By Justyna Petke
This booklet presents an important step in the direction of bridging the components of Boolean satisfiability and constraint delight by way of answering the query why SAT-solvers are effective on convinced periods of CSP cases that are not easy to resolve for normal constraint solvers. the writer additionally offers theoretical purposes for selecting a selected SAT encoding for a number of vital periods of CSP instances.
Boolean satisfiability and constraint pride emerged independently as new fields of computing device technological know-how, and diversified fixing strategies became regular for challenge fixing within the components. although any propositional formulation (SAT) might be considered for instance of the overall constraint pride challenge (CSP), the consequences of this connection have purely been studied within the previous couple of years.
The publication may be important for researchers and graduate scholars in man made intelligence and theoretical computing device technology.
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Additional resources for Bridging Constraint Satisfaction and Boolean Satisfiability
8. To generate solvable connectedrow-convex CSP instances, we selected a random assignment to all of the variables, and then generated random inequalities of the form above, keeping only those that were satisfied by this fixed assignment. This ensured that the system of inequalities had at least one solution. 5. On this simple set of instances all solvers performed very well, although Minion was noticeably slightly slower. It is worth mentioning that most of these instances were essentially solved at the translation stage.
Divide X into disjoint subsets Xi . If ˆ forces exactly one of x 2 Xi to be satisfied for each Xi , then ˆ is a sparse encoding of some CSP P. V W Proof Let ˆ0 D ˆ ^ Xi 2X . x2Xi x/. 6 and the proof follows. 2 The log encoding The log encoding [Wal00] introduces a Boolean variable for each bit in the value of a CSP variable. For instance, a variable v with domain f0; 1; 2; 3g will be encoded using two Boolean variables, xv0 and xv1 . In this case the Boolean assignment (xv0 D False, xv1 D True) corresponds to the CSP assignment v D 2.
Even though a lot of information about the original CSP instance is usually lost at the translation stage and a large set of propositional clauses is produced, SAT-solvers sometimes outperform conventional CSP-solvers on such instances (see Chapter 3). Furthermore, SAT-solvers often perform well even on instances that were encoded using the most naive encoding (called the direct encoding, see below). In an attempt to compare various solving techniques used for CSP and SAT several different ways of encoding a CSP instance as a propositional formula have been proposed.
Bridging Constraint Satisfaction and Boolean Satisfiability by Justyna Petke