Related papers: Regular realizability problems and regular languag…
Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
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…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
Enhancing the mathematical reasoning capabilities of LLMs has garnered significant attention in both the mathematical and computer science communities. Recent works have made substantial progress in both Natural Language (NL) reasoning and…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
The paper completely characterizes the primality of acyclic DFAs, where a DFA $\mathcal{A}$ is prime if there do not exist DFAs $\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) = \bigcap_{i=1}^{t}…
Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the languages recognized by {\em measure many 1-way quantum finite automata (MM-QFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$ with strict…
Large language models (LLMs) have demonstrated strong performance on formal language tasks, yet whether this reflects genuine symbolic reasoning or pattern matching on familiar constructions remains unclear. We introduce a benchmark for…
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants…
Requirements Engineering (RE) is the initial step towards building a software system. The success or failure of a software project is firmly tied to this phase, based on communication among stakeholders using natural language. The problem…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this long-standing problem which relates, for instance, to the reachability…
Piecewise testable languages form the first level of the Straubing-Th\'erien hierarchy. The membership problem for this level is decidable and testing if the language of a DFA is piecewise testable is NL-complete. The question has not yet…
Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V \subset [0,1], and the `literals' have the form "x \le a" or "x \ge a". We answer some open question regarding…
We show NP-completeness for various problems about the existence of arithmetic expression trees. When given a set of operations, inputs, and a target value does there exist an expression tree with those inputs and operations that evaluates…
Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…