Related papers: The complexity of normal form rewrite sequences fo…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n,…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings…
The normalized substring complexity $\delta$ of a string is defined as $\max_k \{c[k]/k\}$, where $c[k]$ is the number of \textit{distinct} substrings of length $k$. This simply defined measure has recently attracted attention due to its…
We propose to classify the power of algorithms by the complexity of the problems that they can be used to solve. Instead of restricting to the problem a particular algorithm was designed to solve explicitly, however, we include problems…
We investigate the variance of the length of the longest common subsequences of two independent random words of size $n$, where the letters of one word are i.i.d. uniformly drawn from $\{\alpha_1, \alpha_2, \cdots, \alpha_m\}$, while the…
Adaptations of features commonly applied in the field of visual computing, co-occurrence matrix (COM) and run-length matrix (RLM), are proposed for the similarity computation of strings in general (words, phrases, codes and texts). The…
Nfer is a rule-based language for abstracting event streams into a hierarchy of intervals with data. Nfer has multiple implementations and has been applied in the analysis of spacecraft telemetry and autonomous vehicle logs. This work…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
Previous research on relation classification has verified the effectiveness of using dependency shortest paths or subtrees. In this paper, we further explore how to make full use of the combination of these dependency information. We first…
The $K$-length of a form $f$ in $K[x_1,\dots,x_n]$, $K \subset \cc$, is the smallest number of $d$-th powers of linear forms of which $f$ is a $K$-linear combination. We present many results, old and new, about $K$-length, mainly in $n=2$,…
We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1) \leq \Delta C(n) + 2, for all n \in N. For a large class of words it is a better estimate…
Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…
We present a study of morphological irregularity. Following recent work, we define an information-theoretic measure of irregularity based on the predictability of forms in a language. Using a neural transduction model, we estimate this…
Learning to remember long sequences remains a challenging task for recurrent neural networks. Register memory and attention mechanisms were both proposed to resolve the issue with either high computational cost to retain memory…
It is known that the first-order theory of rewriting is decidable for ground term rewrite systems, but the general technique uses tree automata and often takes exponential time. For many properties, including confluence (CR), uniqueness of…
The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary,…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
Sentence simplification is the task of rewriting texts so they are easier to understand. Recent research has applied sequence-to-sequence (Seq2Seq) models to this task, focusing largely on training-time improvements via reinforcement…