The Taming of the (X)OR

Baumgartner, Peter; Massacci, Fabio

doi:10.1007/3-540-44957-4_34

Cited by 18 publications

(15 citation statements)

References 13 publications

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“…4 The alternating use of ethylenediamine tetraacetic acid (EDTA) and sodium hypochlorite (NaOCl) has long been effective in removing the endodontic smear layer. 5 However, prolonged application of EDTA (>1min) may cause unintended erosion of the peritubular dentine, and it also has demonstrated limited antibacterial activity. 6 great physical properties and also ability to produce hydroxyapatite, which affords a direct bond between dentin and the material.…”

Section: |mentioning

confidence: 99%

Effects of Mtad on the Bond Strength of Bioceramic Root Canal Sealer

Dumani¹,

Uçan²,

Ateş³

et al. 2020

J. res. dent.

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Aim: The aim of this in-vitro study was to investigate the effects of MTAD (a mixture of doxycycline, citric acid, and a detergent) on the bond strength of AH Plus (Dentsply DeTrey GmbH, Konstanz, Germany) and EndoSequence BC sealer (Brasseler USA, Savannah, Georgia, USA). Materials & Methods: Eighty-four decoronated single-rooted human incisor teeth were prepared with Reciproc R25 files (VDW, Munich, Germany), and the canal was irrigated with 5 mL 1.3% NaOCl. The roots were randomly assigned to four groups (n = 21), according to the final irrigation protocol and sealer selection: Group 1: distilled water-AH Plus; Group 2: distilled water-EndoSequence BC; Group 3: MTAD-AH Plus; Group 4: MTAD-EndoSequence BC. For the final flush, in Groups 1 and 2, the root canals were irrigated with 5mL of distilled water; in Groups 3 and 4, 5mL of MTAD was used for 1 minute. After root canal obturation, specimens was embedded in an acrylic block and sectioned horizontally at three levels (coronal, middle, apical). Bond strength of sealer to root canal dentin was assessed via push-out test using a universal testing machine. Results: There were no significant differences among the groups in coronal and apical thirds. In the middle root third, Group 4 showed significantly lower push-out bond strength values than Group 2 (p=0.023). No significant difference was found between the two root canal sealers. Conclusions: Overall, MTAD final irrigation caused lower push-out bond strenght values than distilled water with no significancy.

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Section: |mentioning

confidence: 99%

Effects of Mtad on the Bond Strength of Bioceramic Root Canal Sealer

Dumani¹,

Uçan²,

Ateş³

et al. 2020

J. res. dent.

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“…The symmetric width wid : CLS → N 0 is defined in the same way, only that for F ∈ USAT we define wid(F ) as the minimal k ∈ N 0 such that there is T : F ⊢ ⊥, where all clauses of T (axioms and resolvents) have length at most k. 7) Symmetric width is only applied to clause-sets with bounded clause-length, and here everything can be done as well via asymmetric width, as discussed in [54]. It might be that symmetric width could have a relevant combinatorial meaning, so that symmetric and asymmetric width both have their roles.…”

