1 Introduction

For the past two decades, specialised events on finite-state methods have been successful in presenting interesting studies on natural language processing to the public through journals and collections. The FSMNLP workshops have become well-known among researchers and are now the main forum of the Association for Computational Linguistics' (ACL) Special Interest Group on Finite-State Methods (SIGFSM). The current issue on finite-state methods and models in natural language processing was planned in 2008 in this context as a response to a call for special issue proposals. In 2010, the issue received a total of sixteen submissions, some of which were extended and updated versions of workshop papers, and others which were completely new. The final selection, consisting of only seven papers that could fit into one issue, is not fully representative, but complements the prior special issues in a nice way. The selected papers showcase a few areas where finite-state methods have less than obvious and sometimes even groundbreaking relevance to natural language processing (NLP) applications.

These methods have grown around Kleene's classical result that relates languages defined by regular expressions to languages defined by finite automata (Kleene Reference Kleene, Shannon and McCarthy1956). Practical finite-state methods apply and extend this correspondence. The most obvious extensions beyond the ordinary finite automata include finite transducers. Weighted automata provide another natural extension that potentially brings undecidability to the picture if weights are defined carelessly. However, typical definitions for weights are quite practical in applications as witnessed by the success of weighted transducers in automatic speech recognition. It should also be kept in mind that finite tree recognisers and transducers, and the corresponding tree grammars, have many finite-state characteristics as far as their tree languages are concerned.

Finite automata are particularly applicable because of their closure properties: various interesting methods of combining finite automata are guaranteed to yield finite automata. The closure properties are employed e.g. in information retrieval where the queries can be expanded and restricted with finite transducers (Koskenniemi Reference Koskenniemi1996). Natural language question answering (QA) is a similar task (Hirschman and Gaizauskas Reference Hirschman and Gaizauskas2001). Mishra and Bangalore describe a combination of a QA system and a spoken language recognition system and demonstrate nicely the use of weighted transducers in the interface between these.

One of the recurring ways in which finite-state methods prove themselves important is that they expand the possibilities of research by contributing fundamental algorithms to digital libraries and specialised research infrastructures that contain language resources and technology, such as the CLARIN initiative in Europe (www.clarin.eu). Reffle's paper contains a finite-state algorithm that is useful when historical documents are prepared and processed for various kinds of linguistic inquiries. The work demonstrates that (1) finite-state algorithms help to improve the quality and the usability of the research material, (2) the methods used in research infrastructures need to be implemented with a lot of care and attention, and that (3) an on-demand combination of finite transducers is sometimes more efficient than an off-line compiled finite transducer.

String-based finite-state transducers are in fact quite commonly applied to basic language processing tasks such as text normalisation, morphological analysis and surface syntax. These applications were featured prominently in previous special issues of this journal (Kornai Reference Kornai1996; Karttunen, Koskenniemi and van Noord Reference Karttunen, Koskenniemi and van Noord2003), and over time we can discern some interesting trends. Most notably, new open-source software – to mention only OpenFST (www.openfst.org), SFST (www.ims.uni-stuttgart.de), Foma (foma.sourceforge.net) and HFST (hfst.sf.net) – now enable free basic language technology production for under-resourced languages using string-based methods. In this issue, Basque date expression normalisation is tackled by Díaz de Ilarraza, Gojenola, Oronoz, and Alegria whose experiments involve both proprietary and open-source finite-state tools.

At the bottom of the Chomsky hierarchy interesting subclasses of languages have been defined by considering subclasses of finite automata. The most remarkable one was characterised by Schützenberger (Reference Schützenberger1965), who established that languages denoted by star-free regular expressions are the languages defined by aperiodic (or non-counting, or counter-free) finite automata. Aperiodicity is a property exhibited (with certain reservations) in an increasing number of linguistic domains and logics (Kornai Reference Kornai1985; Yli-Jyrä Reference Yli-Jyrä2003, Reference Yli-Jyrä2005; Droste and Gastin Reference Droste and Gastin2007; Hulden Reference Hulden, Piskorski, Watson and Yli-Jyrä2009; Rogers and Pullum to appear), not to mention Linear Temporal Logic (LTL), a popular tool in software verification. Fernando's deep but exciting paper explores the conceptual issues arising when LTL and the associated model-theoretic semantics of time is adapted to natural language applications. This promises tools for entailment relations in the time domain that have applications to query expansion in QA systems.

Finite tree automata and tree grammars are a non-trivial extension of conventional finite-state methods. A good introduction to these models is in the TATA book (Comon et al. Reference Comon, Dauchet, Gilleron, Löding, Jacquemard, Lugiez, Tison and Tommasi2007). Regular tree grammars generalise over context-free grammars by separating the control of derivation from the labeling of the derived trees. Such separate control is employed e.g. in constraints that may be added to context-free grammars (Joshi and Levy Reference Joshi and Levy1982). Thanks to the added control mechanism of the extensions, a finite set of labelled trees can be regular (or recognisable) even if the set is not generated by any context-free grammar: the non-locality in the set is captured by state distinctions in a tree recogniser. Högberg's paper gives an efficient algorithm for relaxing state distinctions in a way that is consistent with given positive and negative data. The algorithm could be applied e.g. to supervised learning from a treebank containing trees exhibiting wrong generalisations in addition to the usual trees that constitute the gold standard.

The interface between syntax and semantics is a key area where the linear structure of strings does not necessarily adhere to the argument structure and some sort of indication of the argument structure needs be assumed. Tree Adjoing Grammar (TAG), especially with feature structures, is reasonably good at capturing the syntax–semantics interface by the tree structures they assign to strings. Gardent, Gottesman and Perez-Beltrachini utilise the well-known relationship between the derivation trees of tree adjoining grammars and derived trees of regular tree grammars. The paper's experiments on natural language generation demonstrate nicely that regular tree grammars may be more efficient in practice, although they preserve the essential interface between syntax and semantics. The impact of such critical evaluation of methodologies can extend to various NLP tasks such as machine translation.

Finite-state methods have already had a significant impact on various approaches to statistical machine translation (SMT). As an interesting trend, tree-based finite-state methods have made their way to SMT. A well-articulated set of desirable formal properties of tree transducers have been a driving force in a lot of recent basic research resulting in a constantly evolving taxonomy of tree transducers (Knight Reference Knight2007). In relation to this grid of desiderata, Maletti proposes an interesting tree transducer model that demonstrates the benefits of finite state control in capturing the non-local context, as opposed to the tree substitution grammar approach where the individual rules aim at capturing locally extended neighbourhoods in phrase-structure trees. Once again, the competitor is asymptotically less efficient than the finite-state approach presented here.