相关论文: Combinatorics on words in information security: Un…

We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way…

In rapid and massive data streams, it is often not possible to estimate the frequency of items with complete accuracy. To perform the operation in a reasonable amount of space and with sufficiently low latency, approximated methods are…

Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…

The braid group has recently attracted much attention. This is primarily based upon the discovery of its usage in various cryptosystems [AAG],[KLCHKP]. One major focus of current research has been in solving decision problems in braid…

Discovering a solution in a combinatorial space is prevalent in many real-world problems but it is also challenging due to diverse complex constraints and the vast number of possible combinations. To address such a problem, we introduce a…

A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…

We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…

Jailbreaking attacks on large language models pose a significant threat to AI safety by enabling the generation of harmful or restricted content. While prior work has explored both handcrafted and automated jailbreak strategies, the…

Cybersecurity has been a concern for quite a while now. In the latest years, cyberattacks have been increasing in size and complexity, fueled by significant advances in technology. Nowadays, there is an unavoidable necessity of protecting…

We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog…

Artificial intelligence (AI) systems, and Large Language Models (LLMs) in particular, are increasingly employed for creative tasks like scientific idea generation, constituting a form of generalization from training data unaddressed by…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…

A great variety of static analyses that compute safety properties of single-thread programs have now been developed. This paper presents a systematic method to extend a class of such static analyses, so that they handle programs with…

We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…

Combinatorial generalization - the ability to understand and produce novel combinations of already familiar elements - is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body…

While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, where the functions map between binary strings of fixed finite…

We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…

Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in…

Regular expressions are a concise yet expressive language for expressing patterns. For instance, in networked software, they are used for input validation and intrusion detection. Yet some widely deployed regular expression matchers based…

Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…