Limitations of restricted branching in clause learning

Järvisalo, Matti; Junttila, Tommi

doi:10.1007/s10601-008-9062-z

Cited by 19 publications

(12 citation statements)

References 43 publications

(73 reference statements)

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“…the parity function. This result is contrasting to the results of Järvisalo and Junttila [11] who show that there are formulas for which it is harmful for a SAT solver to make decisions only on non-auxiliary variables. This suggests that in general, it is neither beneficial to start deciding on auxiliary variables nor on the non-auxiliary ones.…”

Section: Resultscontrasting

confidence: 91%

On Exponential Lower Bounds for Partially Ordered Resolution

Janota

2016

SAT

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Is well-known that the proof size in propositional resolution is sensitive to the order of how variables are resolved on. Indeed, imposing a certain resolution order can lead to an exponential blowup compared to unrestricted resolution. In this paper we study even a weaker restriction. We require that one partition of variables is resolved on before the second partition (this is a special case of a partial order). We show that this also can lead to an exponential blowup. This helps us to understand why dynamic variable orderings in SAT solvers is so successful but also it motivates further investigation in variable orderings in SAT solvers.

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Section: Resultscontrasting

confidence: 91%

On Exponential Lower Bounds for Partially Ordered Resolution

Janota

2016

SAT

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“…[30,31] for a related discussion); however, the experimental analysis in Section 4 shows that this is the case. …”

Section: Theorem 311 For Any Af F = (A R) Argument α ∈ a And σ ∈mentioning

confidence: 99%

Abstract solvers for Dung’s argumentation frameworks

Brochenin

Linsbichler

Maratea

et al. 2018

AAC

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TU Wien, Austria E-mails: linsbich@dbai.tuwien.ac.at, wallner@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at Abstract. Abstract solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have several advantages. In particular, they provide a uniform formal representation that allows for precise comparisons of different algorithms. Recently, this new methodology has proven successful in declarative paradigms such as Propositional Satisfiability and Answer Set Programming. In this paper, we apply this machinery to Dung's abstract argumentation frameworks. We first provide descriptions of several advanced algorithms for the preferred semantics in terms of abstract solvers. We also show how it is possible to obtain new abstract solutions by "combining" concepts of existing algorithms by means of combining abstract solvers. Then, we implemented a new solving procedure based on our findings in CEGARTIX, and call it CEGARTIX+. We finally show that CEGARTIX+ is competitive and complementary in its performance to CEGARTIX on benchmarks of the first and second argumentation competition.Keywords: Abstract argumentation, abstract solvers IntroductionDung's concept of abstract argumentation [23] is nowadays a core formalism in Artificial Intelligence [4,46]. The problem of solving certain reasoning tasks on such frameworks is the centerpiece of many advanced higher-level argumentation systems. The problems to be solved can however be intractable and might even be hard for the second level of the polynomial hierarchy [24,26]. Thus, efficient and advanced algorithms have to be developed in order to deal with real-world size data within reasonable performance bounds. The argumentation community is currently facing this challenge [17] [44]. Hereby, one characterizes the possible states of computation as nodes of a graph, and the techniques (i.e., the computation steps in the algorithms) as arcs between nodes. In this way, the whole solving process amounts to a path in the graph. This concept proved successful for SAT [44], and also has been applied to several variants of Answer Set Programming [6,36,37].In this paper, we apply abstract solvers to certain problems in Dung's argumentation frameworks. In order to understand whether abstract solvers are well suited also for this domain, we consider quite advanced algorithms for solving problems that are hard for the second level of the polynomial hierarchy -the considered algorithms range from dedicated [45] to reduction-based [13,25] approaches (see [19] for a survey). We show that abstract solvers allow for convenient algorithms design resulting in a clear and mathematically precise description. Moreover, formal properties of the algorithms (i.e. correctness) are easily specified by means of related graph properties (i.e. reachability). We then illustrate how abstract solvers allow to highlight in a more clear way similarities and differences among solvin...

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“…-Structure-Based Decision Heuristics [6,7,11,12], -Structure-Exploiting Local Search [9,10], -Hard Satisfiable SAT Benchmark Families [4].…”

Section: Contributions Of the Thesismentioning

confidence: 99%

“…Extending our previous study of structure-based branching in DPLL [8], both static ("input-restricted") [7] and dynamic ("top-down") [6] branching heuristics are considered. Extending our previous study of structure-based branching in DPLL [8], both static ("input-restricted") [7] and dynamic ("top-down") [6] branching heuristics are considered.…”

Section: Structure-based Decision Heuristicsmentioning

confidence: 99%