Hippen, Nicholas

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The University of Nebraska, Omaha

Nick Hippen & Yuliya Lierler University of Nebraska at OmahaAutomatic Program Rewriting for Non-Ground Answer Set ProgramsNick Hippen & Yuliya LierlerUniversity of Nebraska at OmahaBACKGROUNDNick Hippen & Yuliya Lierler University of Nebraska at Omaha 2What is Answer Set Programming (ASP)?• Constraint programming paradigm geared towards solving difficult combinatorial search problems• Prolog-like syntaxNick Hippen & Yuliya Lierler University of Nebraska at Omaha 3MeaningX is a child of Y if Y is a parent of X.X is innocent if I have no reason to believe that X is guiltyLogic Rule𝑐ℎ𝑖𝑙𝑑 𝑋, 𝑌 ← 𝑝𝑎𝑟𝑒𝑛𝑡 𝑌, 𝑋 .𝑖𝑛𝑛𝑜𝑐𝑒𝑛𝑡 𝑋 ← 𝑛𝑜𝑡 𝑔𝑢𝑖𝑙𝑡𝑦 𝑋 .Head              ← BodyASP Solver Architecture & GroundingNick Hippen & Yuliya Lierler University of Nebraska at Omaha 4logicprogramGrounder ASP SolvergroundedprogramanswersetsLogic Program Grounded Program Intelligently Grounded Program𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏, 𝑎𝑙𝑙𝑦 .𝑝𝑎𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑦, 𝑗𝑜ℎ𝑛 .𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑏𝑜𝑏,𝑚𝑎𝑟𝑦 .𝑐𝑜𝑢𝑠𝑖𝑛 𝑋, 𝑌 ← 𝑝𝑎𝑟𝑒𝑛𝑡 𝑃1, 𝑋 ,𝑝𝑎𝑟𝑒𝑛𝑡 𝑃2, 𝑌 ,𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑃1, 𝑃2 ,𝑋 ≠ 𝑌.𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏, 𝑎𝑙𝑙𝑦 .𝑝𝑎𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑦, 𝑗𝑜ℎ𝑛 .𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑏𝑜𝑏,𝑚𝑎𝑟𝑦 .𝑐𝑜𝑢𝑠𝑖𝑛 𝑗𝑜ℎ𝑛,𝑚𝑎𝑟𝑦 ← 𝑝𝑎𝑟𝑒𝑛𝑡 𝑎𝑙𝑙𝑦, 𝑗𝑜ℎ𝑛 ,𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏,𝑚𝑎𝑟𝑦 ,𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑎𝑙𝑙𝑦, 𝑏𝑜𝑏 ,𝑗𝑜ℎ𝑛 ≠ 𝑚𝑎𝑟𝑦.…𝑐𝑜𝑢𝑠𝑖𝑛 𝑏𝑜𝑏, 𝑏𝑜𝑏 ← 𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏, 𝑏𝑜𝑏 ,𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏, 𝑏𝑜𝑏 ,𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑏𝑜𝑏, 𝑏𝑜𝑏 ,𝑏𝑜𝑏 ≠ 𝑏𝑜𝑏.…𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏, 𝑎𝑙𝑙𝑦 .𝑝𝑎𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑦, 𝑗𝑜ℎ𝑛 .𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑏𝑜𝑏,𝑚𝑎𝑟𝑦 .𝑐𝑜𝑢𝑠𝑖𝑛 𝑎𝑙𝑙𝑦, 𝑗𝑜ℎ𝑛 ← 𝑝𝑎𝑟𝑒𝑛𝑡 𝑏𝑜𝑏, 𝑎𝑙𝑙𝑦 ,𝑝𝑎𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑦, 𝑗𝑜ℎ𝑛 ,𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑏𝑜𝑏,𝑚𝑎𝑟𝑦 ,𝑎𝑙𝑙𝑦 ≠ 𝑗𝑜ℎ𝑛.Motivations• Intuitive encodings are not always the most optimal• Fine-tuning requires expertise• Smaller grounding sizes often translate into faster solve times• Eliminating variables from rules can lead to smaller grounding sizeNick Hippen & Yuliya Lierler University of Nebraska at Omaha 5Question• What fine-tuning can be done automatically via program rewriting techniques?ASP Solver Architecture ExtendedNick Hippen & Yuliya Lierler University of Nebraska at Omaha 6PROJECTORrewritten logicprogramGrounder ASP SolvergroundedprogramanswersetslogicprogramOur Direction• Inspired by relational databases• Two considered rewritings• 𝛼-projection• 𝛽-projectionNick Hippen & Yuliya Lierler University of Nebraska at Omaha 7Our Direction• Inspired by relational databases• Two considered rewritings• 𝛼-projection• 𝜷-projectionNick Hippen & Yuliya Lierler University of Nebraska at Omaha 8𝛃-PROJECTIONNick Hippen & Yuliya Lierler University of Nebraska at Omaha 9𝛽-ProjectionGoal: Eliminate any unnecessary variables from the rule by isolating them in a newly introduced rule.• Need to make sure this rule does not contain the same variables as the original• Carry “guards” for variables when possible• Attempts to restrict the domain of variables in a rule as much as possible without introducing new variablesNick Hippen & Yuliya Lierler University of Nebraska at Omaha 10Example: PermutationPatternMatchingNick Hippen & Yuliya Lierler University of Nebraska at Omaha 11Logic Programkval(K) :- p(K,P),patternlength(L),K <= L.Consider if K,P,L have 100 possible distinct ground values for this rule.𝑇𝑜𝑡𝑎𝑙𝐺𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑜𝑟𝑖𝑔 = |𝐾| ∗ |𝑃| ∗ |𝐿| = 1003 = 1,000,000Example: PermutationPatternMatchingNick Hippen & Yuliya Lierler University of Nebraska at Omaha 12Logic Program PROJECTOR: 𝜷-projection (Project P)kval(K) :- p(K,P),patternlength(L),K <= L.p_0(K) :- p(K,P).kval(K) :- p_0(K),patternlength(L),K <= L.Project P2 variables2 variables3 variablesConsider if K,P,L have 100 possible distinct ground values for both rules.