Related papers: Lower Bounds on the Algebraic Immunity of Boolean …
Algebraic Manipulation Detection (AMD) codes is a cryptographic primitive that was introduced by Cramer, Dodis, Fehr, Padro and Wichs. They are keyless message authentication codes that protect messages against additive tampering by the…
The Unitary Synthesis Problem (Aaronson-Kuperberg 2007) asks whether any $n$-qubit unitary $U$ can be implemented by an efficient quantum algorithm $A$ augmented with an oracle that computes an arbitrary Boolean function $f$. In other…
Suppose $X$ is a uniformly distributed $n$-dimensional binary vector and $Y$ is obtained by passing $X$ through a binary symmetric channel with crossover probability $\alpha$. A recent conjecture by Courtade and Kumar postulates that…
Finding Boolean functions suitable for cryptographic primitives is a complex combinatorial optimization problem, since they must satisfy several properties to resist cryptanalytic attacks, and the space is very large, which grows super…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
This manuscript establishes information-theoretic limitations for robustness of AI security and alignment by extending G\"odel's incompleteness theorem to AI. Knowing these limitations and preparing for the challenges they bring is…
We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…
Large language models (LLMs) are widely used for task understanding and action planning in embodied intelligence (EI) systems, but their adoption substantially increases vulnerability to jailbreak attacks. While recent work explores…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
We study the relation among some security parameters for vectorial Boolean functions which prevent attacks on the related block cipher. We focus our study on a recently-introduced security criterion, called weak differential uniformity,…
Adversarial Imitation Learning (AIL) faces challenges with sample inefficiency because of its reliance on sufficient on-policy data to evaluate the performance of the current policy during reward function updates. In this work, we study the…
Artificial immune systems primarily mimic the adaptive nature of biological immune functions. Their ability to adapt to varying pathogens makes such systems a suitable choice for various robotic applications. Generally, AIS-based robotic…
In this paper, we present a new axiomatic system that is a minimal axiomatization of Boolean algebras. Furthermore, the symmetric difference is shown to be algebraically analogous to the modular difference of two numbers. Finally, a new…
The increased adoption of Artificial Intelligence (AI) presents an opportunity to solve many socio-economic and environmental challenges; however, this cannot happen without securing AI-enabled technologies. In recent years, most AI models…
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…
For over a decade, cybersecurity has relied on human labor scarcity to limit attackers to high-value targets manually or generic automated attacks at scale. Building sophisticated exploits requires deep expertise and manual effort, leading…
We develop a theory of boundary functions for ideals in trivially analytic subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which includes all full nest algebras. Boundary functions are maps from the spectrum of the…
This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…
Let $\mathcal{F}_{n}^*$ be the set of Boolean functions depending on all $n$ variables. We prove that for any $f\in \mathcal{F}_{n}^*$, $f|_{x_i=0}$ or $f|_{x_i=1}$ depends on the remaining $n-1$ variables, for some variable $x_i$. This…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…