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There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…
Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…
Accurately segmenting a citation string into fields for authors, titles, etc. is a challenging task because the output typically obeys various global constraints. Previous work has shown that modeling soft constraints, where the model is…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Latent tree learning(LTL) methods learn to parse sentences using only indirect supervision from a downstream task. Recent advances in latent tree learning have made it possible to recover moderately high quality tree structures by training…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret,…
This paper aims to develop a verification method for procedural programs via a transformation into Logically Constrained Term Rewriting Systems (LCTRSs). To this end, we extend transformation methods based on integer TRSs to handle…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…
In this article we investigate how a subterm pattern matching algorithm can be exploited to implement efficient term rewriting procedures. From the left-hand sides of the rewrite system we construct a set automaton, which can be used to…
The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…
In this paper, we proposed a deep learning-based end-to-end method on the domain specified automatic term extraction (ATE), it considers possible term spans within a fixed length in the sentence and predicts them whether they can be…
We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting…
This paper describes a method for compiling a constraint-based grammar into a potentially more efficient form for processing. This method takes dependent disjunctions within a constraint formula and factors them into non-interacting groups…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
This paper defines a notion of binding trees that provide a suitable model for second-order type systems with F-bounded quantifiers and equirecursive types. It defines a notion of regular binding trees that correspond in the right way to…
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…
There are many evaluation strategies for term rewrite systems, but proving termination automatically is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies full termination. We adapt…