Sparrow 2011

SPARROW is a stochastic local search (SLS) solver for SAT formulae in CNF format [2]. It was named after the mascot of the German city of Ulm. SPARROW2011 is a variant of SPARROW that was developed for the 2011 SAT competition. The core SPARROW2011 algorithm is identical to SPARROW; it has been re-implemented in UBCSAT [9] and a mechanism has been added to automatically select optimized parameter settings based on the maximum clause length of the input instance. These parameter settings were obtained from configurations found using the automated parameter configurator PARAMILS [5,4]. In the following, we describe the basic algorithm underlying SPARROW and the specifics of SPARROW2011. SPARROW is largely based on the GNOVELTY algorithm [7] (version 1.2). The core component of GNOVELTY that SPARROW borrows is the combination of the clause penalty-based dynamic local search with a promising variable scheme. In GNOVELTY (and in SPARROW), clause penalties (weights) are assigned to each clause and are increased similar to the PAWS algorithm [8] and smoothed probabilistically similar to the SAPS algorithm [6] whenever there are no promising variables (as opposed to being in a local minimum as in PAWS and SAPS). Because the clauses are penalized, a penalized variable score penScore is used in lieu of score , and variables are considered promising based on their penalized score (see original paper [7] and the 2009 competition source code for more details). We use the notation that a positive score corresponds to an increase in the number of satisfied clauses if the variable were to be flipped. The behaviour of SPARROW differs from GNOVELTY when there are no (penalized) promising variables. SPARROW replaces the WALKSAT-based component in GNOVELTY with a stochastic decision procedure based on a probability distribution. SPARROW uses two properties we shall call sparrowScore and sparrowAge that depend on the penScore and age properties, respectively: The sparrowScore property uses the penScore property in the following way: if a penScore is positive but not promising, then the value of penScore is one, otherwise an exponential function is used. The full definition of sparrowScore is as follows: