Classifying formal languages according to the expressiveness of grammars able to generate them is a fundamental problem in computational linguistics and, therefore, in the theory of computation. Furthermore, such kind of analysis can give insight into the classification of abstract algebraic structure such as groups, for example through the correspondence given by the word problem. While many such classification problems remain open, others have been settled. Recently, it was proved that $n$-balanced languages (i.e., whose strings contain the same occurrences of letters $a_i$ and $A_i$ with $1\leq i \leq n$) can be generated by multiple context-free grammars (MCFGs), which are one of the several slight extensions of context free grammars added to the classical Chomsky hierarchy to make the mentioned classification more precise. This paper analyses the existing proofs from the computational and the proof-theoretical point of views, systematically studying whether each proof can lead to a verified (i.e., checked by a proof assistant) algorithm parsing balanced languages via MCFGs. We conclude that none of the existing proofs is realistically suitable against this practical goal, and proceed to provide a radically new, elementary, extremely short proof for the crucial case $n \leq 2$. A comparative analysis with respect to the existing proofs is finally performed to justify why the proposed proof is a substantial step towards concretely obtaining a verified parsing algorithm for $O_2$.

On hearing the term "password-cracking," many will think this post will be about how to guess someone's password or somewhat similar, but the reality is not always so satisfying. In general, whenever anybody types a password on any device or software, passwords don't get stored in the raw format in the database. Instead, raw passwords are first passed through the hashing algorithm, which converts the raw passwords into some particular sequence of letters, numbers, and special characters which looks entirely random for an ordinary being. Now there are several password database leaks and breaches all over the world. One such dataset is Rockyou Dataset, which contains about 31 million passwords; this is a widely used dataset because this dataset contains passwords in plain text format without any hashing.

On hearing the term "password-cracking," many will think this post will be about how to guess someone's password or somewhat similar, but the reality is not always so satisfying. In general, whenever anybody types a password on any device or software, passwords don't get stored in the raw format in the database. Instead, raw passwords are first passed through the hashing algorithm, which converts the raw passwords into some particular sequence of letters, numbers, and special characters which looks entirely random for an ordinary being. Now there are several password database leaks and breaches all over the world. One such dataset is Rockyou Dataset, which contains about 31 million passwords; this is a widely used dataset because this dataset contains passwords in plain text format without any hashing.