Parallel SAT Solving: Past, Present and Future PCR 2017, Gothenburg, - - PowerPoint PPT Presentation

Parallel SAT Solving: Past, Present and Future

PCR 2017, Gothenburg, Sweden

Carsten Sinz

Institute for Theoretical Informatics (ITI) Karlsruhe Institute of Technology (KIT) 06.08.2017

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Outline

• Guided by Historical Development
• Search Space Splitting Approach
• Portfolio Approach
• Empirical Observations
• Parallel Solvers in the SAT Competition
• Current and Future Approaches

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

SAT: Combinatorial Search

Search Space

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Sequential DPLL Algorithm

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

DPLL: Search Tree & Splitting

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x ¬x ¬y y

• Splitting similar to DPLL recursion

step

• F|x,¬y, e.g., describes a fraction of

the search space

• Splitting Schedule
• When and how to split
• Static vs Dynamic Splitting
• Static: computed before solving

process starts; typically with „over- saturation“

• Dynamic: splitting interleaved with

solving F|x,¬y F F|x,y F|¬x

Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Splitting Tree with Non-Overlapping Formulas

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Guiding Paths [Zhang:96]

• Guiding Path
• Describes state in DPLL search
• Trail plus, for each entry, whether

backtracking is needed (B) or not (N)

• Can be used for dynamic search

space splitting, e.g.:

• ((x,B),(y,N),(¬z,B)) splits into


((x,N),(y,N),(¬z,B)) and
 ((¬x,N))

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((x,B),(y,N),(¬z,B))

Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Dynamic Splitting: Focus on Workload Management

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Search Space Splitting Solvers

• Early days of parallel SAT solving
• Böhm, Speckenmeyer (1996): A Fast Parallel SAT-Solver - Efficient

Workload Balancing

• Speckenmeyer (1988): Is average superlinear speedup possible?
• Zhang, Bonacina, Hsiang (1996): PSATO: a distributed propositional prover

and its application to quasigroup problems

• With clause learning and clause exchange
• Sinz, Blochinger, Küchlin (2001): PaSAT - parallel SAT-checking with lemma

exchange: Implementation and applications

• Schubert, Lewis, Becker (2005): PaMira - A Parallel SAT Solver with

Knowledge Sharing

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

PaSAT: Run-Time Observations

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SAT UNSAT

Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Portfolio Approach

• Basic Idea
• Run several solvers (without search space splitting, independently) in

parallel

• SAT Competition 2011
• ppfolio// wins 11 medals, best solver in competition
• „ppfolio is essentially equivalent to typing


solver1 & solver2 & ... solvern &“

• Extensions
• Current solvers also exchange learned clauses and have evolved

diversification strategies

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Portfolio Solvers

• Early portfolio solvers
• Hamadi, Jabbour, Sais (2008): ManySAT Solver Description
• Xu, Hutter, Hoos, Leyton-Brown: SATzilla: Portfolio-based Algorithm

Selection for SAT

• Roussel (2011): Description of ppfolio
• Current portfolio solvers
• Biere (2010-): plingeling, clingeling, treengeling
• Balyo, Sanders, Sinz (2015): HordeSat: A Massively Parallel Portfolio SAT

Solver

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Diversification & Clause Exchange

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• Random 3-SAT, only satisfiable instances

Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Diversification & Clause Exchange

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• Random 3-SAT, only unsatisfiable instances

Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

HordeSAT: Massive Parallelization

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[545 instances from SAT Competitions 2011 & 2014 Application Track]

Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

HordeSAT: Massive Parallelization

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Why Parallelization? Power Wall

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Parallel SAT in the SAT Competitions

• 2009: First Parallel Track
• „Multi-threading is everywehere except in our solvers“
• „Solvers are expected to be deterministic“
• 4 solvers submitted (plus variants): ManySAT, satake, ttsth and gNovelty
• 4 cores (partially 16 cores)
• 2010: SAT-Race, only industrial instances
• 5 solvers participating, 8 cores
• „Solvers are expected to be non-deterministic“: 3 runs per solver and

instance, high deviation in run-time

• 2011: No separation between sequential and parallel solvers
• Two rankings: wall clock and CPU time
• 2017 SAT Competition
• 48 threads, 56 GB per solver

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Carsten Sinz • Parallel SAT Solving: Past, Present and Future • PCR 2017, Gothenburg, Sweden • 06.08.2017

Current Trends and Future Directions

• Current Trends
• Refined approaches for portfolio solvers (diversification & clause sharing)
• Cube-and-Conquer (especially for hard instances)
• Future Directions
• Integrating sub-solvers in portfolio
• Based on SAT sweeping / sampling, e.g. equivalence detection
• Based on abstraction?
• Still mostly open: make use of GPUs

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