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Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
In 2011, Fici and Lipt\'ak introduced prefix normal words. A binary word is prefix normal if it has no factor (substring) that contains more occurrences of the letter 1 than the prefix of the same length. Among the open problems regarding…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in the same way, where by subword we mean subsequence. We study the quotient…
Natural language generation (NLG) is a critical component in a spoken dialogue system. This paper presents a Recurrent Neural Network based Encoder-Decoder architecture, in which an LSTM-based decoder is introduced to select, aggregate…
A regular language $L$ is said to be prime, if it is not the product of two non-trivial languages. Martens et al. settled the exact complexity of deciding primality for deterministic finite automata in 2010. For finite languages, Mateescu…
We consider languages generated by weighted context-free grammars. It is shown that the behaviour of large texts is controlled by saddle-point equations for an appropriate generating function. We then consider ensembles of grammars, in…
Fixed-vocabulary language models fail to account for one of the most characteristic statistical facts of natural language: the frequent creation and reuse of new word types. Although character-level language models offer a partial solution…
{log} (read 'setlog') was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, {log} is a constraint satisfiability solver implementing…
Slang is a commonly used type of informal language that poses a daunting challenge to NLP systems. Recent advances in large language models (LLMs), however, have made the problem more approachable. While LLM agents are becoming more widely…
Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
Large language models have advanced natural language understanding and generation, but their use as autonomous agents introduces architectural challenges for multi-step tasks. Existing frameworks often mix cognition, memory, and control in…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such…
In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final…
Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…
Many current artificial general intelligence (AGI) and natural language processing (NLP) architectures do not possess general conversational intelligence--that is, they either do not deal with language or are unable to convey knowledge in a…
The left-corner transform removes left-recursion from (probabilistic) context-free grammars and unification grammars, permitting simple top-down parsing techniques to be used. Unfortunately the grammars produced by the standard left-corner…
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a…