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Compositional generalization, the ability to predict complex meanings from training on simpler sentences, poses challenges for powerful pretrained seq2seq models. In this paper, we show that data augmentation methods that sample MRs and backtranslate them can be effective for compositional generalization, but only if we sample from the right distribution. Remarkably, sampling from a uniform distribution performs almost as well as sampling from the test distribution, and greatly outperforms earlier methods that sampled from the training distribution. We further conduct experiments to investigate the reason why this happens and where the benefit of such data augmentation methods come from.

Seq2seq models have been shown to struggle with compositional generalization in semantic parsing, i.e. generalizing to unseen compositions of phenomena that the model handles correctly in isolation. We phrase semantic parsing as a two-step process: we first tag each input token with a multiset of output tokens. Then we arrange the tokens into an output sequence using a new way of parameterizing and predicting permutations. We formulate predicting a permutation as solving a regularized linear program and we backpropagate through the solver. In contrast to prior work, our approach does not place a priori restrictions on possible permutations, making it very expressive. Our model outperforms pretrained seq2seq models and prior work on realistic semantic parsing tasks that require generalization to longer examples. We also outperform non-tree-based models on structural generalization on the COGS benchmark. For the first time, we show that a model without an inductive bias provided by trees achieves high accuracy on generalization to deeper recursion., Comment: ACL 2023

In the last five years, there has been a significant focus in Natural Language Processing (NLP) on developing larger Pretrained Language Models (PLMs) and introducing benchmarks such as SuperGLUE and SQuAD to measure their abilities in language understanding, reasoning, and reading comprehension. These PLMs have achieved impressive results on these benchmarks, even surpassing human performance in some cases. This has led to claims of superhuman capabilities and the provocative idea that certain tasks have been solved. In this position paper, we take a critical look at these claims and ask whether PLMs truly have superhuman abilities and what the current benchmarks are really evaluating. We show that these benchmarks have serious limitations affecting the comparison between humans and PLMs and provide recommendations for fairer and more transparent benchmarks., Comment: 9 pages, long paper at ACL 2023 proceedings

Ambiguity is an intrinsic feature of natural language. Managing ambiguity is a key part of human language understanding, allowing us to anticipate misunderstanding as communicators and revise our interpretations as listeners. As language models (LMs) are increasingly employed as dialogue interfaces and writing aids, handling ambiguous language is critical to their success. We characterize ambiguity in a sentence by its effect on entailment relations with another sentence, and collect AmbiEnt, a linguist-annotated benchmark of 1,645 examples with diverse kinds of ambiguity. We design a suite of tests based on AmbiEnt, presenting the first evaluation of pretrained LMs to recognize ambiguity and disentangle possible meanings. We find that the task remains extremely challenging, including for GPT-4, whose generated disambiguations are considered correct only 32% of the time in human evaluation, compared to 90% for disambiguations in our dataset. Finally, to illustrate the value of ambiguity-sensitive tools, we show that a multilabel NLI model can flag political claims in the wild that are misleading due to ambiguity. We encourage the field to rediscover the importance of ambiguity for NLP., Comment: EMNLP 2023 camera-ready

In the last five years, there has been a significant focus in Natural Language Processing (NLP) on developing larger Pretrained Language Models (PLMs) and introducing benchmarks such as SuperGLUE and SQuAD to measure their abilities in language understanding, reasoning, and reading comprehension. These PLMs have achieved impressive results on these benchmarks, even surpassing human performance in some cases. This has led to claims of superhuman capabilities and the provocative idea that certain tasks have been solved. In this position paper, we take a critical look at these claims and ask whether PLMs truly have superhuman abilities and what the current benchmarks are really evaluating. We show that these benchmarks have serious limitations affecting the comparison between humans and PLMs and provide recommendations for fairer and more transparent benchmarks.

The ability to predict an NLP model's accuracy on unseen, potentially out-of-distribution data is a prerequisite for trustworthiness. We present a novel model that establishes upper and lower bounds on the accuracy, without requiring gold labels for the unseen data. We achieve this by training a discriminator which predicts whether the output of a given sequence-to-sequence model is correct or not. We show across a variety of tagging, parsing, and semantic parsing tasks that the gold accuracy is reliably between the predicted upper and lower bounds, and that these bounds are remarkably close together.