𝐺𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑆𝑖𝑧𝑒𝑝_0 = |𝐾| ∗ |𝑃| = 1002 = 10,000𝐺𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑆𝑖𝑧𝑒𝑘𝑣𝑎𝑙 = |𝐾| ∗ |𝐿| = 1002 = 10,000𝑇𝑜𝑡𝑎𝑙𝐺𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑝𝑟𝑜𝑗 = 𝐺𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑆𝑖𝑧𝑒𝑝_0 + 𝐺𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑆𝑖𝑧𝑒𝑘𝑣𝑎𝑙 = 20,000More Details… But No Time…• Supported languages features• Variable selection• Non-deterministic behavior• Safety• Algorithm & Implementation DetailsNick Hippen & Yuliya Lierler                                                                                                 University of Nebraska at Omaha 13EXPERIMENTAL RESULTSNick Hippen & Yuliya Lierler University of Nebraska at Omaha 14Experimental Analysis• ASPCCG: ASP based natural language parser• 3 encodings of increasing levels of human optimization• Created by Matthew Buddenhagen, Yuliya Lierler & Peter Schuller• Enc1: No human optimization• Enc7: Moderate human optimization• Enc19: Notable human optimization• ASPComp14• Stable Marriage• Permutation Pattern Matching• Knight Tour with Holes• Misc.Nick Hippen & Yuliya Lierler University of Nebraska at Omaha 15ASPCCG: OverallNick Hippen & Yuliya Lierler University of Nebraska at Omaha 16Related Work: Lpopt• Lpopt (Bichler, Morak, Woltran, 2016)• Very similar ideas (reduce # of variables in rules)• Different processBichler, Manuel. "Optimizing non-ground answer set programs via rule decomposition." Bachelor thesis. TU Wien (2015).Bichler, Manuel, Michael Morak, and Stefan Woltran. "lpopt: A rule optimization tool for answer set programming." International Symposiumon Logic-Based Program Synthesis and Transformation. Springer, Cham, 2016.Yuliya Lierler & Nick Hippen                                                                                                 University of Nebraska at Omaha 17Full ASPComp 2014 Benchmarks• 22 total benchmarks• 4 benchmarks had no rewrites from both lpopt & projector• 6 benchmarks had rewrites but lpopt & projector made no significant performance effect• 12 benchmarks had rewrites with performance impact• 20 instances for each program• Timeout of 5 minutesNick Hippen & Yuliya Lierler University of Nebraska at Omaha 18Lpopt SuccessNick Hippen & Yuliya Lierler University of Nebraska at Omaha 19• Lpopt performed better on average than Projector on 3 programs• Hanoi Tower• Projector performed worse than base encoding• Labyrinth• Lpopt solved 19 of 20 instances vs. 18 of 20 for base encoding & 17 of 20 for Projector• Nomistery• Projector performed better than base encoding but ~50% worse than LpoptProjector SuccessNick Hippen & Yuliya Lierler University of Nebraska at Omaha 20• Lpopt performed better on average than both the base encoding & projector on 3 programs• Graph Colouring• Knight Tour With Holes• Permutation Pattern Matching• Significant improvementSimilar Rewrite PerformanceNick Hippen & Yuliya Lierler University of Nebraska at Omaha 21• Both Lpopt & Projector hurt performance:• Minimal Diagnosis• Valves Location Problem• Both Lpopt & Projector improve performance:• Ricochet Robots• No significant difference between Lpopt & Projector in both casesConclusions, Current & Future WorkConclusions• Automatic rewriting techniques are worth exploring• System PROJECTOR available on the UNO NLPKR Lab website• “Automatic Program Rewriting in Non-Ground Answer Set Programs” (Hippen, Lierler, 2019) presented at International Symposium on Practical Aspects of Declarative Languages 2019 (PADL 2019)Current Work• Improve language supportFuture Work• Better heuristics for variable selection (grounding size prediction)Nick Hippen & Yuliya Lierler University of Nebraska at Omaha 22AcknowledgementsUniversity of Nebraska Omaha• Brian Hodges• Jacob LeeNick Hippen & Yuliya Lierler University of Nebraska at Omaha 23NSF Project: Automated Optimization of Programs and Processing Tools in Answer Set Programming OptimizationUniversity of Kentucky• Michael Dingess• Daniel Houston• Liu Liu• Shelby Stocker• Dr. Mirek TruszczynskiMisc.• Roland Kaminski• Stefan WoltranThank You!Questions?Nick Hippen & Yuliya Lierler University of Nebraska at Omaha 24

Automatic Program Rewriting for Non-Ground Answer Set Programs

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Automatic Program Rewriting for Non-Ground Answer Set Programs

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