Weakening Cardinality Constraints Creates Harder Satisfiability Benchmarks

For some time, the satisfiability formulae that have been the most difficult to solve for their size have been crafted to be unsatisfiable by the use of cardinality constraints. Recent solvers have introduced explicit checking of such constraints, rendering previously difficult formulae trivial to solve. A family of unsatisfiable formulae is described that is derived from the sgen4 family but cannot be solved using cardinality constraints detection and reasoning alone. These formulae were found to be the most difficult during the SAT2014 competition by a significant margin and include the shortest unsolved benchmark in the competition, sgen6-1200-5-1.cnf.

Zero-One Designs Produce Small Hard SAT Instances

Some basics of combinatorial block design are combined with certain constraint satisfaction problems of interest to the satisfiability community. The paper shows how such combinations lead to satisfiability problems, and shows empirically that these are some of the smallest very hard satisfiability problems ever constructed. Partially balanced (0,1) designs (PB01Ds) are introduced as an extension of balanced incomplete block designs (BIBDs) and (0,1) designs. Also, (0,1) difference sets are introduced as an extension of certain cyclical difference sets. Constructions based on (0,1) difference sets enable generation of PB01Ds over a much wider range of parameters than is possible for BIBDs. Building upon previous work of Spence, it is shown how PB01Ds lead to small, very hard, unsatisfiable formulas. A new three-dimensional form of combinatorial block design is introduced, and leads to small, very hard, satisfiable formulas. The methods are validated on solvers that performed well in the SAT 2009 and earlier competitions.

sgen1: A generator of small but difficult satisfiability benchmarks

The satisfiability problem is known to be NP-Complete; therefore, there should be relatively small problem instances that take a very long time to solve. However, most of the smaller benchmarks that were once thought challenging, especially the satisfiable ones, can be processed quickly by modern SAT-solvers. We describe and make available a generator that produces both unsatisfiable and, more significantly, satisfiable formulae that take longer to solve than any others known. At the two most recent international SAT Competitions, the smallest unsolved benchmarks were created by this generator. We analyze the results of all solvers in the most recent competition when applied to these benchmarks and also present our own more focused experiments.

tts: A SAT-Solver for Small, Difficult Instances

The Ternary Tree Solver (tts) is a complete solver for propositional satisfiability which was designed to have good performance on the most difficult small instances. It uses a static ternary tree data structure to represent the simplified proposition under all permissible partial assignments and maintains a database of derived propositions known to be unsatisfiable. In the SAT2007 competition version 4.0 won the silver medal for the category handmade, speciality UNSAT solvers and was the top qualifier for the second stage for handmade benchmarks, solving 11 benchmarks which were not solved by any other entrant. We describe the methods used by the solver and analyse the competition Phase 1 results on small benchmarks. We propose a first version of a comprehensive suite of small difficult satisfiability benchmarks (sdsb) and compare the worst-case performance of the competition medallists on these benchmarks.

The Paralax Infrastructure: Automatic Parallelization With a Helping Hand

Speeding up sequential programs on multicores is a challenging problem that is in urgent need of a solution. Automatic parallelization of irregular pointer-intensive codes, exempli?ed by the SPECint codes, is a very hard problem. This paper shows that, with a helping hand, such auto-parallelization is possible and fruitful. This paper makes the following contributions: (i) A compiler framework for extracting pipeline-like parallelism from outer program loops is presented. (ii) Using a light-weight programming model based on annotations, the programmer helps the compiler to ?nd thread-level parallelism. Each of the annotations speci?es only a small piece of semantic information that compiler analysis misses, e.g. stating that a variable is dead at a certain program point. The annotations are designed such that correctness is easily veri?ed. Furthermore, we present a tool for suggesting annotations to the programmer. (iii) The methodology is applied to autoparallelize several SPECint benchmarks. For the benchmark with most parallelism (hmmer), we obtain a scalable 7-fold speedup on an AMD quad-core dual processor. The annotations constitute a parallel programming model that relies extensively on a sequential program representation. Hereby, the complexity of debugging is not increased and it does not obscure the source code. These properties could prove valuable to increase the ef?ciency of parallel programming.

Mechanical fatigue and spectrum analysis of small-satellite

Mechanical fatigue due to environmental loads and spectrum analysis due to launch loads of the primary structure of a low cost, low-earth orbit small satellite intended for earth observation missions are presented. The payload of the satellite under consideration is a precise optical unit to image the earth’s surface having a mass of 45 kg. 3-D Finite Element Model for the satellite structure is generated by applying substructure method. Modal analysis is required to determine natural frequencies of the satellite and define its mode shape. Then, ranking of mode shapes according to specific constraint is performed. Harmonic analysis at resonance frequencies with the highest ranking is done and cumulative fatigue damage analysis is performed. Spectrum analysis is performed for Small Sat structure to verify the satellite structure reliability under all dynamic random vibration loads applied during transportation and launch cases.