LLMs are being increasingly used for planning-style tasks, but their capabilities for planning and reasoning are poorly understood. We present AutoPlanBench, a novel method for automatically converting planning benchmarks written in PDDL into textual descriptions and offer a benchmark dataset created with our method. We show that while the best LLM planners do well on some planning tasks, others remain out of reach of current methods.

Large Language Models (LLMs) are increasingly being used for interactive decision-making tasks requiring planning and adapting to the environment. Recent works employ LLMs-as-agents in broadly two ways: iteratively determining the next action (iterative executors) or generating plans and executing sub-tasks using LLMs (plan-and-execute). However, these methods struggle with task complexity, as the inability to execute any sub-task may lead to task failure. To address these shortcomings, we introduce As-Needed Decomposition and Planning for complex Tasks (ADaPT), an approach that explicitly plans and decomposes complex sub-tasks as-needed, i.e., when the LLM is unable to execute them. ADaPT recursively decomposes sub-tasks to adapt to both task complexity and LLM capability. Our results demonstrate that ADaPT substantially outperforms established strong baselines, achieving success rates up to 28.3% higher in ALFWorld, 27% in WebShop, and 33% in TextCraft -- a novel compositional dataset that we introduce. Through extensive analysis, we illustrate the importance of multilevel decomposition and establish that ADaPT dynamically adjusts to the capabilities of the executor LLM as well as to task complexity., Comment: NAACL 2024 (findings) camera-ready. Project Page: https://allenai.github.io/adaptllm

The goal of compositional generalization benchmarks is to evaluate how well models generalize to new complex linguistic expressions. Existing benchmarks often focus on lexical generalization, the interpretation of novel lexical items in syntactic structures familiar from training; structural generalization tasks, where a model needs to interpret syntactic structures that are themselves unfamiliar from training, are often underrepresented, resulting in overly optimistic perceptions of how well models can generalize. We introduce SLOG, a semantic parsing dataset that extends COGS (Kim and Linzen, 2020) with 17 structural generalization cases. In our experiments, the generalization accuracy of Transformer models, including pretrained ones, only reaches 40.6%, while a structure-aware parser only achieves 70.8%. These results are far from the near-perfect accuracy existing models achieve on COGS, demonstrating the role of SLOG in foregrounding the large discrepancy between models' lexical and structural generalization capacities., Comment: Accepted to EMNLP 2023

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

Strong inductive biases enable learning from little data and help generalization outside of the training distribution. Popular neural architectures such as Transformers lack strong structural inductive biases for seq2seq NLP tasks on their own. Consequently, they struggle with systematic generalization beyond the training distribution, e.g. with extrapolating to longer inputs, even when pre-trained on large amounts of text. We show how a structural inductive bias can be efficiently injected into a seq2seq model by pre-training it to simulate structural transformations on synthetic data. Specifically, we inject an inductive bias towards Finite State Transducers (FSTs) into a Transformer by pre-training it to simulate FSTs given their descriptions. Our experiments show that our method imparts the desired inductive bias, resulting in improved systematic generalization and better few-shot learning for FST-like tasks. Our analysis shows that fine-tuned models accurately capture the state dynamics of the unseen underlying FSTs, suggesting that the simulation process is internalized by the fine-tuned model.

Sequence-to-sequence (seq2seq) models have been successful across many NLP tasks, including ones that require predicting linguistic structure. However, recent work on compositional generalization has shown that seq2seq models achieve very low accuracy in generalizing to linguistic structures that were not seen in training. We present new evidence that this is a general limitation of seq2seq models that is present not just in semantic parsing, but also in syntactic parsing and in text-to-text tasks, and that this limitation can often be overcome by neurosymbolic models that have linguistic knowledge built in. We further report on some experiments that give initial answers on the reasons for these limitations., Comment: Accepted in EMNLP 2022

Seq2seq models have been shown to struggle with compositional generalisation, i.e. generalising to new and potentially more complex structures than seen during training. Taking inspiration from grammar-based models that excel at compositional generalisation, we present a flexible end-to-end differentiable neural model that composes two structural operations: a fertility step, which we introduce in this work, and a reordering step based on previous work (Wang et al., 2021). To ensure differentiability, we use the expected value of each step. Our model outperforms seq2seq models by a wide margin on challenging compositional splits of realistic semantic parsing tasks that require generalisation to longer examples. It also compares favourably to other models targeting compositional generalisation., Comment: EACL 2023 camera-ready

A rapidly growing body of research on compositional generalization investigates the ability of a semantic parser to dynamically recombine linguistic elements seen in training into unseen sequences. We present a systematic comparison of sequence-to-sequence models and models guided by compositional principles on the recent COGS corpus (Kim and Linzen, 2020). Though seq2seq models can perform well on lexical tasks, they perform with near-zero accuracy on structural generalization tasks that require novel syntactic structures; this holds true even when they are trained to predict syntax instead of semantics. In contrast, compositional models achieve near-perfect accuracy on structural generalization; we present new results confirming this from the AM parser (Groschwitz et al., 2021). Our findings show structural generalization is a key measure of compositional generalization and requires models that are aware of complex structure.

AM dependency parsing is a method for neural semantic graph parsing that exploits the principle of compositionality. While AM dependency parsers have been shown to be fast and accurate across several graphbanks, they require explicit annotations of the compositional tree structures for training. In the past, these were obtained using complex graphbank-specific heuristics written by experts. Here we show how they can instead be trained directly on the graphs with a neural latent-variable model, drastically reducing the amount and complexity of manual heuristics. We demonstrate that our model picks up on several linguistic phenomena on its own and achieves comparable accuracy to supervised training, greatly facilitating the use of AM dependency parsing for new sembanks.

AM dependency parsing is a method for neural semantic graph parsing that exploits the principle of compositionality. While AM dependency parsers have been shown to be fast and accurate across several graphbanks, they require explicit annotations of the compositional tree structures for training. In the past, these were obtained using complex graphbank-specific heuristics written by experts. Here we show how they can instead be trained directly on the graphs with a neural latent-variable model, drastically reducing the amount and complexity of manual heuristics. We demonstrate that our model picks up on several linguistic phenomena on its own and achieves comparable accuracy to supervised training, greatly facilitating the use of AM dependency parsing for new sembanks., Comment: Accepted at the 5th Workshop on Structured Prediction for NLP (http://structuredprediction.github.io/SPNLP21)

The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. These MRs exhibit structural differences that reflect different theoretical and design considerations, presenting challenges to uniform linguistic analysis and cross-framework semantic parsing. Here, we ask the question of which design differences between MRs are meaningful and semantically-rooted, and which are superficial. We present a methodology for normalizing discrepancies between MRs at the compositional level (Lindemann et al., 2019), finding that we can normalize the majority of divergent phenomena using linguistically-grounded rules. Our work significantly increases the match in compositional structure between MRs and improves multi-task learning (MTL) in a low-resource setting, demonstrating the usefulness of careful MR design analysis and comparison., Comment: 16 pages, 6 figures

When generating technical instructions, it is often convenient to describe complex objects in the world at different levels of abstraction. A novice user might need an object explained piece by piece, while for an expert, talking about the complex object (e.g. a wall or railing) directly may be more succinct and efficient. We show how to generate building instructions at different levels of abstraction in Minecraft. We introduce the use of hierarchical planning to this end, a method from AI planning which can capture the structure of complex objects neatly. A crowdsourcing evaluation shows that the choice of abstraction level matters to users, and that an abstraction strategy which balances low-level and high-level object descriptions compares favorably to ones which don't., Comment: Accepted COLING 2020 long paper

AM dependency parsing is a linguistically principled method for neural semantic parsing with high accuracy across multiple graphbanks. It relies on a type system that models semantic valency but makes existing parsers slow. We describe an A* parser and a transition-based parser for AM dependency parsing which guarantee well-typedness and improve parsing speed by up to 3 orders of magnitude, while maintaining or improving accuracy., Comment: Accepted at EMNLP 2020, camera-ready version

We describe the Saarland University submission to the shared task on Cross-Framework Meaning Representation Parsing (MRP) at the 2019 Conference on Computational Natural Language Learning (CoNLL).

