Checks if a given decomposition of relations is lossless.

4. is_decomposition_2NF(fds, decomposition, doPrint=True): Checks if a given decomposition is in 2NF.

5. is_decomposition_3NF(fds, decomposition, doPrint=True): Checks if a given decomposition is in 3NF.

6. is_decomposition_BCNF(fds, decomposition, doPrint=True): Checks if a given decomposition is in BCNF.

7. all_canonical_cover(fds): Finds all possible canonical covers for a set of functional dependencies.

Other functions

Here is a brief description of the functions provided in the script:

• check_strings(list_of_strings, given_string): Checks if all characters in at least one string exist in the given string.

• fds_to_items(data): Converts a set of functional dependencies to a string of all the attributes in the dependencies.

• get_closure(attributes, fds): Computes the closure of a set of attributes under a set of functional dependencies.

• candidate_key_list(fds): Finds all candidate keys in a set of functional dependencies.

• isSetClosureEqual(fds1, fds2): Checks if the closures of two sets of functional dependencies are equal.

• find_canonical_cover(fds): Finds the canonical cover of a set of functional dependencies.

• clean_fds(data): Cleans up a set of functional dependencies by removing redundant dependencies.

• call_canonical_cover(fds): Calls find_canonical_cover until no further changes are made to obtain the canonical cover.

• subrelation_fds(fds, relation_list): Decomposes a set of functional dependencies based on a list of relations.

• is_pair_lossless(fds, R1, R2): Checks if two relations can be joined losslessly.

• is_lossless(fds, notJoinedRelations, joinedAttributes, joinOrder): Checks if a set of relations can be joined losslessly.

• prime_attributes(fds): Finds all prime attributes in a set of functional dependencies.

Disclaimer

This script is a tool for educational and analytical purposes. It may not cover all edge cases, and you should thoroughly test it with your own datasets before relying on it for critical tasks.