Related papers: Multi-Sequential Word Relations
In [2] M. Farber constructed invariants of m-component boundary links with values in algebra of noncommutative rational functions. In this paper we simplify his constructions and express them by using noncommutative generalizations of…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Neural rationale models are popular for interpretable predictions of NLP tasks. In these, a selector extracts segments of the input text, called rationales, and passes these segments to a classifier for prediction. Since the rationale is…
In this paper, we investigate the synthesis problem of terminating reactive systems from quantitative specifications. Such systems are modeled as finite transducers whose executions are represented as finite words in $(I\times O)^*$, where…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
We consider the problem of partitioning effectively a given symmetric (and irreflexive) rational relation R into two asymmetric rational relations. This problem is motivated by a recent method of embedding an R-independent language into one…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Non-sentential utterances (NSUs) are utterances that lack a complete sentential form but whose meaning can be inferred from the dialogue context, such as "OK", "where?", "probably at his apartment". The interpretation of non-sentential…
In this work, we propose Reinforced Functional Token Tuning (RFTT), a novel reinforced fine-tuning framework that empowers Large Language Models (LLMs) with self-play learn-to-reason capabilities. Unlike prior prompt-driven reasoning…
We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting…
Rule-based decision models are attractive due to their interpretability. However, existing rule induction methods often result in long and consequently less interpretable rule models. This problem can often be attributed to the lack of…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
Relational reasoning is a central component of generally intelligent systems, enabling robust and data-efficient inductive generalization. Recent empirical evidence shows that many existing neural architectures, including Transformers,…
The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szeg\H{o} as well as Askey and Gasper, who inspired more recent work. It is…
Many machine learning tasks can be expressed as the transformation---or \emph{transduction}---of input sequences into output sequences: speech recognition, machine translation, protein secondary structure prediction and text-to-speech to…
Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…