Most semantic parsers that map sentences to graph-based meaning representations are hand-designed for specific graphbanks. We present a compositional neural semantic parser which achieves, for the first time, competitive accuracies across a diverse range of graphbanks. Incorporating BERT embeddings and multi-task learning improves the accuracy further, setting new states of the art on DM, PAS, PSD, AMR 2015 and EDS., Comment: Accepted at ACL 2019

We investigate the capacity of mechanisms for compositional semantic parsing to describe relations between sentences and semantic representations. We prove that in order to represent certain relations, mechanisms which are syntactically projective must be able to remember an unbounded number of locations in the semantic representations, where nonprojective mechanisms need not. This is the first result of this kind, and has consequences both for grammar-based and for neural systems., Comment: Accepted at ACL 2019

We present a semantic parser for Abstract Meaning Representations which learns to parse strings into tree representations of the compositional structure of an AMR graph. This allows us to use standard neural techniques for supertagging and dependency tree parsing, constrained by a linguistically principled type system. We present two approximative decoding algorithms, which achieve state-of-the-art accuracy and outperform strong baselines., Comment: This paper will be presented at ACL 2018 (see https://acl2018.org/programme/papers/)

Chart constraints, which specify at which string positions a constituent may begin or end, have been shown to speed up chart parsers for PCFGs. We generalize chart constraints to more expressive grammar formalisms and describe a neural tagger which predicts chart constraints at very high precision. Our constraints accelerate both PCFG and TAG parsing, and combine effectively with other pruning techniques (coarse-to-fine and supertagging) for an overall speedup of two orders of magnitude, while improving accuracy.

We present a model which predicts how individual users of a dialog system understand and produce utterances based on user groups. In contrast to previous work, these user groups are not specified beforehand, but learned in training. We evaluate on two referring expression (RE) generation tasks; our experiments show that our model can identify user groups and learn how to most effectively talk to them, and can dynamically assign unseen users to the correct groups as they interact with the system., Comment: 9 pages, 7 Figures, Accepted for SIGDIAL 2018

The field of statistical machine translation has made tremendous progress due to the rise of statistical methods, making it possible to obtain a translation system automatically from a bilingual collection of text. Some approaches do not even need any kind of linguistic annotation, and can infer translation rules from raw, unannotated data. However, most state-of-the art systems do linguistic structure little justice, and moreover many approaches that have been put forward use ad-hoc formalisms and algorithms. This inevitably leads to duplication of effort, and a separation between theoretical researchers and practitioners. In order to remedy the lack of motivation and rigor, the contributions of this dissertation are threefold: 1. After laying out the historical background and context, as well as the mathematical and linguistic foundations, a rigorous algebraic model of machine translation is put forward. We use regular tree grammars and bimorphisms as the backbone, introducing a modular architecture that allows different input and output formalisms. 2. The challenges of implementing this bimorphism-based model in a machine translation toolkit are then described, explaining in detail the algorithms used for the core components. 3. Finally, experiments where the toolkit is applied on real-world data and used for diagnostic purposes are described. We discuss how we use exact decoding to reason about search errors and model errors in a popular machine translation toolkit, and we compare output formalisms of different generative capacity.

The field of statistical machine translation has made tremendous progress due to the rise of statistical methods, making it possible to obtain a translation system automatically from a bilingual collection of text. Some approaches do not even need any kind of linguistic annotation, and can infer translation rules from raw, unannotated data. However, most state-of-the art systems do linguistic structure little justice, and moreover many approaches that have been put forward use ad-hoc formalisms and algorithms. This inevitably leads to duplication of effort, and a separation between theoretical researchers and practitioners. In order to remedy the lack of motivation and rigor, the contributions of this dissertation are threefold: 1. After laying out the historical background and context, as well as the mathematical and linguistic foundations, a rigorous algebraic model of machine translation is put forward. We use regular tree grammars and bimorphisms as the backbone, introducing a modular architecture that allows different input and output formalisms. 2. The challenges of implementing this bimorphism-based model in a machine translation toolkit are then described, explaining in detail the algorithms used for the core components. 3. Finally, experiments where the toolkit is applied on real-world data and used for diagnostic purposes are described. We discuss how we use exact decoding to reason about search errors and model errors in a popular machine translation toolkit, and we compare output formalisms of different generative capacity.