Section: W-hardness and Wc Kmentioning

confidence: 99%

On SAT Representations of XOR Constraints

Gwynne

Kullmann

2014

Language and Automata Theory and Applications

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We study the problem of finding good CNF-representations F of systems of linear equations S over the two-element field, also known as systems of XORconstraints x1 ⊕ · · · ⊕ x k = ε, ε ∈ {0, 1}, or systems of parity-constraints. The number of equations in S is m, the number of variables is n. These representations are used as parts of SAT problems F * ⊃ F , such that F has "good" properties for SAT solving in the context of F * ; here F * may for example represent the problem of finding the key for a cryptographic cipher. The basic quality criterion is "arc consistency" (AC), that is, for every partial assignment ϕ to the variables of S, all assignments xi = ε forced by ϕ are determined by unit-clause propagation on the result ϕ * F of the application.We show there is no AC-representation of polynomial size for arbitrary S. We use the lower bound on monotone circuits for monotone span programs from [2], and we show a close relation between monotone circuits and ACrepresentations, based on the work in [9]. We then turn to constructing good representations. We analyse the basic translation F = X1(S), which translates each constraint on its own, by splitting up x1 ⊕ · · · ⊕ x k into sums x1 ⊕ x2 = y2, y2 ⊕ x3 = y3, . . . , y k−1 ⊕ x k = ε, introducing auxiliary variables yi. We show that X1(S * ), where S * is obtained from S by considering all derived equations, is an AC-representation of S. The derived equations are obtained by adding up the equations of all sub-systems S ′ ⊆ S. There are 2 m such S ′ , and computing an AC-representation is fixed-parameter tractable (fpt) in the parameter m, improving [61], which showed fpt in n.To obtain stronger representations, instead of mere AC we consider the class PC of propagation-complete clause-sets, as introduced in [12]. The stronger criterion is F ∈ PC, which requires for all partial assignments, possibly involving also the auxiliary (new) variables in F , that forced assignments can be determined by unit-clause propagation. Using "propagation hardness" phd(F ) ∈ N0 as introduced in [37], we have F ∈ PC ⇔ phd(F ) ≤ 1. We show that X1 applied to a single equation (m = 1) yields a translation in PC, i.e., phd(X1(S)) ≤ 1. Then we study m = 2. Now S * has two equations more, and X1(S * ) is an AC-representation, but the "distance" to PC is arbitrarily high, i.e., phd(X1(S * )) is unbounded (using results from [54]). We show two possibilities to remedy this (for m = 2). On the one hand, if instead of unit-clause propagation we allow (arbitrary) resolution with clauses of length at most 3 (i.e., 3-resolution), and only require refutation of inconsistencies after (arbitrary, partial) instantiations, then even just X1(S) suffices. On the other hand, with a more intelligent translation, which avoids duplication of equivalent auxiliary variables yi, we obtain a (short) representation in PC. We conjecture that also the general case can be handled this way, that is, computing a representation F ∈ PC of S is fpt in m.Recall that the two-element field Z 2 has elements 0, 1, where ad...

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“…The correctness of Expl ⊕ (v, W ), formalized in the following theorem, can be established by induction and using Eqs. ( 4) and (5).…”

Section: Parity Explanationsmentioning

confidence: 99%

“…Related work. In [5] a calculus combining basic DPLL without clause learning and Gauss elimination is proposed; their Gauss rules are similar to the general rule ⊕-Gen we use in Sect. 8.…”

Section: Introductionmentioning

confidence: 99%

Conflict-Driven XOR-Clause Learning

Laitinen

Junttila

Niemelä

2012

Theory and Applications of Satisfiability Testing – SAT 2012

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Abstract. Modern conflict-driven clause learning (CDCL) SAT solvers are very good in solving conjunctive normal form (CNF) formulas. However, some application problems involve lots of parity (xor) constraints which are not necessarily efficiently handled if translated into CNF. This paper studies solving CNF formulas augmented with xor-clauses in the DPLL(XOR) framework where a CDCL SAT solver is coupled with a separate xor-reasoning module. New techniques for analyzing xor-reasoning derivations are developed, allowing one to obtain smaller CNF clausal explanations for xor-implied literals and also to derive and learn new xor-clauses. It is proven that these new techniques allow very short unsatisfiability proofs for some formulas whose CNF translations do not have polynomial size resolution proofs, even when a very simple xor-reasoning module capable only of unit propagation is applied. The efficiency of the proposed techniques is evaluated on a set of challenging logical cryptanalysis instances.

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The Taming of the (X)OR

Cited by 18 publications

References 13 publications

Effects of Mtad on the Bond Strength of Bioceramic Root Canal Sealer

Effects of Mtad on the Bond Strength of Bioceramic Root Canal Sealer

On SAT Representations of XOR Constraints

Conflict-Driven XOR-Clause Learning

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