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Gent, Ian P.; MacIntyre, Ewan; Prosser, Patrick; Smith, Barbara M.; Walsh, Toby

doi:10.1023/a:1011454308633

Cited by 106 publications

(11 citation statements)

References 26 publications

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“…We hope that our experimental study of phase transitions for knowledge compilations would lead to similar developments in the knowledge compilation community. Our results in this work are similar in spirit to the seminal work by the CSP community in empirical identification of phase transition phenomenon in the early 1990s and their summarization in the form of conjectures [10,21,22,23]. It is worth emphasizing that theoretical proofs of these conjectures were presented nearly 20 years since the first empirical studies [15], and the efforts to establishing these conjectures contributed to the development of several theoretical tools of widespread applicability [2].…”

Section: Introductionsupporting

confidence: 80%

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Phase Transition Behavior in Knowledge Compilation

Gupta¹,

Roy²,

Meel³

2020

Preprint

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The study of phase transition behaviour in SAT has led to deeper understanding and algorithmic improvements of modern SAT solvers. Motivated by these prior studies of phase transitions in SAT, we seek to study the behaviour of size and compile-time behaviour for random k-CNF formulas in the context of knowledge compilation. We perform a rigorous empirical study and analysis of the size and runtime behavior for different knowledge compilation forms (and their corresponding compilation algorithms): d-DNNFs, SDDs and OBDDs across multiple tools and compilation algorithms. We employ instances generated from the random k-CNF model with varying generation parameters to empirically reason about the expected and median behavior of size and compilation-time for these languages. Our work is similar in spirit to the early work in CSP community on phase transition behavior in SAT/CSP. In a similar spirit, we identify the interesting behavior with respect to different parameters: clause density and solution density, a novel control parameter that we identify for the study of phase transition behavior in the context of knowledge compilation. Furthermore, we summarize our empirical study in terms of two concrete conjectures; a rigorous study of these conjectures will possibly require new theoretical tools.

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Section: Introductionsupporting

confidence: 80%

“…Subsequently, exploring phase transition behaviors with various random generative models has drawn considerable attention. [3,21,22,23,34,27].…”

Section: Related Workmentioning

confidence: 99%

Phase Transition Behavior in Knowledge Compilation

Gupta¹,

Roy²,

Meel³

2020

Preprint

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“…The random CSP model, also known as the random CSP instances generator, is proposed to enrich the study of the CSP. The initial proposed random models [10] [11] are called models A, B, C, and D, where the constraint scope size and domain size are fixed. Unfortunately for these models, it was proved by Achlioptas et al [12] that the generated instances suffer trivial unsatisfiability, that is, almost all instances are unsatisfiable when the number of variables is large.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome this flaw, many alternative models have been proposed. One technique is to incorporate a special combinatorial structure on constraints and ensure that the generated instance has certain consistency properties [10] [13]. Another technique is to change the scales of the parameters, including the size of the domain and the length of the constraint scope [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Clustering phase of a general constraint satisfaction problem model d-k-CSP

Wei

Gong

Zhou

2020

Physica A: Statistical Mechanics and its Applications

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“…-QCP: random quasi-group completion (the task of determining whether the missing entries of a partial Latin square can be filled in to obtain a complete Latin square [7]); using a range of parameter settings, we generated 30,620 SAT-encoded instances with a satisfiable/unsatisfiable ratio of 58.7/41.3. -SW-GCP: graph-coloring on small-world graphs [6]; using a range of parameter settings, we generated 20,000 SAT-encoded instances with a satisfiable/unsatisfiable ratio of 55.9/44.1.…”

Section: Methodsmentioning

confidence: 99%

Hierarchical Hardness Models for SAT

Hoos

Leyton‐Brown

Principles and Practice of Constraint Programming – CP 2007

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Abstract. Empirical hardness models predict a solver's runtime for a given instance of an N P-hard problem based on efficiently computable features. Previous research in the SAT domain has shown that better prediction accuracy and simpler models can be obtained when models are trained separately on satisfiable and unsatisfiable instances. We extend this work by training separate hardness models for each class, predicting the probability that a novel instance belongs to each class, and using these predictions to build a hierarchical hardness model using a mixture-of-experts approach. We describe and analyze classifiers and hardness models for four well-known distributions of SAT instances and nine high-performance solvers. We show that surprisingly accurate classifications can be achieved very efficiently. Our experiments show that hierarchical hardness models achieve higher prediction accuracy than the previous state of the art. Furthermore, the classifier's confidence correlates strongly with prediction error, giving a useful per-instance estimate of prediction error.

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Cited by 106 publications

References 26 publications

Phase Transition Behavior in Knowledge Compilation

Phase Transition Behavior in Knowledge Compilation

Clustering phase of a general constraint satisfaction problem model d-k-CSP

Hierarchical Hardness Models for SAT

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