2011
DOI: 10.1007/978-3-642-21581-0_34
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The Order Encoding: From Tractable CSP to Tractable SAT

Abstract: Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). One way to solve a CSP instance is to encode it into SAT and use a SAT-solver. However, important information about the problem can get lost during the translation stage. For example, although the general constraint satisfaction problem is known to be NP-complete, there are some classes of CSP instances that have been shown to be tractable. These include the classes of CSP instances that contain only max-close… Show more

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Cited by 18 publications
(10 citation statements)
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“…To perform this analysis in SAT one has to encode everything in Boolean values. With some limitations we can encode LAI constraints in SAT using order encoding [25] where each expression of the form x ≤ c is represented by a different Boolean variable. Membership expressions in the set theory can be encoded in SAT using a similar approach where the relation between a variable and a value from its domain is represented with a different Boolean variable for each value.…”
Section: Experiments 1: Sat Vs Smtmentioning
confidence: 99%
“…To perform this analysis in SAT one has to encode everything in Boolean values. With some limitations we can encode LAI constraints in SAT using order encoding [25] where each expression of the form x ≤ c is represented by a different Boolean variable. Membership expressions in the set theory can be encoded in SAT using a similar approach where the relation between a variable and a value from its domain is represented with a different Boolean variable for each value.…”
Section: Experiments 1: Sat Vs Smtmentioning
confidence: 99%
“…We note that ...,n;p=1,...,d−1 ψ j,p is Horn (resp., TVPI (i.e., a 2-CNF) and q-Horn) if so is the original integer linear system Gx ≥ h (Petke & Jeavons, 2011). It is known by Kullmann (2000) and van Maaren (2000) that 2-, Horn and q-Horn CNFs can be solved by repeatedly finding nontrivial unweighted linear autark assignments.…”
Section: The Case Of General Integer Linear Systemsmentioning
confidence: 99%
“…Present-day solvers do not explicitly look for tractable classes, but by analysis of the algorithms they use it is sometimes possible to show that they automatically solve certain tractable classes. For instance, translating CSP instances with max-closed constraints [112] or CSP instances with connected row-convex constraints [77] into SAT instances using the order encoding produces instances that fall into known tractable classes of SAT which are solved efficiently by modern clause-learning SAT-solvers [108,143]. Tractable classes that are automatically solved by standard algorithms are nevertheless useful since proving that the solver will always execute in polynomial time in a given application provides a potentially important guarantee of efficiency.…”
mentioning
confidence: 99%