Related papers: An SMT Theory for n-Indexed Sequences

Neural Machine Translation (NMT) models achieve their best performance when large sets of parallel data are used for training. Consequently, techniques for augmenting the training set have become popular recently. One of these methods is…

Neural machine translation (NMT) usually works in a seq2seq learning way by viewing either source or target sentence as a linear sequence of words, which can be regarded as a special case of graph, taking words in the sequence as nodes and…

This tutorial introduces a new and powerful set of techniques variously called "neural machine translation" or "neural sequence-to-sequence models". These techniques have been used in a number of tasks regarding the handling of human…

Modern assembly processes require flexibility and adaptability to handle increasing product variety and customization. Traditional assembly planning methods often prioritize finding an optimal assembly sequence, overlooking the requirements…

#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…

Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…

Most of modern neural machine translation (NMT) models are based on an encoder-decoder framework with an attention mechanism. While they perform well on standard datasets, they can have trouble in translation of long inputs that are rare or…

Generative large language models (LLMs) with instruct training such as GPT-4 can follow human-provided instruction prompts and generate human-like responses to these prompts. Apart from natural language responses, they have also been found…

Training of neural machine translation (NMT) models usually uses mini-batches for efficiency purposes. During the mini-batched training process, it is necessary to pad shorter sentences in a mini-batch to be equal in length to the longest…

We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. sequential algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates defining the class of RSAs, an…

Sequence learning is an essential aspect of intelligence. In Artificial Intelligence, sequence prediction task is usually used to test a sequence learning model. In this paper, a model of sequence learning, which is interpretable through…

Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…

State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast…

Constraint solving is an elementary way for verification of deep neural networks (DNN). In the domain of AI safety, a DNN might be modified in its structure and parameters for its repair or attack. For such situations, we propose the…

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…

Structured, procedural reasoning is essential for Large Language Models (LLMs), especially in mathematics. While post-training methods have improved LLM performance, they still fall short in capturing deep procedural logic on complex tasks.…

Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…

We count the number of alignments of $N \ge 1$ sequences when match-up types are from a specified set $S\subseteq \mathbb{N}^N$. Equivalently, we count the number of nonnegative integer matrices whose rows sum to a given fixed vector and…

Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…

Sequence set is a widely-used type of data source in a large variety of fields. A typical example is protein structure prediction, which takes an multiple sequence alignment (MSA) as input and aims to infer structural information from it.…