In finite-state language processing pipelines, a lexicon is often a key component. It needs to be comprehensive to ensure accuracy, reducing out-of-vocabulary misses. However, in memory-constrained environments (e.g., mobile phones), the size of the component automata must be kept small. Indeed, a delicate balance between comprehensiveness, speed, and memory must be struck to conform to device requirements while providing a good user experience.In this paper, we describe a compression scheme for lexicons when represented as finite-state transducers. We efficiently encode the graph of the transducer while storing transition labels separately. The graph encoding scheme is based on the LOUDS (Level Order Unary Degree Sequence) tree representation, which has constant time tree traversal for queries while being information-theoretically optimal in space. We find that our encoding is near the theoretical lower bound for such graphs and substantially outperforms more traditional representations in space while remaining competitive in latency benchmarks.

Probabilistic finite automata (PFAs) are com- mon statistical language model in natural lan- guage and speech processing. A typical task for PFAs is to compute the probability of all strings that match a query pattern. An impor- tant special case of this problem is computing the probability of a string appearing as a pre- fix, suffix, or infix. These problems find use in many natural language processing tasks such word prediction and text error correction. Recently, we gave the first incremental algorithm to efficiently compute the infix probabilities of each prefix of a string (Cognetta et al., 2018). We develop an asymptotic improvement of that algorithm and solve the open problem of computing the infix probabilities of PFAs from streaming data, which is crucial when process- ing queries online and is the ultimate goal of the incremental approach.

We continue the study of generating se-mantically correct regular expressions from natural language descriptions (NL). The current state-of-the-art model SemRegex produces regular expressions from NLs by rewarding the reinforced learning based on the semantic (rather than syntactic) equivalence between two regular expressions. Since the regular expression equivalence problem is PSPACE-complete, we introduce the EQ_Reg model for computing the simi-larity of two regular expressions using deep neural networks. Our EQ_Reg mod-el essentially softens the equivalence of two regular expressions when used as a reward function. We then propose a new regex generation model, SoftRegex, us-ing the EQ_Reg model, and empirically demonstrate that SoftRegex substantially reduces the training time (by a factor of at least 3.6) and produces state-of-the-art results on three benchmark datasets.

In natural language processing, a common task is to compute the probability of a phrase appearing in a document or to calculate the probability of all phrases matching a given pattern. For instance, one computes affix (prefix, suffix, infix, etc.) probabilities of a string or a set of strings with respect to a probability distribution of patterns. The problem of computing infix probabilities of strings when the pattern distribution is given by a probabilistic context-free grammar or by a probabilistic finite automaton is already solved, yet it was open to compute the infix probabilities in an incremental manner. The incremental computation is crucial when a new query is built from a previous query. We tackle this problem and suggest a method that computes infix probabilities incrementally for probabilistic finite automata by representing all the probabilities of matching strings as a series of transition matrix calculations. We show that the proposed approach is theoretically faster than the previous method and, using real world data, demonstrate that our approach has vastly better performance in practice.