Related papers: Counting and Sampling Traces in Regular Languages
We describe an approach to robust domain-independent syntactic parsing of unrestricted naturally-occurring (English) input. The technique involves parsing sequences of part-of-speech and punctuation labels using a unification-based grammar…
The identification of syllables within phonetic sequences is known as syllabification. This task is thought to play an important role in natural language understanding, speech production, and the development of speech recognition systems.…
We aim at enforcing hard constraints to impose a global structure on sequences generated from Markov models. In this report, we study the complexity of sampling Markov sequences under two classes of constraints: Binary Equalities and…
We give a Markov chain based perfect sampler for uniform sampling solutions of constraint satisfaction problems (CSP). Under some mild Lov\'asz local lemma conditions where each constraint of the CSP has a small number of forbidden local…
The approximate uniform sampling of graphs with a given degree sequence is a well-known, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we…
We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…
The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
Automatic segmentation of text into minimal content-bearing units is an unsolved problem even for languages like English. Spaces between words offer an easy first approximation, but this approximation is not good enough for machine…
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…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
Co-lex partial orders were recently introduced in (Cotumaccio et al., SODA 2021 and JACM 2023) as a powerful tool to index finite state automata, with applications to regular expression matching. They generalize Wheeler orders (Gagie et…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
In the Intersection Non-Emptiness problem, we are given a list of finite automata $A_1,A_2,\dots,A_m$ over a common alphabet $\Sigma$ as input, and the goal is to determine whether some string $w\in \Sigma^*$ lies in the intersection of the…
Sampling from multivariate normal distributions, subjected to a variety of restrictions, is a problem that is recurrent in statistics and computing. In the present work, we demonstrate a general framework to efficiently sample a…
We generalise a multiple string pattern matching algorithm, recently proposed by Fredriksson and Grabowski [J. Discr. Alg. 7, 2009], to deal with arbitrary dictionaries on an alphabet of size $s$. If $r_m$ is the number of words of length…
Piecewise testable languages are a subclass of the regular languages. There are many equivalent ways of defining them; Simon's congruence $\sim_k$ is one of the most classical approaches. Two words are $\sim_k$-equivalent if they have the…
Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to…