On Deciding Whether a Boolean Function is Constant or Not

Boolean function is constant or not ∗

We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.

On deciding whether a surface is parabolic or hyperbolic

In our book [3], Laurie Snell and I tell how a method from the classical theory of electricity called Rayleigh’s short-cut method can be used to determine whether or not a person walking around at random on the vertices of a given infinite graph is certain to return to the starting point. In this paper, I will present an application of Rayleigh’s method to the classical type problem for Riemann...

Deciding whether the ordering is necessary in a Presburger formula

Whether post-ureteroscopy stenting is necessary or not?

OBJECTIVE To verify if post-ureteroscopy (URS) stenting is still necessary as a routine strategy, or if some cases can be treated without. METHODS Between August 2004 and April 2005, 85 patients were admitted to the Urology Department at the Nephrology and Urology Center, Al-Thawra Hospital, Yemen with ureteric stones of different size and site. All were scheduled and treated by the ureterosc...

Is it possible to decide whether a cryptographic protocol is secure or not ?

We consider the so called “cryptographic protocols” whose aim is to ensure some security properties when communication channels are not reliable. Such protocols usually rely on cryptographic primitives. Even if it is assumed that the cryptographic primitives are perfect, the security goals may not be achieved: the protocol itself may have weaknesses which can be exploited by an attacker. We sur...