Related papers: Combinatorics on words in information security: Un…
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
This paper describes an enumeration of all words having a combinatoric property called "rhythmic oddity property"named \emph{rop-words}.\ This property was introduced by Simha Aron in the 1990s. The set of rop-words is not a subset of the…
In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete…
After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of…
Combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits. Intriguingly, this seems to be an ongoing…
As the prevalence and everyday use of machine learning algorithms, along with our reliance on these algorithms grow dramatically, so do the efforts to attack and undermine these algorithms with malicious intent, resulting in a growing…
We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a…
Modern authentication systems store hashed values of passwords of users using cryptographic hash functions. Therefore, to crack a password an attacker needs to guess a hash function input that is mapped to the hashed value, as opposed to…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent"…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
Large bilingual parallel texts (also known as bitexts) are usually stored in a compressed form, and previous work has shown that they can be more efficiently compressed if the fact that the two texts are mutual translations is exploited.…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
$B$-terms are built from the $B$ combinator alone defined by $B\equiv\lambda fgx. f(g~x)$, which is well known as a function composition operator. This paper investigates an interesting property of $B$-terms, that is, whether repetitive…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…