The field of statistical machine translation has made tremendous progress due to the rise of statistical methods, making it possible to obtain a translation system automatically from a bilingual collection of text. Some approaches do not even need any kind of linguistic annotation, and can infer translation rules from raw, unannotated data. However, most state-of-the art systems do linguistic structure little justice, and moreover many approaches that have been put forward use ad-hoc formalisms and algorithms. This inevitably leads to duplication of effort, and a separation between theoretical researchers and practitioners. In order to remedy the lack of motivation and rigor, the contributions of this dissertation are threefold: 1. After laying out the historical background and context, as well as the mathematical and linguistic foundations, a rigorous algebraic model of machine translation is put forward. We use regular tree grammars and bimorphisms as the backbone, introducing a modular architecture that allows different input and output formalisms. 2. The challenges of implementing this bimorphism-based model in a machine translation toolkit are then described, explaining in detail the algorithms used for the core components. 3. Finally, experiments where the toolkit is applied on real-world data and used for diagnostic purposes are described. We discuss how we use exact decoding to reason about search errors and model errors in a popular machine translation toolkit, and we compare output formalisms of different generative capacity.

The field of statistical machine translation has made tremendous progress due to the rise of statistical methods, making it possible to obtain a translation system automatically from a bilingual collection of text. Some approaches do not even need any kind of linguistic annotation, and can infer translation rules from raw, unannotated data. However, most state-of-the art systems do linguistic structure little justice, and moreover many approaches that have been put forward use ad-hoc formalisms and algorithms. This inevitably leads to duplication of effort, and a separation between theoretical researchers and practitioners. In order to remedy the lack of motivation and rigor, the contributions of this dissertation are threefold: 1. After laying out the historical background and context, as well as the mathematical and linguistic foundations, a rigorous algebraic model of machine translation is put forward. We use regular tree grammars and bimorphisms as the backbone, introducing a modular architecture that allows different input and output formalisms. 2. The challenges of implementing this bimorphism-based model in a machine translation toolkit are then described, explaining in detail the algorithms used for the core components. 3. Finally, experiments where the toolkit is applied on real-world data and used for diagnostic purposes are described. We discuss how we use exact decoding to reason about search errors and model errors in a popular machine translation toolkit, and we compare output formalisms of different generative capacity.

The weak equivalence of Combinatory Categorial Grammar (CCG) and Tree-Adjoining Grammar (TAG) is a central result of the literature on mildly context-sensitive grammar formalisms. However, the categorial formalism for which this equivalence has been established differs significantly from the versions of CCG that are in use today. In particular, it allows restriction of combinatory rules on a per grammar basis, whereas modern CCG assumes a universal set of rules, isolating all cross-linguistic variation in the lexicon. In this article we investigate the formal significance of this difference. Our main result is that lexicalized versions of the classical CCG formalism are strictly less powerful than TAG.

The weak equivalence of Combinatory Categorial Grammar (CCG) and Tree-Adjoining Grammar (TAG) is a central result of the literature on mildly context-sensitive grammar formalisms. However, the categorial formalism for which this equivalence has been established differs significantly from the versions of CCG that are in use today. In particular, it allows restriction of combinatory rules on a per grammar basis, whereas modern CCG assumes a universal set of rules, isolating all cross-linguistic variation in the lexicon. In this article we investigate the formal significance of this difference. Our main result is that lexicalized versions of the classical CCG formalism are strictly less powerful than TAG.

The specification of a decoder, i.e., a program that translates sentences from one natural language into another, is an intricate process, driven by the application and lacking a canonical methodology. The practical nature of decoder development inhibits the transfer of knowledge between theory and application, which is unfortunate because many contemporary decoders are in fact related to formal-language theory. This thesis proposes an algebraic framework where a decoder is specified by an expression built from a fixed set of operations. As yet, this framework accommodates contemporary syntax-based decoders, it spans two levels of abstraction, and, primarily, it encourages mutual stimulation between the theory of weighted tree automata and the application.

