91 research outputs found
Symmetry within Solutions
We define the concept of an internal symmetry. This is a symmety within a
solution of a constraint satisfaction problem. We compare this to solution
symmetry, which is a mapping between different solutions of the same problem.
We argue that we may be able to exploit both types of symmetry when finding
solutions. We illustrate the potential of exploiting internal symmetries on two
benchmark domains: Van der Waerden numbers and graceful graphs. By identifying
internal symmetries we are able to extend the state of the art in both cases.Comment: AAAI 2010, Proceedings of Twenty-Fourth AAAI Conference on Artificial
Intelligenc
Constructing Minimal Perfect Hash Functions Using SAT Technology
Minimal perfect hash functions (MPHFs) are used to provide efficient access
to values of large dictionaries (sets of key-value pairs). Discovering new
algorithms for building MPHFs is an area of active research, especially from
the perspective of storage efficiency. The information-theoretic limit for
MPHFs is 1/(ln 2) or roughly 1.44 bits per key. The current best practical
algorithms range between 2 and 4 bits per key. In this article, we propose two
SAT-based constructions of MPHFs. Our first construction yields MPHFs near the
information-theoretic limit. For this construction, current state-of-the-art
SAT solvers can handle instances where the dictionaries contain up to 40
elements, thereby outperforming the existing (brute-force) methods. Our second
construction uses XOR-SAT filters to realize a practical approach with
long-term storage of approximately 1.83 bits per key.Comment: Accepted for AAAI 202
SAT Competition 2018
Peer reviewe
Exponential separations using guarded extension variables
We study the complexity of proof systems augmenting resolution with inference
rules that allow, given a formula in conjunctive normal form, deriving
clauses that are not necessarily logically implied by but whose
addition to preserves satisfiability. When the derived clauses are
allowed to introduce variables not occurring in , the systems we
consider become equivalent to extended resolution. We are concerned with the
versions of these systems without new variables. They are called BC,
RAT, SBC, and GER, denoting respectively blocked clauses,
resolution asymmetric tautologies, set-blocked clauses, and generalized
extended resolution. Each of these systems formalizes some restricted version
of the ability to make assumptions that hold "without loss of generality,"
which is commonly used informally to simplify or shorten proofs.
Except for SBC, these systems are known to be exponentially weaker than
extended resolution. They are, however, all equivalent to it under a relaxed
notion of simulation that allows the translation of the formula along with the
proof when moving between proof systems. By taking advantage of this fact, we
construct formulas that separate RAT from GER and vice versa. With
the same strategy, we also separate SBC from RAT. Additionally, we
give polynomial-size SBC proofs of the pigeonhole principle, which
separates SBC from GER by a previously known lower bound. These
results also separate the three systems from BC since they all simulate
it. We thus give an almost complete picture of their relative strengths
- …