Related papers: Skolem Functions for Factored Formulas
One approach to probabilistic inference involves counting the number of models of a given Boolean formula. Here, we are interested in inferences involving higher-order objects, i.e., functions. We study the following task: Given a Boolean…
Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…
We propose a new decision procedure for dependency quantified Boolean formulas (DQBF) that uses interpolation-based definition extraction to compute Skolem functions in a counter-example guided inductive synthesis (CEGIS) loop. In each…
Boolean Skolem function synthesis concerns synthesizing outputs as Boolean functions of inputs such that a relational specification between inputs and outputs is satisfied. This problem, also known as Boolean functional synthesis, has…
Given a Boolean formula F(X,Y), where X is a vector of outputs and Y is a vector of inputs, the Boolean functional synthesis problem requires us to compute a Skolem function vector G(Y)for X such that F(G(Y),Y) holds whenever \exists X…
In this paper we show that PSPACE is equal to 4th level in the polynomial hierarchy. We also deduce a lot of important consequences. True quantified Boolean formula is a generalisation of the Boolean Satisfiability Problem, where…
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that…
This is a thesis that was defended in 2009 at Lomonosov Moscow State University. In Chapter 1: 1. It is proved that that the class of lower (Skolem) elementary functions is the set of all polynomial-bounded functions that can be obtained by…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
Given a Boolean relational specification between inputs and outputs, the problem of functional synthesis is to construct a function that maps each assignment of the input to an assignment of the output such that each tuple of input and…
The realizability problem in requirements engineering is to determine the existence of an implementation that meets the given formal requirements. A step forward after realizability is proven, is to construct such an implementation…
In this work, a functional variant of the polynomial analogue of the classical Gandy's fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of the recursive function does not go beyond the…
First-order model counting emerged recently as a novel reasoning task, at the core of efficient algorithms for probabilistic logics. We present a Skolemization algorithm for model counting problems that eliminates existential quantifiers…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
A quantified Boolean formula (QBF) is a propositional formula extended with universal and existential quantification over propositions. There are two methodologies in CEGAR based QBF solving techniques, one that is based on a refinement…
We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result - which shows that the Excluded Middle principle can be used to…
Reasoning on large and complex real-world models is a computationally difficult task, yet one that is required for effective use of many AI applications. A plethora of inference algorithms have been developed that work well on specific…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
Factorization machine (FM) variants are widely used for large scale real-time content recommendation systems, since they offer an excellent balance between model accuracy and low computational costs for training and inference. These systems…
Generating executable simulations from natural language specifications remains a challenging problem due to the limited reasoning capacity of large language models (LLMs) when confronted with large, interconnected codebases. This paper…