DeepAI

# Hard satisfiable formulas for DPLL algorithms using heuristics with small memory

DPLL algorithm for solving the Boolean satisfiability problem (SAT) can be represented in the form of a procedure that, using heuristics A and B, select the variable x from the input formula φ and the value b and runs recursively on the formulas φ[x := b] and φ[x := 1 - b]. Exponential lower bounds on the running time of DPLL algorithms on unsatisfiable formulas follow from the lower bounds for tree-like resolution proofs. Lower bounds on satisfiable formulas are also known for some classes of DPLL algorithms such as "myopic" and "drunken" algorithms. All lower bounds are made for the classes of DPLL algorithms that limit heuristics access to the formula. In this paper we consider DPLL algorithms with heuristics that have unlimited access to the formula but use small memory. We show that for any pair of heuristics with small memory there exists a family of satisfiable formulas Φ_n such that a DPLL algorithm that uses these heuristics runs in exponential time on the formulas Φ_n.

02/20/2020

### Algorithms and Lower Bounds for de Morgan Formulas of Low-Communication Leaf Gates

The class FORMULA[s] ∘𝒢 consists of Boolean functions computable by size...
09/26/2013

### Lower Bounds for Exact Model Counting and Applications in Probabilistic Databases

The best current methods for exactly computing the number of satisfying ...
06/18/2017

### The impact of Entropy and Solution Density on selected SAT heuristics

In a recent article [Oh'15], Oh examined the impact of various key heuri...
02/04/2000

### On the accuracy and running time of GSAT

Randomized algorithms for deciding satisfiability were shown to be effec...
01/01/1998

### Incremental Recompilation of Knowledge

Approximating a general formula from above and below by Horn formulas (i...
09/15/2017

### The Orthogonal Vectors Conjecture for Branching Programs and Formulas

In the Orthogonal Vectors (OV) problem, we wish to determine if there is...
09/26/2011

### Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas

Resolution is the rule of inference at the basis of most procedures for ...