Related papers: An algorithm for 3-SAT problems
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
Classically, for many computational problems one can conclude time lower bounds conditioned on the hardness of one or more of key problems: k-SAT, 3SUM and APSP. More recently, similar results have been derived in the quantum setting…
As one of the three main pillars of fine-grained complexity theory, the 3SUM problem explains the hardness of many diverse polynomial-time problems via fine-grained reductions. Many of these reductions are either directly based on or…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…
We study a broad class of algorithmic problems with an "additive flavor" such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers,…
We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy…
An analysis of the average-case complexity of solving random 3-Satisfiability (SAT) instances with backtrack algorithms is presented. We first interpret previous rigorous works in a unifying framework based on the statistical physics…
We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known -- e.g.~[Fischer,…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
A 3-SAT problem is called positive and planar if all the literals are positive and the clause-variable incidence graph (i.e., SAT graph) is planar. The NAE 3-SAT and 1-in-3-SAT are two variants of 3-SAT that remain NP-complete even when…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
For each integer $n$ we present an explicit formulation of a compact linear program, with $O(n^3)$ variables and constraints, which determines the satisfiability of any 2SAT formula with $n$ boolean variables by a single linear…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of…
Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
There is a number of known NP class problems, and majority of them have been shown to be equivalent to others. In particular now it is clear that construction of a Gr\"{o}bner basis (or Buchberger algorithm) must be one of equivalent…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…