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An Abstract Domain Extending Difference-Bound Matrices with Disequality Constraints [chapter]

Mathias Péron, Nicolas Halbwachs
Lecture Notes in Computer Science  
"Difference-bound matrices" (or DBMs) is a domain proposed by David Dill, for expressing relations of the form "x − y ≤ c" or "c1 ≤ x ≤ c2".  ...  We give algorithms on d DBMs, for deciding the emptiness, computing a normal form, and performing the usual operations of an abstract domain.  ...  Difference-Bound Matrices [Dil89] Difference-Bound Matrices (DBMs) are a practical representation of potential constraints (x − y ≤ c) introduced by D. Dill [Dil89] .  ... 
doi:10.1007/978-3-540-69738-1_20 dblp:conf/vmcai/PeronH07 fatcat:d5mvodd3obhi7kdjhfnuyneqma

An Abstract Domain to Infer Octagonal Constraints with Absolute Value [chapter]

Liqian Chen, Jiangchao Liu, Antoine Miné, Deepak Kapur, Ji Wang
2014 Lecture Notes in Computer Science  
In this paper, we intend to extend the octagon abstract domain with absolute value, to infer certain non-convex properties by exploiting the absolute value function.  ...  The octagon abstract domain, devoted to discovering octagonal constraints (also called Unit Two Variable Per Inequality or UTVPI constraints) of a program, is one of the most commonly used numerical abstractions  ...  Extending difference-bound matrices Now, we show how to encode AV octagonal constraints using DBMs.  ... 
doi:10.1007/978-3-319-10936-7_7 fatcat:ozvzgtekrbhoniyhkranp6m3au

SMT-based Induction Methods for Timed Systems [article]

Roland Kindermann, Tommi Junttila, Ilkka Niemelä
2012 arXiv   pre-print
Handling of the infinite state spaces of timed system in the extended IC3 algorithm is based on suitably adapting the well-known region abstraction for timed systems.  ...  Furthermore, fully symbolic treatment of both timing related and non-timing related elements of the state space seems to offer an attractive approach to model checking timed systems with a large amount  ...  These regions are then manipulated symbolically with difference bounded matrices or decision diagram structures (see e.g. [5] ).  ... 
arXiv:1204.5639v1 fatcat:j52p5s7csnbmvf2jh5xwsiv2ji

An Abstract Domain to Infer Types over Zones in Spreadsheets [chapter]

Tie Cheng, Xavier Rival
2012 Lecture Notes in Computer Science  
Our abstract domain consists in a cardinal power from a numerical abstraction describing zones in a spreadsheet to an abstraction of cell values, including type properties.  ...  Last, we propose a representation for abstract values and present an implementation of our analysis.  ...  v ∈ γ i (V) ∧ (ρ v , ρ s ) ∈ γ Z ({(Z 0 , t 0 ), An Instantiation with Difference-Bound Matrices When abstracting array properties, bounds of the form c or x + c are often expressive enough to capture  ... 
doi:10.1007/978-3-642-33125-1_9 fatcat:edi5z7a4zbblvgujq3lb4vcw2u

A procedure for deciding symbolic equivalence between sets of constraint systems

Vincent Cheval, Hubert Comon-Lundh, Stéphanie Delaune
2017 Information and Computation  
The results presented in the current paper yield a decision procedure for bounded processes, with conditional branching and non-determinism.  ...  More precisely, we consider symbolic equivalence between sets of constraint systems, and we also consider disequations.  ...  This yields matrices of constraint systems: the different columns correspond to constraint systems that share the same structure, but may yield different outputs of the protocol, whereas the different  ... 
doi:10.1016/j.ic.2017.05.004 fatcat:4bbrwmeztbdijoeql4it7iqqhq

Optimization in SMT with LA(Q) Cost Functions [article]

Roberto Sebastiani, Silvia Tomasi
2012 arXiv   pre-print
Surprisingly, very few work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any work on SMT solvers able to produce solutions which minimize cost functions  ...  Due to the lack of competitors in AR and SMT domains, we experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP),  ...  SMT] with PB constraints (see e.g.  ... 
arXiv:1202.1409v1 fatcat:adeovx2rczcvpkba3tjfxywkxm

Optimization in SMT with ${\mathcal LA}$ (ℚ) Cost Functions [chapter]

Roberto Sebastiani, Silvia Tomasi
2012 Lecture Notes in Computer Science  
Surprisingly, very few work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any work on SMT solvers able to produce solutions which minimize cost functions  ...  Due to the absence of competitors in AR and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming  ...  SMT] with PB constraints (see e.g.  ... 
doi:10.1007/978-3-642-31365-3_38 fatcat:zyqcahrmdvgbzg5xxpyixx5q3q

