N. Heintze and J. Jaffar. A decision procedure for a class of Herbrand set constraints. In Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science (LICS), pages 42--51, June 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....analysis eciently nds the exact least xpoint by exploiting the structure of ane constraints, but only applies to a less general class of transfer functions. Our techniques also bear relation to earlier work on constraint solving in general [9 12, 28] especially that of solving set constraints [1 4,17,22 24,43]. The class of tractable constraints we consider is closely related to de nite set constraints (set constraints of the form c(e 1 ; en ) X) 24] which always have a least solution. 9 Conclusions We have presented ecient algorithms for solving a general class of integer range ....

.... also bear relation to earlier work on constraint solving in general [9 12, 28] especially that of solving set constraints [1 4,17,22 24,43] The class of tractable constraints we consider is closely related to de nite set constraints (set constraints of the form c(e 1 ; en ) X) [24], which always have a least solution. 9 Conclusions We have presented ecient algorithms for solving a general class of integer range constraints with applications in program analysis and veri cation. The algorithms are based on a graph representation of the constraints. Because of the special ....

N. Heintze and J. Jaar. A Decision Procedure for a Class of Herbrand Set Constraints. In Symposium on Logic in Computer Science, pages 42-51, June 1990.

....sets of infinite trees. Infinite trees can be viewed as a formalization of potentially infinite data structures such as streams. 3 Positive Set Constraints Set constraints over the domain of finite trees have been used in program analysis for expressing types and approximations to programs [7, 8, 9, 23, 13, 20, 21]. Here we use set constraints over the domain of rational trees as a tool for defining sets of rational trees. Definition 1 A set expression is defined inductively as follows: ffl a variable X 2 V AR or a constant, or , is a set expression; ffl f(s 1 ; s n ) is a set expression if f ....

....X. Regular sets [28] of finite trees are defined analogously to regular sets of strings. Equivalently, the regular sets are those recognized by non deterministic top down tree automata. Least models of sets of positive constraints (in simplified form) over finite trees determine regular sets [8]. Using this fact and the previous lemma, we can show Proposition 3 If C is a set of positive constraints in simplified form then, there are regular sets SX of finite terms in the language Sigma [ f g such that, for every variable X, lm(C) X) S s2SX jsj. Hence the constraints can only ....

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N.C. Heintze and J. Jaffar, A Decision Procedure for a Class of Herbrand Set Constraints, Proc. 5 th IEEE Symposium on Logic in Computer Science, 42--51, 1990.

....converts the constraints into explicit form. In each transformation step SC = SC 0 , a 11 condition on explicit(SC) must be satisfied before the step is applied. Thus some key subroutines of the algorithm are for reasoning about explicit constraints. These subroutines can be adapted from [8] which contained an algorithm to construct a representation 11 of the least model of given explicit constraints. Let SC denote the conjunction of set constraints at hand. Let X 6= 6 fl abbreviate X 1 6= 6 fl Delta Delta Delta X N 6= 6 fl where X 1 ; Delta Delta Delta ; XN ....

N.C. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", Proceedings 5 th IEEE Symposium on Logic in Computer Science, June 1990, pp 42 - 51.

....number of models that must be checked, and these models themselves can be infinite. However, for certain syntactic classes of protocols, the problem of checking protocol security may be reduced to looking at a subclass of models 23 whose behavior can be finitely represented using set constraints [13]. The key property of this subclass of models is that if the protocol is secure in this subclass, then it is secure in all models. For a general discussion of the model checking versus other methods, see [12] Acknowledgments The first author was supported in part by IBM through a graduate ....

N. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", Proceedings 5 th IEEE Symposium on Logic in Computer Science, pp. 42-51, June 1990.

....fundamental difference between the unfolding and standard engines is that the standard engine iterates over a fixed collection of semantic equations, whereas the unfolding engine iterates over dynamically changing equations. Roughly speaking, the unfolding engine combines set constraint techniques [4, 5, 3] with abstract interpretation techniques [1] The former provides a superior ability to reason about term structures, but ignores all dependencies between variables; the latter provides an ability to reason about dependencies. Unfortunately, the unfolding engine relies directly on a specialized ....

N. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", Proceedings 5 th IEEE-LICS, 1990, pp 42--51.

....an infinite number of models that must be checked, and these models themselves can be infinite. However, for certain syntactic classes of protocols, the problem of checking protocol security may be reduced to checking a single universal model which can be finitely represented using set constraints [12]. The key property of this universal model is that if the protocol is secure in the universal model, then it is secure in all models. For a general discussion of the model checking versus other methods, see [11] Thus, we can prove p 1 ( A : shared (fA;Bg;K) shared(fA; Bg;M ) send (f(A; M ....

N. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", Proceedings 5 th IEEE Symposium on Logic in Computer Science, pp. 42-51, June 1990.

....of our cycle elimination algorithm. Section 5 studies an analytical model that explains why IF can outperform SF. Finally, Section 6 presents related work, and Section 7 concludes. 2 Definitions 2. 1 Set Constraints In this paper we use a small subset of the full language of set constraints [HJ90, AW92] Constraints in our constraint language are of the form L R, where L and R are set expressions. Set expressions consist of set variables X ; Y; from a family of variables Vars, terms constructed from n ary constructors c 2 Con, an empty set 0, and a universal set 1. L; R 2 se ....

N. Heintze and J. Jaffar. A decision procedure for a class of Herbrand set constraints. In Symposium on Logic in Computer Science, pages 42--51, June 1990.

....yields the analysis of the program. It is our thesis that many constraint based analyses can be expressed using a particular constraint theory known as set constraints. Set constraints are a simple, general, and well studied theory that is powerful enough to express many program analyses [HJ90, AW92, Hei92, Aik94]. In testing our thesis, it became apparent that dynamic typing is in some ways fundamentally different from other examples of constraint theories used in program analysis. The main technical challenge, and our central result, is establishing that set constraints can encode dynamic typing. This ....

N. Heintze and J. Jaffar. A decision procedure for a class of Herbrand set constraints. In Symposium on Logic in Computer Science, pages 42--51, June 1990.

....systems of set constraints for the basic language. The situation with the various extensions is less clear. Table 1 summarizes the current state of knowledge. Of the open problems in Table 1, decidability of the satisfiability of set constraints with projections has been open for the longest time [HJ90a]. Constraint resolution algorithms for restricted forms of the general problem are known [HJ90a, Hei92] the current state of the art permits the full basic language and restricts only projections [BGW93] Work on set constraints extended with negative constraints has been motivated in part ....

....less clear. Table 1 summarizes the current state of knowledge. Of the open problems in Table 1, decidability of the satisfiability of set constraints with projections has been open for the longest time [HJ90a] Constraint resolution algorithms for restricted forms of the general problem are known [HJ90a, Hei92]; the current state of the art permits the full basic language and restricts only projections [BGW93] Work on set constraints extended with negative constraints has been motivated in part because it appears to be an intermediate step toward handling projections. To see this, consider the ....

[Article contains additional citation context not shown here]

N. Heintze and J. Jaffar. A decision procedure for a class of herbrand set constraints. In Symposium on Logic in Computer Science, pages 42--51, June 1990.

....1. It is decidable whether a system of set constraints is satisfiable. Furthermore, all solutions can be finitely presented. It is important to note that the definition of set constraints used here does damage to history. The original formulation of set constraints, due to Heintze and Jaffar [HJ90a], also includes projection operations in the constraint language. However, it is convenient pedagogically to present results as extensions of the definition above. This organization also reflects the manner in which recent research has progressed. From the definition above, it is easy to see ....

....representations of the solutions of systems of set constraints for the basic language. The situation with the various extensions is less clear. Table 1 summarizes the current state of knowledge. The decidability of the satisfiability of set constraints with projections was open for several years [HJ90a] and has only very recently been resolved [CP94b] Constraint resolution algorithms for restricted forms of the general problem are known [HJ90a, Hei92] the current state of the art permits the full basic language and restricts only projections [BGW93] Work on set constraints extended with ....

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N. Heintze and J. Jaffar. A decision procedure for a class of Herbrand set constraints. In Symposium on Logic in Computer Science, pages 42--51, June 1990.

