207 research outputs found
On QBF Proofs and Preprocessing
QBFs (quantified boolean formulas), which are a superset of propositional
formulas, provide a canonical representation for PSPACE problems. To overcome
the inherent complexity of QBF, significant effort has been invested in
developing QBF solvers as well as the underlying proof systems. At the same
time, formula preprocessing is crucial for the application of QBF solvers. This
paper focuses on a missing link in currently-available technology: How to
obtain a certificate (e.g. proof) for a formula that had been preprocessed
before it was given to a solver? The paper targets a suite of commonly-used
preprocessing techniques and shows how to reconstruct certificates for them. On
the negative side, the paper discusses certain limitations of the
currently-used proof systems in the light of preprocessing. The presented
techniques were implemented and evaluated in the state-of-the-art QBF
preprocessor bloqqer.Comment: LPAR 201
A Logical Approach to Efficient Max-SAT solving
Weighted Max-SAT is the optimization version of SAT and many important
problems can be naturally encoded as such. Solving weighted Max-SAT is an
important problem from both a theoretical and a practical point of view. In
recent years, there has been considerable interest in finding efficient solving
techniques. Most of this work focus on the computation of good quality lower
bounds to be used within a branch and bound DPLL-like algorithm. Most often,
these lower bounds are described in a procedural way. Because of that, it is
difficult to realize the {\em logic} that is behind.
In this paper we introduce an original framework for Max-SAT that stresses
the parallelism with classical SAT. Then, we extend the two basic SAT solving
techniques: {\em search} and {\em inference}. We show that many algorithmic
{\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in
{\em logic} terms with our framework in a unified manner.
Besides, we introduce an original search algorithm that performs a restricted
amount of {\em weighted resolution} at each visited node. We empirically
compare our algorithm with a variety of solving alternatives on several
benchmarks. Our experiments, which constitute to the best of our knowledge the
most comprehensive Max-sat evaluation ever reported, show that our algorithm is
generally orders of magnitude faster than any competitor
Classical simulation complexity of extended Clifford circuits
Clifford gates are a winsome class of quantum operations combining
mathematical elegance with physical significance. The Gottesman-Knill theorem
asserts that Clifford computations can be classically efficiently simulated but
this is true only in a suitably restricted setting. Here we consider Clifford
computations with a variety of additional ingredients: (a) strong vs. weak
simulation, (b) inputs being computational basis states vs. general product
states, (c) adaptive vs. non-adaptive choices of gates for circuits involving
intermediate measurements, (d) single line outputs vs. multi-line outputs. We
consider the classical simulation complexity of all combinations of these
ingredients and show that many are not classically efficiently simulatable
(subject to common complexity assumptions such as P not equal to NP). Our
results reveal a surprising proximity of classical to quantum computing power
viz. a class of classically simulatable quantum circuits which yields universal
quantum computation if extended by a purely classical additional ingredient
that does not extend the class of quantum processes occurring.Comment: 17 pages, 1 figur
Clause Redundancy and Preprocessing in Maximum Satisfiability
The study of clause redundancy in Boolean satisfiability (SAT) has proven significant in various terms, from fundamental insights into preprocessing and inprocessing to the development of practical proof checkers and new types of strong proof systems. We study liftings of the recently-proposed notion of propagation redundancy-based on a semantic implication relationship between formulas-in the context of maximum satisfiability (MaxSAT), where of interest are reasoning techniques that preserve optimal cost (in contrast to preserving satisfiability in the realm of SAT). We establish that the strongest MaxSAT-lifting of propagation redundancy allows for changing in a controlled way the set of minimal correction sets in MaxSAT. This ability is key in succinctly expressing MaxSAT reasoning techniques and allows for obtaining correctness proofs in a uniform way for MaxSAT reasoning techniques very generally. Bridging theory to practice, we also provide a new MaxSAT preprocessor incorporating such extended techniques, and show through experiments its wide applicability in improving the performance of modern MaxSAT solvers.Peer reviewe
Even shorter proofs without new variables
Proof formats for SAT solvers have diversified over the last decade, enabling
new features such as extended resolution-like capabilities, very general
extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.
Interference-based methods have been proven effective, and some theoretical
work has been undertaken to better explain their limits and semantics. In this
work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and
the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural
generalizations then become apparent, enabling even shorter proofs of the
pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and
smaller unsatisfiable core generation.Comment: 21 page
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