The Order Encoding: From Tractable CSP to Tractable SAT

Petke, Justyna; Jeavons, Peter

doi:10.1007/978-3-642-21581-0_34

Cited by 18 publications

(10 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

Analysis of XACML Policies with SMT

Türkmen

Hartog

Ranise

et al. 2015

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. The eXtensible Access Control Markup Language (XACML) is an extensible and flexible XML language for the specification of access control policies. However, the richness and flexibility of the language (along with the verbose syntax of XML) come with a price: errors are easy to make and difficult to detect when policies grow in size. If these errors are not detected and rectified, they can result in serious data leakage and/or privacy violations leading to significant legal and financial consequences. To assist policy authors in the analysis of their policies, several policy analysis tools have been proposed based on different underlying formalisms. However, most of these tools either abstract away functions over non-Boolean domains (hence they cannot provide information about them) or produce very large encodings which hinder the performance. In this paper, we present a generic policy analysis framework that employs SMT as the underlying reasoning mechanism. The use of SMT does not only allow more fine-grained analysis of policies but also improves the performance. We demonstrate that a wide range of security properties proposed in the literature can be easily modeled within the framework. A prototype implementation and its evaluation are also provided.

show abstract

Section: Experiments 1: Sat Vs Smtmentioning

confidence: 99%

Analysis of XACML Policies with SMT

Türkmen

Hartog

Ranise

et al. 2015

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…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%

Linear Satisfiability Preserving Assignments

Kimura

Makino

2018

jair

View full text Add to dashboard Cite

In this paper, we study several classes of satisfiability preserving assignments to the constraint satisfaction problem (CSP). In particular, we consider fixable, autark and satisfying assignments. Since it is in general NP-hard to find a nontrivial (i.e., nonempty) satisfiability preserving assignment, we introduce linear satisfiability preserving assignments, which are defined by polyhedral cones in an associated vector space. The vector space is obtained by the identification, introduced by Kullmann, of assignments with real vectors. We consider arbitrary polyhedral cones, where only restricted classes of cones for autark assignments are considered in the literature. We reveal that cones in certain classes are maximal as a convex subset of the set of the associated vectors, which can be regarded as extensions of Kullmann's results for autark assignments of CNFs. As algorithmic results, we present a pseudo-polynomial time algorithm that computes a linear fixable assignment for a given integer linear system, which implies the well known pseudo-polynomial solvability for integer linear systems such as two-variable-per-inequality (TVPI), Horn and q-Horn systems.

show abstract

“…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%

Tractability in constraint satisfaction problems: a survey

Carbonnel

Cooper

2015

Constraints

View full text Add to dashboard Cite

Even though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP. What is tractability?The idea that an algorithm is efficient if its time complexity is a polynomial function of the size of its input can be traced back to pioneering work of Cobham [45] and Edmonds [83], but the foundations of complexity theory are based on the seminal work of Cook [52] and Karp [118]. A computational decision problem (such as the constraint satisfaction problem or CSP) consists of a generic instance (in the case of the CSP, a set of variables, their

show abstract

The Order Encoding: From Tractable CSP to Tractable SAT

Cited by 18 publications

References 17 publications

Analysis of XACML Policies with SMT

Analysis of XACML Policies with SMT

Linear Satisfiability Preserving Assignments

Tractability in constraint satisfaction problems: a survey

Contact Info

Product

Resources

About