....languages. 1 Introduction Set constraints are naturally involved in many computer science areas and there is a large agreement about their value in programming languages. For instance, considering variables as sets of possible values for program analysis leads to systems of inclusion constraints [11, 12]. In functional programming, some type inference mechanisms use the notion of subtypes and thus, the associated typing algorithms are in fact set inclusion constraint systems ( 3] On another hand, an increasing number of works has been developed for embedding sets as a native data structure in ....

N. Heintze and J. Jaffar. A Decision Procedure for a Class Herbrand Set Constraints. In Proceedings of the 5 th Symposium on Logic in Computer Science, pages 42--51, Philadelphia, June 1990.

....logical programming language. 1 Introduction Set constraints are naturally involved in many computer science areas and there is a large agreement about their value [6] For instance, considering variables as sets of possible values for program analysis leads to systems of inclusion constraints [13, 14]. In functional programming, some type inference mechanisms use the notion of subtypes and thus, the associated typing algorithms are in fact set inclusion constraint systems [4] On another hand, research in software technology has shown the need for a formal specification step prior to any other ....

N. Heintze and J. Jaffar. A Decision Procedure for a Class Herbrand Set Constraints. In Proceedings of the 5 th Symposium on Logic in Computer Science, pages 42--51, Philadelphia, June 1990.

....between these new systems is made clear, formalizing the description in [SH97] The differences between the two algorithms are expressed in a minimal fashion as a choice between inclusion and equality constraints. Our type systems are designed using term and set constraints. Set constraints [AW92, AW93, FA96, HJ90, Hei92] define inclusion relationships between types; we use set constraints to describe Andersen s analysis. Term constraints define equality relationships between types (e.g. ML type inference [Mil78] we use term equations to describe Steensgaard s analysis. We have implemented these new type systems ....

N. Heintze and J. Jaffar. A Decision Procedure for a Class of Herbrand Set Constraints. In Symposium on Logic in Computer Science, pages 42--51, June 1990.

....logic programming language, gives rise to the subset relational programming paradigm. The language is restricted to finite sets and no intensional notation is provided. Concerning the logic programming field, several attempts have been made for dealing with sets using constraint solving techniques [7, 9, 10, 11, 16]. Generally, set terms are defined by adding sequentially an element to a primitive set (the empty set) This way allows to consider this mechanism as a kind of cons operator, taking into account the fact that order and multiple occurrences are meaningless. As explained in our introduction, a nice ....

N. Heintze and J. Jaffar. A Decision Procedure for a Class Herbrand Set Constraints. In Proceedings of the 5 th Symposium on Logic in Computer Science, pages 42--51, Philadelphia, June 1990.

....yields the analysis of the program. It is our thesis that many constraintbased analyses can be expressed using a particular constraint theory known as set constraints. Set constraints are a simple, general, and well studied theory that is powerful enough to express many program analyses [HJ90, AW92, Hei92, Aik94]. In testing our thesis on a variety of program analyses, it became apparent that dynamic typing is in some ways fundamentally different from other examples of constraint theories used in program analysis. The main technical challenge, and our central result, is establishing that set constraints ....

N. Heintze and J. Jaffar. A decision procedure for a class of Herbrand set constraints. In Symposium on Logic in Computer Science, pages 42--51, June 1990.

....functional compositions and intersection connectives. Without loss of generality, we may assume that those constraints are in shallow form 2 : f(X 1 ; Xm ) X X Y Z X f(X 1 ; Xm ) This class of set constraints is equivalent to the class of definite set constraints presented in [HJ90] and used for program analysis [Hei92a] Such a system of set constraints is either unsatisfiable or has a least solution. We propose an algorithm which builds a tree automata representation of the least solution of a system SC if SC is satisfiable and returns otherwise. 4.1 Algorithm Let SC be ....

N. Heintze and J. Jaffar. A decision procedure for a class of herbrand set constraints. In Proceedings 5 th IEEE Conference on LICS, pages 42--51, jun 1990.

....apparaissent naturellement dans de nombreux domaines relatifs a l informatique. Pour l analyse de programmes par exemple, o u l on raisonne sur les variables consid er ees comme ensembles de valeurs possibles, ce qui conduit a des syst emes de contraintes d inclusion ou non inclusion ( 9] [10]) En programmation fonctionnelle, certains m ecanismes de typage utilisent la notion de sous types, et les algorithmes de typage associ es sont en fait des algorithmes de r esolution de contraintes ensemblistes ( 2] Enfin un certain nombre de travaux portent sur l int egration de la notion ....

