Related papers: Random Logic Programs: Linear Model
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Randomized linear solvers randomly compress and solve a linear system with compelling theoretical convergence rates and computational complexities. However, such solvers suffer a substantial disconnect between their theoretical rates and…
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…
Alignment has quickly become a default ingredient in LLM development, with techniques such as reinforcement learning from human feedback making models act safely, follow instructions, and perform ever-better on complex tasks. While these…
We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a…
Selectivity estimation of a boolean query based on frequent itemsets can be solved by describing the problem by a linear program. However, the number of variables in the equations is exponential, rendering the approach tractable only for…
Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…
This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented…
We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this we use the two different mathematical tools of Propositional Logic and…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Large Language Models (LLMs) have transformed text generation through inherently probabilistic context-aware mechanisms, mimicking human natural language. In this paper, we systematically investigate the performance of various LLMs when…
We study the following problem: given a class of logic programs C, determine the maximum number of stable models of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…
A major problem in the study of large language models is to understand their inherent low-dimensional structure. We introduce an approach to study the low-dimensional structure of language models at a model-agnostic level: as sequential…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…