Painolliset äärellistilaiset menetelmät oikaisulukuun

This dissertation is a large-scale study of spell-checking and correction using finite-state technology. Finite-state spell-checking is a key method for handling morphologically complex languages in a computationally efficient manner. This dissertation discusses the technological and practical considerations that are required for finite-state spell-checkers to be at the same level as state-of-the-art non-finite-state spell-checkers. Three aspects of spell-checking are considered in the thesis: modelling of correctly written words and word-forms with finite-state language models, applying statistical information to finite-state language models with a specific focus on morphologically complex languages, and modelling misspellings and typing errors using finite-state automata-based error models. The usability of finite-state spell-checkers as a viable alternative to traditional non-finite-state solutions is demonstrated in a large-scale evaluation of spell-checking speed and the quality using languages with morphologically different natures. The selected languages display a full range of typological complexity, from isolating English to polysynthetic Greenlandic with agglutinative Finnish and the Saami languages somewhere in between.Tässä väitöskirjassa tutkin äärellistilaisten menetelmien käyttöä oikaisuluvussa. Äärellistilaiset menetelmät mahdollistavat sananmuodostukseltaan monimutkaisempien kielten, kuten suomen tai grönlannin, sanaston sujuvan käsittelyn oikaisulukusovelluksissa. Käsittelen tutkielmassani tieteellisiä ja käytännöllisiä toteutuksia, jotka ovat tarpeen, jotta tällaisia sananmuodostukseltaan monimutkallisempia kieliä voisi käsitellä oikaisuluvussa yhtä tehokkaasti kuin yksinkertaisempia kieliä, kuten englantia tai muita indo-eurooppalaisia kieliä nyt käsitellään. Tutkielmassa esitellään kolme keskeistä tutkimusongelmaa, jotka koskevat oikaisuluvun toteuttamista sanarakenteeltaan monimutkaisemmille kielille: miten mallintaa oikeinkirjoitetut sanamuodot äärellistilaisin mallein, miten soveltaa tilastollista mallinnusta monimutkaisiin sanarakenteisiin kuten yhdyssanoihin, ja miten mallintaa kirjoitusvirheitä äärellistilaisin mentelmin. Tutkielman tuloksena esitän äärellistilaisia oikaisulukumenetelmiä soveltuvana vaihtoehtona nykyisille oikaisulukimille, tämän todisteena esitän mittaustuloksia, jotka näyttävät, että käyttämäni menetelmät toimivat niin rakenteellisesti yksinkertaisille kielille kuten englannille yhtä hyvin kuin nykyiset menetelmät että rakenteellisesti monimutkaisemmille kielille kuten suomelle, saamelle ja jopa grönlannille riittävän hyvin tullakseen käytetyksi tyypillisissä oikaisulukimissa

From Specific to Generic Learned Sorted Set Dictionaries: A Theoretically Sound Paradigm Yelding Competitive Data Structural Boosters in Practice

This research concerns Learned Data Structures, a recent area that has emerged at the crossroad of Machine Learning and Classic Data Structures. It is methodologically important and with a high practical impact. We focus on Learned Indexes, i.e., Learned Sorted Set Dictionaries. The proposals available so far are specific in the sense that they can boost, indeed impressively, the time performance of Table Search Procedures with a sorted layout only, e.g., Binary Search. We propose a novel paradigm that, complementing known specialized ones, can produce Learned versions of any Sorted Set Dictionary, for instance, Balanced Binary Search Trees or Binary Search on layouts other that sorted, i.e., Eytzinger. Theoretically, based on it, we obtain several results of interest, such as (a) the first Learned Optimum Binary Search Forest, with mean access time bounded by the Entropy of the probability distribution of the accesses to the Dictionary; (b) the first Learned Sorted Set Dictionary that, in the Dynamic Case and in an amortized analysis setting, matches the same time bounds known for Classic Dictionaries. This latter under widely accepted assumptions regarding the size of the Universe. The experimental part, somewhat complex in terms of software development, clearly indicates the nonobvious finding that the generalization we propose can yield effective and competitive Learned Data Structural Booster, even with respect to specific benchmark models

Efficient Pattern Matching in Python

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules. We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems

Online Sorting via Searching and Selection

In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As a side-effect of answering these online selection and search queries, we progressively sort the list. Our algorithms are based on Hoare's Quickselect, and are parameterized based on the pivot selection method. For example, if we choose the pivot as the last item in a subinterval, our framework yields algorithms that will answer q<=n unique selection and/or search queries in a total of O(n log q) average time. After q=\Omega(n) queries the list is sorted. Each repeated selection query takes constant time, and each repeated search query takes O(log n) time. The two query types can be interleaved freely. By plugging different pivot selection methods into our framework, these results can, for example, become randomized expected time or deterministic worst-case time. Our methods are easy to implement, and we show they perform well in practice

Forgotten Islands of Regularity in Phonology

Open access publication of this volume supported by National Research, Development and Innovation Office grant NKFIH #120145 `Deep Learning of Morphological Structure'.Giving birth to Finite State Phonology is classically attributed to Johnson (1972), and Kaplan and Kay (1994). However, there is an ear- lier discovery that was very close to this achievement. In 1965, Hennie presented a very general sufficient condition for regularity of Turing machines. Although this discovery happened chronologically before Generative Phonology (Chomsky and Halle, 1968), it is a mystery why its relevance has not been realized until recently (Yli-Jyrä, 2017). The antique work of Hennie provides enough generality to advance even today’s frontier of finite-state phonology. First, it lets us construct a finite-state transducer from any grammar implemented by a tightly bounded one- tape Turing machine. If the machine runs in o(n log n), the construction is possible, and this case is reasonably decidable. Second, it can be used to model the regularity in context-sensitive derivations. For example, the suffixation in hunspell dictionaries (Németh et al., 2004) corresponds to time-bounded two-way computations performed by a Hennie machine. Thirdly, it challenges us to look for new forgotten islands of regularity where Hennie’s condition does not necessarily hold.Hennie presented a very general sufficient condition for regularity of Turing machines. This happened chronologically before Generative Phonology (Chomsky & Halle 1968) and the related finite-state research (Johnson 1972; Kaplan & Kay 1994). Hennie’s condition lets us (1) construct a finite-state transducer from any grammar implemented by a linear-time Turing machine, and (2) to model the regularity in context-sensitive derivations. For example, the suffixation in hunspell dictionaries (Németh et al. 2004) corresponds to time-bounded two way computations performed by a Hennie machine. Furthermore, it challenges us to look for new forgotten islands of regularity where Hennie’s condition does not necessarily hold.Peer reviewe