Related papers: The multiplicative complexity of interval checking
When the search algorithm QuickSelect compares keys during its execution in order to find a key of target rank, it must operate on the keys' representations or internal structures, which were ignored by the previous studies that quantified…
The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance $h$ between two strings of length $n$ is greater than $a$ or less than $b$, where the gap $g=|a-b|\geq 1$ and $a$ and $b$ could depend on $n$. In…
We introduce the interaction cost of a non-local gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and…
We consider the problem of a decision-maker searching for information on multiple alternatives when information is learned on all alternatives simultaneously. The decision-maker has a running cost of searching for information, and has to…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
Test-time compute scaling, the practice of spending extra computation during inference via repeated sampling, search, or extended reasoning, has become a powerful lever for improving large language model performance. Yet deploying these…
Practitioners often navigate LLM performance trade-offs by plotting Pareto frontiers of optimal accuracy-cost trade-offs. However, this approach offers no way to compare between LLMs with distinct strengths and weaknesses: for example, a…
In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both…
We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…
Alice and Bob are given $n$-bit integer pairs $(x,y)$ and $(a,b)$, respectively, and they must decide if $y=ax+b$. We prove that the randomised communication complexity of this Point--Line Incidence problem is $\Theta(\log n)$. This…
In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the…
Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution…
In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…
The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
We analyze the caching overhead incurred by a class of multithreaded algorithms when scheduled by an arbitrary scheduler. We obtain bounds that match or improve upon the well-known $O(Q+S \cdot (M/B))$ caching cost for the randomized work…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
Reachability and LTL model-checking problems for flat counter systems are known to be decidable but whereas the reachability problem can be shown in NP, the best known complexity upper bound for the latter problem is made of a tower of…
A Metric Interval Temporal Logic (MITL) verification algorithm is presented. It verifies continuous-time signals without relying on high frequency sampling. Instead, it is assumed that collections of over- and under-approximating intervals…
We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound…