66 research outputs found
QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property
The QRAT (quantified resolution asymmetric tautology) proof system simulates
virtually all inference rules applied in state of the art quantified Boolean
formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding
and deleting clauses and universal literals that have a certain redundancy
property. To check for this redundancy property in QRAT, propositional unit
propagation (UP) is applied to the quantifier free, i.e., propositional part of
the QBF. We generalize the redundancy property in the QRAT system by QBF
specific UP (QUP). QUP extends UP by the universal reduction operation to
eliminate universal literals from clauses. We apply QUP to an abstraction of
the QBF where certain universal quantifiers are converted into existential
ones. This way, we obtain a generalization of QRAT we call QRAT+. The
redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT
based on UP. We report on proof theoretical improvements and experimental
results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer,
including appendi
Efficient Certified Resolution Proof Checking
We present a novel propositional proof tracing format that eliminates complex
processing, thus enabling efficient (formal) proof checking. The benefits of
this format are demonstrated by implementing a proof checker in C, which
outperforms a state-of-the-art checker by two orders of magnitude. We then
formalize the theory underlying propositional proof checking in Coq, and
extract a correct-by-construction proof checker for our format from the
formalization. An empirical evaluation using 280 unsatisfiable instances from
the 2015 and 2016 SAT competitions shows that this certified checker usually
performs comparably to a state-of-the-art non-certified proof checker. Using
this format, we formally verify the recent 200 TB proof of the Boolean
Pythagorean Triples conjecture
Efficient Certified RAT Verification
Clausal proofs have become a popular approach to validate the results of SAT
solvers. However, validating clausal proofs in the most widely supported format
(DRAT) is expensive even in highly optimized implementations. We present a new
format, called LRAT, which extends the DRAT format with hints that facilitate a
simple and fast validation algorithm. Checking validity of LRAT proofs can be
implemented using trusted systems such as the languages supported by theorem
provers. We demonstrate this by implementing two certified LRAT checkers, one
in Coq and one in ACL2
Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer
We solved a long-outstanding open problem in Ramsey theory, using SAT solving
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
MaxPre : An Extended MaxSAT Preprocessor
We describe MaxPre, an open-source preprocessor for (weighted partial) maximum satisfiability (MaxSAT). MaxPre implements both SAT-based and MaxSAT-specific preprocessing techniques, and offers solution reconstruction, cardinality constraint encoding, and an API for tight integration into SAT-based MaxSAT solvers.Peer reviewe
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
We present the latest major release version 6.0 of the quantified Boolean
formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of
the conflict-driven clause learning (CDCL) paradigm implemented in state of the
art propositional satisfiability (SAT) solvers. The Q-resolution calculus
(QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce
QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of
the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0
implements a variant of QCDCL which is based on a generalization of QRES. This
generalization is due to a set of additional axioms and leaves the original
Q-resolution rules unchanged. The generalization of QRES enables QCDCL to
potentially produce exponentially shorter proofs than the traditional variant.
We present an overview of the features implemented in DepQBF and report on
experimental results which demonstrate the effectiveness of generalized QRES in
QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS,
Springer, 201
Lifting QBF Resolution Calculi to DQBF
We examine the existing resolution systems for quantified Boolean formulas (QBF) and answer the question which of these calculi can be lifted to the more powerful Dependency QBFs (DQBF). An interesting picture emerges: While for QBF we have the strict chain of proof systems Q-Res < IR-calc < IRM-calc, the situation is quite different in DQBF. Q-Res and likewise universal resolution are too weak: they are not complete. IR-calc has the right strength: it is sound and complete. IRM-calc is too strong: it is not sound any more, and the same applies to long-distance resolution. Conceptually, we use the relation of DQBF to EPR and explain our new DQBF calculus based on IR-calc as a subsystem of first-order resolutio
A review of literature on parallel constraint solving
As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint algorithms are amenable to parallelisation; whether to use shared memory or distributed computation; whether to use static or dynamic decomposition; and how to best exploit portfolios and cooperating search. We review the literature, and see that we can sometimes do quite well, some of the time, on some instances, but we are far from a general solution. Yet there seems to be little overall guidance that can be given on how best to exploit multicore computers to speed up constraint solving. We hope at least that this survey will provide useful pointers to future researchers wishing to correct this situation
The Function of Anal Fin Egg-Spots in the Cichlid Fish Astatotilapia burtoni
Color and pigmentation patterns of animals are often targets of sexual selection because of their role in communication. Although conspicuous male traits are typically implicated with intersexual selection, there are examples where sex-specific displays play a role in an intrasexual context, e.g. when they serve as signals for aggression level and/or status. Here, we focus on the function of a conspicuous male ornament in the most species-rich tribe of cichlid fishes, the haplochromines. A characteristic feature of these ca. 1500 species are so-called egg-spots in form of ovoid markings on the anal fins of males, which are made up of carotenoid based pigment cells. It has long been assumed that these yellow, orange or reddish egg-spots play an important role in the courtship and spawning behavior of these maternal mouth-brooding fishes by mimicking the eggs of a conspecific female. The exact function of egg-spots remains unknown, however, and there are several hypotheses about their mode of action. To uncover the function of this cichlid-specific male ornament, we used female mate choice experiments and a male aggression test in the haplochromine species Astatotilapia burtoni. We manipulated the number and arrangement of egg-spots on the anal fins of males, or removed them entirely, and tested (1) female preference with visual contact only using egg-traps, (2) female preference with free contact using paternity testing with microsatellites and (3) male aggression. We found that females did not prefer males with many egg-spots over males with fewer egg-spots and that females tended to prefer males without egg-spots over males with egg-spots. Importantly, males without egg-spots sired clutches with the same fertilization rate as males with egg-spots. In male aggression trials, however, males with fewer egg-spots received significantly more attacks, suggesting that egg-spots are an important signal in intrasexual communication
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