Corrections to <i>Canonical expressions in Boolean algebra</i>

Blake, Archie

doi:10.2307/2267595

Cited by 85 publications

(99 citation statements)

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“…The consensus method has been proposed [4,32,35] as a way of enumerating all the prime implicants of a propositional function in DNF. If f is in CNF, then it is straightforward to derive a DNF representation of ¬f , to which the consensus procedure can be applied to find its prime implicants.…”

Section: Consensus Methods and Resolutionmentioning

confidence: 99%

Existential Quantification as Incremental SAT

Brauer

King

Kriener

2011

Computer Aided Verification

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Abstract. This paper presents an elegant algorithm for existential quantifier elimination using incremental SAT solving. This approach contrasts with existing techniques in that it is based solely on manipulating the SAT instance rather than requiring any reengineering of the SAT solver or needing an auxiliary data-structure such as a BDD. The algorithm combines model enumeration with the generation of shortest prime implicants so as to converge onto a quantifier-free formula presented in CNF. We apply the technique to a number of hardware circuits and transfer functions to demonstrate the effectiveness of the method.

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Section: Consensus Methods and Resolutionmentioning

confidence: 99%

Existential Quantification as Incremental SAT

Brauer

King

Kriener

2011

Computer Aided Verification

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“…Resolution (Res), introduced by Blake [1937] and Robinson [1965], is a refutational proof system for formulas in CNF. The lines in the Res proofs are clauses.…”

Section: Resolution Calculimentioning

confidence: 99%

Are Short Proofs Narrow? QBF Resolution Is Not So Simple

Beyersdorff

Chew

Mahajan

et al. 2017

ACM Trans. Comput. Logic

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The groundbreaking paper 'Short proofs are narrow -resolution made simple' by Ben-Sasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in their fundamental work, Atserias and Dalmau (J. Comput. Syst. Sci. 2008) show that lower bounds for space again can be obtained via lower bounds for width.In this paper we assess whether similar techniques are effective for resolution calculi for quantified Boolean formulas (QBF). There are a number of different QBF resolution calculi like Q-resolution (the classical extension of propositional resolution to QBF) and the more recent calculi A Exp+Res and IR-calc. For these systems a mixed picture emerges. Our main results show that both the relations between size and width as well as between space and width drastically fail in Q-resolution, even in its weaker tree-like version. On the other hand, we obtain positive results for the expansion-based resolution systems A Exp+Res and IR-calc, however only in the weak tree-like models.Technically, our negative results rely on showing width lower bounds together with simultaneous upper bounds for size and space. For our positive results we exhibit space and width-preserving simulations between QBF resolution calculi.

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“…Previous Work At the core, CDCL searches for proofs in the proof system resolution [14]. While pre-and inprocessing techniques can, and sometimes do, go significantly beyond resolution (incorporating, e.g., solving of linear equations mod 2 and reasoning with cardinality constraints), understanding the power of even just the fundamental CDCL algorithm seems like an interesting and challenging problem in its own right.…”

Section: Introductionmentioning

confidence: 99%

Trade-offs Between Time and Memory in a Tighter Model of CDCL SAT Solvers

Elffers

Johannsen

Lauria

et al. 2016

Theory and Applications of Satisfiability Testing – SAT 2016

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Abstract. A long line of research has studied the power of conflictdriven clause learning (CDCL) and how it compares to the resolution proof system in which it searches for proofs. It has been shown that CDCL can polynomially simulate resolution even with an adversarially chosen learning scheme as long as it is asserting. However, the simulation only works under the assumption that no learned clauses are ever forgotten, and the polynomial blow-up is significant. Moreover, the simulation requires very frequent restarts, whereas the power of CDCL with less frequent or entirely without restarts remains poorly understood. With a view towards obtaining results with tighter relations between CDCL and resolution, we introduce a more fine-grained model of CDCL that captures not only time but also memory usage and number of restarts. We show how previously established strong size-space trade-offs for resolution can be transformed into equally strong trade-offs between time and memory usage for CDCL, where the upper bounds hold for CDCL without any restarts using the standard 1UIP clause learning scheme, and the (in some cases tightly matching) lower bounds hold for arbitrarily frequent restarts and arbitrary clause learning schemes.

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Corrections to Canonical expressions in Boolean algebra

Cited by 85 publications

References 1 publication

Existential Quantification as Incremental SAT

Existential Quantification as Incremental SAT

Are Short Proofs Narrow? QBF Resolution Is Not So Simple

Trade-offs Between Time and Memory in a Tighter Model of CDCL SAT Solvers

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