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A few graphbased relational numerical abstract domains
 Static Analysis: Proceedings of the 9th International Symposium
, 2002
"... Abstract. This article presents the systematic design of a class of relational numerical abstract domains from nonrelational ones. Constructed domains represent sets of invariants of the form (vj − vi ∈ C), where vj and vi are two variables, and C lives in an abstraction of P(Z), P(Q), or P(R). We ..."
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Abstract. This article presents the systematic design of a class of relational numerical abstract domains from nonrelational ones. Constructed domains represent sets of invariants of the form (vj − vi ∈ C), where vj and vi are two variables, and C lives in an abstraction of P(Z), P(Q), or P(R). We will call this family of domains weakly relational domains. The underlying concept allowing this construction is an extension of potential graphs and shortestpath closure algorithms in exoticlike algebras. Example constructions are given in order to retrieve wellknown domains Interpretation framework in order to design various static analyses. A major benefit of this construction is its modularity, allowing to quickly implement new abstract domains from existing ones. 1
Binary Decision Graphs
 Static Analyis Symposium SAS’99, LNCS 1694
, 1999
"... Binary Decision Graphs are an extension of Binary Decision Diagrams that can represent some infinite boolean functions. Three refinements of BDGs corresponding to classes of infinite functions of increasing complexity are presented. The first one is closed by intersection and union, the second o ..."
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Cited by 6 (3 self)
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Binary Decision Graphs are an extension of Binary Decision Diagrams that can represent some infinite boolean functions. Three refinements of BDGs corresponding to classes of infinite functions of increasing complexity are presented. The first one is closed by intersection and union, the second one by intersection, and the last one by all boolean operations. The first two classes give rise to a canonical representation, which, when restricted to finite functions, are the classical BDDs. The paper also gives new insights in to the notion of variable names and the possibility of sharing variable names that can be of interest in the case of finite functions.
Efficient HashConsing of Recursive Types
, 2000
"... Efficient storage of types within a compiler is necessary to avoid large blowups in space during compilation. Recursive ..."
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Cited by 6 (1 self)
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Efficient storage of types within a compiler is necessary to avoid large blowups in space during compilation. Recursive
Incremental algorithms and a minimal graph representation for regular trees. Available from http://www.ps.unisb.de/~horbach/fopra.html
, 2002
"... In this paper we present an ecient way of representing regular trees, which allows operations such as subtree checking and equality tests to be computed eciently. To do so, we represent regular trees as minimal graphs which are constructed incrementally. Our work is primarily based on the paper An i ..."
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Cited by 3 (0 self)
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In this paper we present an ecient way of representing regular trees, which allows operations such as subtree checking and equality tests to be computed eciently. To do so, we represent regular trees as minimal graphs which are constructed incrementally. Our work is primarily based on the paper An incremental unique Representation for Regular Trees [1] by Laurent Mauborgne, where he studies an algorithm that incrementally nds a unique, minimized representation for regular trees in time O(n2). We rene some of his algorithms to gain better complexity, and give a proof of correctness. Furthermore we give our work a theoretical base that allows us to develop useful properties of the trees and graphs we work on, as well as the possibility to use hashing techniques on regular trees.
Analysis of communicating infinite state machines using lattice automata
"... Communication protocols can be formally described by the Communicating FiniteState Machines (CFSM) model. This model is expressive, but not expressive enough to deal with complex protocols that involve structured messages encapsulating integers or lists of integers. This is the reason why we propos ..."
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Communication protocols can be formally described by the Communicating FiniteState Machines (CFSM) model. This model is expressive, but not expressive enough to deal with complex protocols that involve structured messages encapsulating integers or lists of integers. This is the reason why we propose an extension of this model: the Symbolic Communicating Machines (SCM). We also propose an approximate reachability analysis method, based on lattice automata. Lattice automata are finite automata, the transitions of which are labeled with elements of an atomic lattice. We tackle the problem of the determinization as well as the definition of a widening operator for these automata. We also show that lattice automata are useful for the interprocedural analysis.
Infinitary Relations and Their Representation DI, Abstract
"... This papers presents extensions of Binary Decision Diagrams to represent some infinitary relations (coded as infinite boolean functions). Four classes of infinitary relations are presented, and their representations are discussed. The widest class is closed under all boolean operations. The three ot ..."
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This papers presents extensions of Binary Decision Diagrams to represent some infinitary relations (coded as infinite boolean functions). Four classes of infinitary relations are presented, and their representations are discussed. The widest class is closed under all boolean operations. The three others give rise to a canonical representation, which, when restricted to finite relations, are the classical BDDs. The paper also gives new insights in to the notion of variables and the possibility of sharing variables that can be of interest in the case of finite relations.
Nordic Journal of Computing An Incremental Unique Representation for Regular Trees
"... Abstract. In order to deal with infinite regular trees (or other pointed graph structures) efficiently, we give new algorithms to store such structures. The trees are stored in such a way that their representation is unique and shares substructures as much as possible. This maximal sharing allows su ..."
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Abstract. In order to deal with infinite regular trees (or other pointed graph structures) efficiently, we give new algorithms to store such structures. The trees are stored in such a way that their representation is unique and shares substructures as much as possible. This maximal sharing allows substantial memory gain and speed up over previous techniques. For example, equality testing becomes constant time (instead of O(n log(n))). The algorithms are incremental, and as such allow good reactive behavior. These new algorithms are then applied in a representation of sets of trees. The expressive power of this new representation is exactly what is needed by the original setbased analyses of Heintze and Jaffar [1990], or Heintze [1994]. CR Classification: See Computing Revues
IT
, 2007
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. I R