From Support Propagation to Belief Propagation in Constraint Programming

Gilles Pesant
2019 The Journal of Artificial Intelligence Research  
From that exposed structure in the form of so-called global constraints, powerful inference algorithms have shared information between constraints by propagating it through shared variables' domains, traditionally  ...  The necessary architectural changes to a constraint programming solver are described and an empirical study of the proposal is conducted on its implementation.  ...  Acknowledgements The author wishes to thank Arthur Godet for an initial implementation of this work, Alessandro Zanarini for early discussions, and the anonymous referees for their constructive criticism  ... 
doi:10.1613/jair.1.11487 fatcat:7m55dd4bnbfg5dfwaww73owqnq

A Partial-Order Approach to Array Content Analysis [article]

Graeme Gange and Jorge A. Navas and Peter Schachte and Harald Sondergaard and Peter J. Stuckey
2014 arXiv   pre-print
The resulting analysis can be used with arbitrary numeric relational abstract domains; we evaluate the domain on a range of array manipulating program fragments.  ...  We present a parametric abstract domain for array content analysis.  ...  2MB of RAM) using the domain of difference bound matrices with disequalities (dDBM) [13] . 5 The implementation from [9] has not been available and we have not tried to reconstruct it.  ... 
arXiv:1408.1754v1 fatcat:dxkhfejkz5g7vm57muvjc3ucua

Transfer Function Synthesis without Quantifier Elimination

Jörg Brauer, Andy King, Gilles Barthe
2012 Logical Methods in Computer Science  
In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state.  ...  The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.  ...  Computing the update amounts to inferring a relationship between the bound on an output constraint and the bounds on the input constraints.  ... 
doi:10.2168/lmcs-8(3:17)2012 fatcat:bym4uvb5gfcahch3ot3juhpjle

Transfer Function Synthesis without Quantifier Elimination [chapter]

Jörg Brauer, Andy King
2011 Lecture Notes in Computer Science  
Recently it has been shown how transfer functions for linear template constraints can be derived for bit-vector programs by operating over propositional Boolean formulae.  ...  Computing the update amounts to inferring a relationship between the bound on an output constraint and the bounds on the input constraints.  ...  Indeed, we have (M 1 M 2 ) M 3 = i∈N M i where M i are matrices describing different models m i of ξ(X).  ... 
doi:10.1007/978-3-642-19718-5_6 fatcat:spbresxlsfazhlmuf3hpi4iike

Essence: A constraint language for specifying combinatorial problems

Alan M. Frisch, Warwick Harvey, Chris Jefferson, Bernadette Martínez-Hernández, Ian Miguel
2008 Constraints  
Essence provides a high level of abstraction, much of which is the consequence of the provision of decision variables whose values can be combinatorial objects, such as tuples, sets, multisets, relations  ...  Finally, (35) shows that an omitted bound can be combined with an underscore.  ...  However, this conflicts with our design decision not to allow any collection type to contain matrices with different indices.  ... 
doi:10.1007/s10601-008-9047-y fatcat:hw4bnlaumjb3jek2qwqgbuhmu4

Refining Abstract Interpretation-Based Static Analyses with Hints [chapter]

Vincent Laviron, Francesco Logozzo
2009 Lecture Notes in Computer Science  
We introduce a new technique, hints, which allows us to systematically refine the operations defined over elements of an abstract domain.  ...  We focus our attention on the loss of precision induced by abstract domain operations.  ...  ., constraint matrices [24] , shape analysis [26] or constant propagation [3] .  ... 
doi:10.1007/978-3-642-10672-9_24 fatcat:ilynnfsznbe4fiydpqvty2vsee

Protein topology prediction through parallel constraint logic programming

D A Clark, C J Rawlings, J Shirazi, A Veron, M Reeve
1993 Proceedings. International Conference on Intelligent Systems for Molecular Biology  
CBS2e is an extension of CBS1e that addresses the important problem of integrating the use of uncertain (weighted) protein folding constraints with categorical ones, through the use of a cost function  ...  Moreover, we show that for large topological problems CBS1e was approximately 60 times faster than an equivalent Prolog implementation (CBS1) on a sequential device with further performance enhancements  ...  Mark Wallace (ECRC) and two anonymous referees for comments on an earlier draft of this paper. We would also like to thanks all members of the ElipSys team at ECRC.  ... 
pmid:7584374 fatcat:i72prc7vzvfi3lmwu5h5vdrqxu

A Method for Symbolic Computation of Abstract Operations [chapter]

Aditya Thakur, Thomas Reps
2012 Lecture Notes in Computer Science  
by an abstract domain A and operations on A.  ...  The algorithm that goes by the name "Stålmarck's method" is one instantiation of Stålmarck[A] with a certain abstract domain. Abstract value A is a semantic reduction and (ii) A A.  ...  Template Constraint Matrices (TCMs) are a parametrized family of linearinequality domains for expressing invariants in linear real arithmetic. Sankaranarayanan et al.  ... 
doi:10.1007/978-3-642-31424-7_17 fatcat:twgc74naqnelpgpd35fydplq5i
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