Related papers: Parsing Linear Context-Free Rewriting Systems with…
We study grammar induction with mildly context-sensitive grammars for unsupervised discontinuous parsing. Using the probabilistic linear context-free rewriting system (LCFRS) formalism, our approach fixes the rule structure in advance and…
In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing context-free grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser…
Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time $O(|G||w|^{3 - \myeps})$ on a grammar $G$ and a string $w$ can be used to multiply $m \times m$ Boolean…
Tree-adjoining grammars are a generalization of context-free grammars that are well suited to model human languages and are thus popular in computational linguistics. In the tree-adjoining grammar recognition problem, given a grammar…
Transformers excel empirically on tasks that process well-formed inputs according to some grammar, such as natural language and code. However, it remains unclear how they can process grammatical syntax. In fact, under standard complexity…
We consider the problem of computing the rank of an m x n matrix A over a field. We present a randomized algorithm to find a set of r = rank(A) linearly independent columns in \~O(|A| + r^\omega) field operations, where |A| denotes the…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be reordered. We present a new polynomial time algorithm to…
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…
Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…
We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) $x_1...x_n$ is the sum of terms over intervals $[i,j]$ where each term is non-zero only if the…
We study fundamental problems in linear algebra, such as finding a maximal linearly independent subset of rows or columns (a basis), solving linear regression, or computing a subspace embedding. For these problems, we consider input…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph problems. For general m-edge and n-vertex graphs, it is well-known to be solvable in $O(m \sqrt{n})$ time. We develop a linear-time…
Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these…
In this paper we provide an $\tilde{O}(nd+d^{3})$ time randomized algorithm for solving linear programs with $d$ variables and $n$ constraints with high probability. To obtain this result we provide a robust, primal-dual…
In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this…
This paper shows how to solve linear programs of the form $\min_{Ax=b,x\geq0} c^\top x$ with $n$ variables in time $$O^*((n^{\omega}+n^{2.5-\alpha/2}+n^{2+1/6}) \log(n/\delta))$$ where $\omega$ is the exponent of matrix multiplication,…
We study matrix multiplication in the low-bandwidth model: There are $n$ computers, and we need to compute the product of two $n \times n$ matrices. Initially computer $i$ knows row $i$ of each input matrix. In one communication round each…