This paper gives the first complete proof of correctness of the Micali-Vazirani [MV80] general graph maximum cardinality matching algorithm. Our emphasis is on arriving at the simplest possible proof; graph-theoretic machinery developed for this purpose also helps simplify the description of this algorithm. For all practical purposes, this is still the most efficient known algorithm for the pro...

A key problem in automating proof by mathematical induction is choosing an induction rule suitable for a given conjecture. Since Boyer & Moore’s NQTHM system the standard approach has been based on recursion analysis, which uses a combination of induction rules based on the relevant recursive function definitions. However, there are practical examples on which such techniques are known to fail....

Quantum key distribution promises unconditionally secure communications. However, as practical devices tend to deviate from their specifications, the security of some practical systems is no longer valid. In particular, an adversary can exploit imperfect detectors to learn a large part of the secret key, even though the security proof claims otherwise. Recently, a practical approach--measuremen...

A multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants. in such a way a multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets. Up to now, existing MSSs either require too long shares for participants to be perfect secur...

Undeniable signature schemes are not publicly verifiable. Therefore, in order to prove the validity/invalidity of a message-signature pair, the signer needs to provide a proof for the rightful verifier. Since the introduction of undeniable signature schemes, various proof systems with different properties and features have been introduced to be incorporated in the structure of such schemes. Amo...

although mohaghegh khorasani has raised the impossibility of replacement of certitude as to subject by authorized conjectural proof (amara) due to the impediment of conjunction in consideration; sheikh ansari, while rejecting the replacement of certitude as to attribute, has accepted the replacement of declaratory certitude. some islamic scholars believe in classification, according to the basi...

The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas there may be a need to extend the set of operators and proof rules supported by the tool. This paper outlines a new feature of the Rodin tool, the ...