Related papers: Testing Simon's congruence
Machine-translated text plays an important role in modern life by smoothing communication from various communities using different languages. However, unnatural translation may lead to misunderstanding, a detector is thus needed to avoid…
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
Compounding is a highly productive word-formation process in some languages that is often problematic for natural language processing applications. In this paper, we investigate whether distributional semantics in the form of word…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
A classical result (often credited to Y. Medvedev) states that every language recognized by a finite automaton is the homomorphic image of a local language, over a much larger so-called local alphabet, namely the alphabet of the edges of…
A word $w$ over an alphabet $\Sigma$ is a Lyndon word if there exists an order defined on $\Sigma$ for which $w$ is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \emph{universal Lyndon…
Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
We study testing of local properties in one-dimensional and multi-dimensional arrays. A property of $d$-dimensional arrays $f:[n]^d \to \Sigma$ is $k$-local if it can be defined by a family of $k \times \ldots \times k$ forbidden…
In this paper we investigate local to global phenomena for a new family of complexity functions of infinite words indexed by $k \in \Ni \cup \{+\infty\}$ where $\Ni$ denotes the set of positive integers. Two finite words $u$ and $v$ in…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…
Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
We implement a set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold locally testable, strictly locally testable,…
The equivalence problem for unambiguous grammars is an important, but very difficult open question in formal language theory. Consider the \emph{limited} equivalence problem for unambiguous grammars -- for two unambiguous grammars $G_1$ and…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
The fundamental problem of similarity studies, in the frame of data-mining, is to examine and detect similar items in articles, papers, books, with huge sizes. In this paper, we are interested in the probabilistic, and the statistical and…