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We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as…
We approach the problem of computing a $D_{3}$-synchronizing word of minimum length for a given nondeterministic automaton via its encoding as an instance of SAT and invoking a SAT solver. We also present some experimental results.
Satisfiability Modulo Theories (SMT) specifications often rely on quantifiers to remain concise and declarative. However, checking the satisfiability of such specifications directly can be inefficient. A common optimization is to ground the…
Local Search meta-heuristics have been proven a viable approach to solve difficult optimization problems. Their performance depends strongly on the search space landscape, as defined by a cost function and the selected neighborhood…
This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
X3 is a lossless optimizing dictionary-based data compressor. The algorithm uses a combination of a dictionary, context modeling, and arithmetic coding. Optimization adds the ability to find the most appropriate parameters for each file.…
The poset cover problem seeks a minimum set of partial orders whose linear extensions cover a given set of linear orders. Recognizing its NP-completeness, we devised a non-trivial reduction to the Boolean satisfiability problem using a…
We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles…
Test-time scaling investigates whether a fixed diffusion language model (DLM) can generate better outputs when given more inference compute, without additional training. However, naive best-of-$K$ sampling is fundamentally limited because…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as…
We present Woorpje, a string solver for bounded word equations (i.e., equations where the length of each variable is upper bounded by a given integer). Our algorithm works by reformulating the satisfiability of bounded word equations as a…
Modern SMT solvers, such as Z3, offer user-controllable strategies, enabling users to tailor solving strategies for their unique set of instances, thus dramatically enhancing solver performance for their use case. However, this approach of…
We present OSTRICH2, the latest evolution of the SMT solver OSTRICH for string constraints. OSTRICH2 supports a wide range of complex functions on strings and provides completeness guarantees for a substantial fragment of string…
Zero-shot text classification typically relies on prompt engineering, but the inherent prompt brittleness of large language models undermines its reliability. Minor changes in prompt can cause significant discrepancies in model performance.…
Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver…
This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short).…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…