Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms

10/29/2019
by   Tuhin Sahai, et al.
0

Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the hardness of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.

READ FULL TEXT

page 10

page 11

01/01/2020

Reinforcement Quantum Annealing: A Quantum-Assisted Learning Automata Approach

We introduce the reinforcement quantum annealing (RQA) scheme in which a...
03/16/2023

A Quantum SMT Solver for Bit-Vector Theory

Given a formula F of satisfiability modulo theory (SMT), the classical S...
10/21/2019

On speeding up factoring with quantum SAT solvers

There have been several efforts to apply quantum SAT solving methods to ...
08/28/2017

Two-Dimensional Indirect Binary Search for the Positive One-in-Three Satisfiability Problem

In this paper, we propose an algorithm for the positive one-in-three sat...
07/15/2020

A Faster Exact Algorithm to Count X3SAT Solutions

The Exact Satisfiability problem, XSAT, is defined as the problem of fin...
02/04/2019

Factoring semi-primes with (quantum) SAT-solvers

The assumed computationally difficulty of factoring large integers forms...
11/13/2017

Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management

We present the mapping of a class of simplified air traffic management (...

Please sign up or login with your details

Forgot password? Click here to reset