Sound correspondence patterns play a crucial role for linguistic reconstruction. Linguists
 use them to prove language relationship, to reconstruct proto-forms, and for classical
 phylogenetic reconstruction based on shared innovations.Cognate words which fail to
 conform with expected patterns can further point to various kinds of exceptions in sound
 change, such as analogy or assimilation of frequent words. Here we present an automatic
 method for the inference of sound correspondence patterns across multiple languages based
 on a network approach. The core idea is to represent all columns in aligned cognate sets as
 nodes in a network with edges representing the degree of compatibility between the nodes.
 The task of inferring all compatible correspondence sets can then be handled as the well-known minimum clique cover problem in graph theory, which essentially seeks to split the graph into the smallest number of cliques in which each node is represented by exactly one clique. The resulting partitions represent all correspondence patterns which can be
 inferred for a given dataset. By excluding those patterns which occur in only a few cognate
 sets, the core of regularly recurring sound correspondences can be inferred. Based on this
 idea, the paper presents a method for automatic correspondence pattern recognition, which
 is implemented as part of a Python library which supplements the paper. To illustrate the
 usefulness of the method, various tests are presented, and concrete examples of the output
 of the method are provided. In addition to the source code, the study is supplemented by
 a short interactive tutorial that illustrates how to use the new method and how to inspect
 its results. One of the fundamental insights of early historical linguistic research was that -as a result of systemic changes in the sound system of languages -genetically related languages exhibit structural similarities in those parts of their lexicon which were commonly inherited from their ancestral languages. These similarities surface in form of correspondence relations between sounds from different languages in cognate words. English th [θ] , for example, is usually reflected as d in German, as we can see from cognate pairs like English thou vs. German du, or English thorn and German Dorn. English t, on the other hand, is usually reflected as z [ts] in German, as we can see from pairs like English toe vs. German Zeh, or English tooth vs. German Zahn. The identification of these regular sound correspondences plays a crucial role in historical language comparison, serving not only as the basis for the proof of genetic relationship BID11 BID6 or the reconstruction of protoforms BID20 , 72-85, Anttila 1972 , but (indirectly) also for classical subgrouping based on shared innovations (which would not be possible without identified correspondence patterns).Given the increasing application of automatic methods in historical linguistics after the "quantitative turn" (Geisler and List 2013, 111) in the beginning of this millennium, scholars have repeatedly attempted to either directly infer regular sound correspondences across genetically related languages BID30 BID29 BID5 BID26 or integrated the inference into workflows for automatic cognate detection BID17 BID33 BID34 BID40 . What is interesting in this context, however, is that almost all approaches dealing with regular sound correspondences, be it early formal -but classically grounded -accounts BID16 BID20 or computer-based methods BID29 BID28 BID34 only consider sound correspondences between pairs of languages.A rare exception can be found in the work of Anttila (1972, 229-263) , who presents the search for regular sound correspondences across multiple languages as the basic technique underlying the comparative method for historical language comparison. Anttila 's description starts from a set of cognate word forms (or morphemes) across the languages under investigation. These words are then arranged in such a way that corresponding sounds in all words are placed into the same column of a matrix. The extraction of regularly recurring sound correspondences in the languages under investigation is then based on the identification of similar patterns recurring across different columns within the cognate sets. The procedure is illustrated in Figure 1 , where four cognate sets in Sanskrit, Ancient Greek, Latin, and Gothic are shown, two taken from Anttila (1972, 246) and two added by me.Two points are remarkable about Anttila's approach. First, it builds heavily on the phonetic alignment of sound sequences, a concept that was only recently adapted in linguistics (Covington 1996; BID27 BID34 , building heavily on approaches in bioinformatics and computer science BID55 BID45 , although it was implicitly always an integral part of the methodology of historical language comparison (compare Fox 1995, 67f, Dixon and BID9 . Second, it reflects a concrete technique by which regular sound correspondences for multiple languages can be detected and employed as a starting point for linguistic reconstruction. If we look at the framed columns in the four examples in Figure 1 , which are further labeled alphabetically, for example, we can easily see that the patterns A, E, and F are remarkably similar, with the missing reflexes in Gothic in the patterns E and F as the only difference. The same holds, however, for columns C, E, and F. Since A and C differ regarding the reflex sound of Gothic (u vs. au), they cannot be assigned to the same correspondence set at this stage, and if we want to solve the problem of finding the regular sound correspondences for the words in the figure, we need to make a decision which columns in the alignments we assign to the same correspondence sets, thereby 'imputing' missing sounds where we miss a reflex. Assuming that the "regular " pattern in our case is reflected by the group of A, E, and F, we can make predictions about the sounds missing in Gothic in E and F, concluding that, if ever we find the missing reflex in so far unrecognised sources of Gothic in the future, we would expect a -u-in the words for 'daughter-in-law' and 'red'.We can easily see how patterns of sound correspondences across multiple languages can serve as the basis for linguistic reconstruction. Strictly speaking, if two alignment columns are identical (ignoring missing data to some extent), they need to reflect the same proto-sound. But even if they are not identical, they could be assigned to the same proto-sound, provided that one can show that the differences are conditioned by phonetic context. This is the case for Gothic au [o] in pattern C, which has been shown to go back to u when preceding h (Meier-Brügger 2002, 210f) . As a result, scholars usually reconstruct Proto-Indo-European *u for A, C, E, and F. In this study I have presented a new method for the inference of sound correspondence patterns in multi-lingual wordlists. Thanks to its integration with the LingPy software package, the methods can be applied both in the form of fully automated workflows where both cognate sets, alignments, and correspondence patterns are computed, or in computer-assisted workflows where linguists manually annotate parts of the data at any step in the workflow. Having shown that the inference of correspondence patterns can be seen as the crucial step underlying the reconstruction of proto-forms, the method presented here provides a basis for many additional approaches in the fields of computational historical linguistics and computer-assisted language comparison. Among these are (a) automatic approaches for linguistic reconstruction, (b) alignment-based approaches to phylogenetic reconstruction, (c) the detection of borrowings and erroneous cognates, and (d) the prediction of missing reflexes in the data. The approach is not perfect in its current form, and many kinds of improvements are possible. Given its novelty, however, I consider it important to share the approach its current form, hoping that it may inspire colleagues in the field to expand and develop it further.
The paper describes a new algorithm by which sound correspondence patterns for multiple languages can be inferred.
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