Grammar2Regex

Grammar2Regex converts context-free grammars to regular expressions. Left- and right-linear grammars are always converted precisely. Furthermore, some grammars with a regular language but a more general shape can also be converted. For example, a rule <N> ::= a<A><N> is not right-linear due to the occurrence of <A>; but if <A> does not reach <N> and everything else is regular, we obtain a precise regular expression by computing the regular expression for <A> and inserting it into the rule for <N>.

For grammars with a non-regular language or a suboptimal shape, we "unwind" problematic expansion elements. This step loses information, but enables us to compute under-approximating regular expressions for arbitrary context-free grammars. Grammar2Regex returns expressions either in a custom ADT format suitable for further processing or as ReRef objects of the z3 SMT solver.

Example

Consider the following grammar of XML attribute or tag name identifiers:

import string
from typing import Dict, List
from fuzzingbook.Grammars import srange

xml_id_grammar: Dict[str, List[str]] = {
    "<start>": ["<id>"],
    "<id>": [
        "<id-no-prefix>",
        "<id-with-prefix>"
    ],
    "<id-no-prefix>": [
        "<id-start-char>",
        "<id-start-char><id-chars>",
    ],
    "<id-with-prefix>": ["<id-no-prefix>:<id-no-prefix>"],
    "<id-start-char>": srange("_" + string.ascii_letters),
    "<id-chars>": ["<id-char>", "<id-char><id-chars>"],
    "<id-char>": ["<id-start-char>"] + srange("-." + string.digits),
}

Our chosen grammar format is the one from the Fuzzing Book.

This grammar can be precisely converted into a regular expression:

from grammar_to_regex.cfg2regex import RegexConverter

converter = RegexConverter(xml_id_grammar, compress_unions=True)
print(converter.to_regex('<start>', convert_to_z3=False))

which yields an object of type grammar_to_regex.regex.Regex, in pretty print:

((["-" .. "."] | ["0" .. "9"] | ["A" .. "Z"] | "_" | ["a" .. "z"])* • (["-" .. "."] | ["0" .. "9"] | ["A" .. "Z"] | "_" | ["a" .. "z"]))

You can also obtain an output in the regular expression format of the z3 SMT solver if you need this for further processing (simply omit the convert_to_z3=False or set that parameter to True).

Installation

Grammar2Regex requires Python 3.10.

To install Grammar2Regex, run

pip install grammar_to_regex

To install it locally for testing, check this repository out and run

pip install -e .[test]

License and Maintainer

This project is licensed under the GNU GENERAL PUBLIC LICENSE v3. It is maintained by Dominic Steinhöfel.