Solver Description of riss 2 . 0 and priss 2 . 0

The SAT solver RISS 2.0 and its concurrent parallelization PRISS 2.0 are described in the configuration they have been submitted to the SAT Challenge 2012. I. THE SEQUENTIAL SAT SOLVER RISS 2.0 Based on the CDCL procedure, this solver has been implemented as a module based system. The routines for the decision procedure, the learned clause management, unit propagation, preprocessor and the event heuristics for restart and removal can be exchanged easily. This style of implementation comes to a cost, namely the communication overhead among the components. Whereas plain SAT solver implementations can alter for example the watched list of the unit propagation immediately when a clause should be removed, RISS 2.0 has to store this data first, pass it to the unit propagation module and afterwards this module can execute the wanted operation. Based on this overhead, the implementation is a trade-off between providing as many features as possible and having a good performance on application instances. To still achieve a high performance, RISS 2.0 is equipped with a strong preprocessor COPROCESSOR 2.1 [13], which is also be used during search to simplify the formula and the set of learned clauses. A. Features of RISS 2.0 The main goal if RISS 2.0 is to solve formulas in CNF. Furthermore, the solver is used as research platform and thus provides many parameters to enable further techniques. These techniques are not present in general SAT solvers: • Enumeration of all solutions of the input formula • Loading and storing learned clauses of a run • Searching for a solution with a set of assumed literals • Passing an initial model to the solver that should be tested first Additionally to the named features, RISS 2.0 implements many deduction techniques on top of CDCL that can be enabled. Among them there are On-the-fly Self-Subsumption (OTFSS) [7], Lazy Hyper-Binary-Resolution(LHBR) [3] and Dominator Analysis [6]. To speed up search, most of the techniques that are available in COPROCESSOR 2.1 can be used for simplifying the formula during search. The implementation and handling of data structures and memory accesses is based on the insights that have been published in [10]. The solver furthermore uses Blocking Literals introduced in [16] and Both the solver and its preprocessor as well as descriptions are available at tools.computational-logic.org. Implicit Binary Clauses(e.g. [15]) to speed up unit propagation and conflict analysis. The submitted configuration uses the Luby series with a factor 32 as a restart strategy and a geometric series starting with 3000 and an increment factor of 1.1 as removal schedule. The removal is mainly based on the LBD measure [2], but also short clauses are kept. Both OTFSS and LHBR are enabled. We started to implemented RISS from scratch in 2009 as a teaching system in C++. The binary of the tool we provided for the SAT Challenge has been compiled with the GNU compiler and the optimization -O3. Although plenty of parameters are implemented in both RISS 2.0 and its preprocessor automated parameter setting has not been done yet. This is considered the next step, because parameter setup is not considered to be trivial but has high potential to improve the solvers performance. B. Features of Coprocessor The internal preprocessor of RISS 2.0 implements many simplification techniques, that are executed in the specified order. Whenever a technique can reduce the formula, the process is started from the top. 1) Unit propagation 2) Pure literal detection 3) Self-subsuming resolution 4) Equivalence elimination [5] 5) Unhiding [9] 6) Hidden tautology elimination [8] 7) Blocked clause elimination [11] 8) Variable elimination [4] 9) An algorithm based on extended resolution 10) Failed literal probing [12] 11) Clause vivification [14] Equivalent literal detection is done based on binary clauses and on output literals of gates in the formula. The algorithm based on extended resolution to simplify the formula is unpublished, but submitted for publication. Each technique can be limited so that the consumed run time remains reasonable. After preprocessing, COPROCESSOR allows to shrink the formula so that all assigned or eliminated variables are removed and the resulting formula contains consecutive variables again. II. THE PARALLEL SAT SOLVER PRISS 2.0 The SAT solver PRISS 2.0 is a portfolio SAT solver based on RISS 2.0 and supports up to 64 parallel solver incarnations. After using COPROCESSOR on the input formula, n incarnations