Related papers: An Approximate Skolem Function Counter
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…
Given a propositional formula F(x,y), a Skolem function for x is a function \Psi(y), such that substituting \Psi(y) for x in F gives a formula semantically equivalent to \exists F. Automatically generating Skolem functions is of significant…
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…
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…
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…
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…
Propositional model counting} (#SAT), i.e., counting the number of satisfying assignments of a propositional formula, is a problem of significant theoretical and practical interest. Due to the inherent complexity of the problem, approximate…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
Boolean functional synthesis is the process of constructing a Boolean function from a Boolean specification that relates input and output variables. Despite significant recent developments in synthesis algorithms, Boolean functional…
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…
Given a Boolean formula $\phi$ over $n$ variables, the problem of model counting is to compute the number of solutions of $\phi$. Model counting is a fundamental problem in computer science with wide-ranging applications. Owing to the…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
Hashing-based model counting has emerged as a promising approach for large-scale probabilistic inference on graphical models. A key component of these techniques is the use of xor-based 2-universal hash functions that operate over Boolean…
First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
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…
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…
Given a relational specification R(X, Y), where X and Y are sequences of input and output variables, we wish to synthesize each output as a function of the inputs such that the specification holds. This is called the Boolean functional…
We give two approximation algorithms solving the Stochastic Boolean Function Evaluation (SBFE) problem for symmetric Boolean functions. The first is an $O(\log n)$-approximation algorithm, based on the submodular goal-value approach of…