Related papers: Regular realizability problems and context-free la…
We introduce p-equivalence by asymptotic probabilities, which is a weak almost-equivalence based on zero-one laws in finite model theory. In this paper, we consider the computational complexities of p-equivalence problems for regular…
We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…
Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…
To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
Studying language models (LMs) in terms of well-understood formalisms allows us to precisely characterize their abilities and limitations. Previous work has investigated the representational capacity of recurrent neural network (RNN) LMs in…
Reasoning-Intensive Retrieval (RIR) targets retrieval settings where relevance is mediated by latent inferential links between a query and supporting evidence, rather than semantic similarity. Motivated by the emergent reasoning abilities…
We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
Reading comprehension (RC)---in contrast to information retrieval---requires integrating information and reasoning about events, entities, and their relations across a full document. Question answering is conventionally used to assess RC…
Routing problems are common in mobile robotics, encompassing tasks such as inspection, surveillance, and coverage. Depending on the objective and constraints, these problems often reduce to variants of the Traveling Salesman Problem (TSP),…
Reinforcement Learning (RL) problems are being considered under increasingly more complex structures. While tabular and linear models have been thoroughly explored, the analytical study of RL under nonlinear function approximation,…
For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…
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…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Designing query languages for graph structured data is an active field of research. Evaluating a query on a graph results in a relation on the set of its nodes. In other words, a query is a mechanism for defining relations on a graph. Some…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
Large Language Models (LLMs) have shown remarkable success on a wide range of math and reasoning benchmarks. However, we observe that they often struggle when faced with unreasonable math problems. Instead of recognizing these issues,…
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable…