Related papers: Regular realizability problems and context-free la…
In a recent thread of papers, we have introduced FQL, a precise specification language for test coverage, and developed the test case generation engine FShell for ANSI C. In essence, an FQL test specification amounts to a set of regular…
We initiate a complexity theoretic study of the language based graph reachability problem (L-REACH) : Fix a language L. Given a graph whose edges are labeled with alphabet symbols of the language L and two special vertices s and t, test if…
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of…
State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study…
Kleinberg and Mullainathan showed that language generation in the limit is always possible at the level of computability: given enough positive examples, a learner can eventually generate data indistinguishable from a target language.…
The Int_reg-problem of a combinatorial problem P asks, given a nondeterministic automaton M as input, whether the language L(M) accepted by M contains any positive instance of the problem P. We consider the Int_reg-problem for a number of…
The task of reading comprehension (RC), often implemented as context-based question answering (QA), provides a primary means to assess language models' natural language understanding (NLU) capabilities. Yet, when applied to large language…
We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word,…
Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable…
The purpose of this paper is to investigate the connection between context-free grammars and normal ordering problem, and then to explore various extensions of the Stirling grammar. We present grammatical characterizations of several well…
We show that testing inclusion between languages represented by regular expressions with numerical occurrence indicators (RE#s) is NP-hard, even if the expressions satisfy the requirement of "unambiguity", which is required for XML Schema…
Mathematical reasoning is a central challenge for large language models (LLMs), requiring not only correct answers but also faithful reasoning processes. Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising…
In recent years some researchers have explored the use of reinforcement learning (RL) algorithms as key components in the solution of various natural language processing tasks. For instance, some of these algorithms leveraging deep neural…
What can large language models learn? By definition, language models (LM) are distributions over strings. Therefore, an intuitive way of addressing the above question is to formalize it as a matter of learnability of classes of…
Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are…
Let $\Sigma = X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,..., x_m^{-1} \}$ and let $G$ be a group with set of generators $\Sigma$. Let $\mathfrak{L} (G) =\left\{ \left. \omega \in \Sigma^* \; \right\vert \;\omega \equiv e \;…
The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries…
A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…