The specification of a decoder, i.e., a program that translates sentences from one natural language into another, is an intricate process, driven by the application and lacking a canonical methodology. The practical nature of decoder development inhibits the transfer of knowledge between theory and application, which is unfortunate because many contemporary decoders are in fact related to formal-language theory. This thesis proposes an algebraic framework where a decoder is specified by an expression built from a fixed set of operations. As yet, this framework accommodates contemporary syntax-based decoders, it spans two levels of abstraction, and, primarily, it encourages mutual stimulation between the theory of weighted tree automata and the application.

The specification of a decoder, i.e., a program that translates sentences from one natural language into another, is an intricate process, driven by the application and lacking a canonical methodology. The practical nature of decoder development inhibits the transfer of knowledge between theory and application, which is unfortunate because many contemporary decoders are in fact related to formal-language theory. This thesis proposes an algebraic framework where a decoder is specified by an expression built from a fixed set of operations. As yet, this framework accommodates contemporary syntax-based decoders, it spans two levels of abstraction, and, primarily, it encourages mutual stimulation between the theory of weighted tree automata and the application.

The weak equivalence of Combinatory Categorial Grammar (CCG) and Tree-Adjoining Grammar (TAG) is a central result of the literature on mildly context-sensitive grammar formalisms. However, the categorial formalism for which this equivalence has been established differs significantly from the versions of CCG that are in use today. In particular, it allows restriction of combinatory rules on a per grammar basis, whereas modern CCG assumes a universal set of rules, isolating all cross-linguistic variation in the lexicon. In this article we investigate the formal significance of this difference. Our main result is that lexicalized versions of the classical CCG formalism are strictly less powerful than TAG.

The specification of a decoder, i.e., a program that translates sentences from one natural language into another, is an intricate process, driven by the application and lacking a canonical methodology. The practical nature of decoder development inhibits the transfer of knowledge between theory and application, which is unfortunate because many contemporary decoders are in fact related to formal-language theory. This thesis proposes an algebraic framework where a decoder is specified by an expression built from a fixed set of operations. As yet, this framework accommodates contemporary syntax-based decoders, it spans two levels of abstraction, and, primarily, it encourages mutual stimulation between the theory of weighted tree automata and the application.

The weak equivalence of Combinatory Categorial Grammar (CCG) and Tree-Adjoining Grammar (TAG) is a central result of the literature on mildly context-sensitive grammar formalisms. However, the categorial formalism for which this equivalence has been established differs significantly from the versions of CCG that are in use today. In particular, it allows restriction of combinatory rules on a per grammar basis, whereas modern CCG assumes a universal set of rules, isolating all cross-linguistic variation in the lexicon. In this article we investigate the formal significance of this difference. Our main result is that lexicalized versions of the classical CCG formalism are strictly less powerful than TAG.

The weak equivalence of Combinatory Categorial Grammar (CCG) and Tree-Adjoining Grammar (TAG) is a central result of the literature on mildly context-sensitive grammar formalisms. However, the categorial formalism for which this equivalence has been established differs significantly from the versions of CCG that are in use today. In particular, it allows restriction of combinatory rules on a per grammar basis, whereas modern CCG assumes a universal set of rules, isolating all cross-linguistic variation in the lexicon. In this article we investigate the formal significance of this difference. Our main result is that lexicalized versions of the classical CCG formalism are strictly less powerful than TAG.

We review a number of different ‘algebraic’ perspectives on TAG and STAG in the framework of interpreted regular tree grammars (IRTGs). We then use this framework to derive a new parsing algorithm for TAGs, based on two algebras that describe strings and derived trees. Our algorithm is extremely modular, and can easily be adapted to the synchronous case.

We review a number of different ‘algebraic’ perspectives on TAG and STAG in the framework of interpreted regular tree grammars (IRTGs). We then use this framework to derive a new parsing algorithm for TAGs, based on two algebras that describe strings and derived trees. Our algorithm is extremely modular, and can easily be adapted to the synchronous case.

We present a formal framework that generalizes a variety of monolingual and synchronous grammar formalisms for parsing and translation. Our framework is based on regular tree grammars that describe derivation trees, which are interpreted in arbitrary algebras. We obtain generic parsing algorithms by exploiting closure properties of regular tree languages.