N. Heintze and J. Jaffar. A Decision Procedure for a Class Herbrand Set Constraints. In Proceedings of the 5 th Symposium on Logic in Computer Science, pages 42--51, Philadelphia, June 1990.

....one unit, and then performing the analysis directly on the abstract syntax trees (AST) of the entire code base would require substantial computing resources especially memory. A better approach would be to convert the ASTs into a more compact representation such as some form of set constraints [1, 2, 8, 11, 9, 10]. However, even this representation is problematic when the number of initial constraints approaches one million. Worse, the usual indexing schemes used to speed up analysis (e.g. dependency lists for each set variable so that when a set variable is changed the change can be efficiently propagated ....

N. Heintze and J. Jaffar, "A decision procedure for a class of Herbrand set constraints" IEEE LICS, pp. 42-51, 1990.

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N. Heintze and J. Jaffar, "A decision procedure for a class of Herbrand set constraints" LICS, 1990.

....fundamental difference between the unfolding and standard engines is that the standard engine iterates over a fixed collection of semantic equations, whereas the unfolding engine iterates over dynamically changing equations. Roughly speaking, the unfolding engine combines set constraint techniques [4, 5, 3] with abstract interpretation techniques [1] The former provides a superior ability to reason about term structures, but ignores all dependencies between variables; the latter provides an ability to reason about dependencies. Unfortunately, the unfolding engine relies directly on a specialized ....

N. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", Proceedings 5 th IEEE-LICS, 1990, pp 42--51.

....the redundancy which is typically present. An implementation is described and experimental evidence is presented which suggests that set based analysis can be made practical for comprehensive and accurate analysis of logic programs. 1 Introduction The set based approach to program analysis [3, 4, 5] has its origins in the use of constraints to perform type analysis of programs [12, 8, 10] In essence set based analysis involves first writing set constraints (a calculus for expressing relationships between sets of program values) to describe the runtime behaviour of a program, and then ....

....in terms of accuracy, it also has substantial disadvantages in terms of computational cost. To address the question of whether the cost is prohibitive, this paper develops and evaluates an implementation of set constraints. Although straightforward implementation of the algorithms described in [3, 4] is unworkable, substantial progress has been made towards a practical system by developing an algorithm specifically for implementation purposes, designing appropriate representations techniques and exploiting the redundancy which is typically present. After reviewing how set constraints can be ....

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N. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", Proceedings 5 th IEEE-LICS, June 1990, pp 42 - 51.

....the meaning of P is defined to be the smallest interpretation which models P , define the approximate meaning of P to be the smallest set based model of P . 7 The satisfiability problem for conjunctions of set equations is open. A decision procedure for a restricted class of equations appears in [5]. Section 3: The Approximate Meaning of a Logic Program 7 An equivalent definition of the exact meaning of P is that it is the least fixpoint of the following function which maps from and into interpretations of P : T P (I) def = H fi : H Gamma B is in P , and fi 2 f : B Ig ....

N.C. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", draft manuscript (extended abstract to appear in Proceedings 5 th IEEE Symposium on Logic in Computer Science June 1990).

....I(s) respectively. This mapping, in turn, induces a mapping from collections C of set constraints into ftrue, falseg in the obvious way. If I(C) is true, we say that I is a model of C. 6 The solvability problem for set constraints is open. A decision procedure for a restricted class appears in [5]. Let P be an arbitrary program and denote its rules by R 1 ; Delta Delta Delta ; RN , 1 N . We assume that rules are written so that they do not share variables. Let Pi P denote the predicate symbols in P . Let P j p denote the subset of rules in P defining the relation p. Let R i be of ....

....functions while ours mainly served to eliminate occurrences of the intersection function 9 . The second and main part of our algorithm is also based upon a group of transformations. When used directly, these transformations do not always lead to a terminating computation. The key aspect 9 In [5], we deals with both projection and intersection. of the main algorithm, therefore, is in its controlled use of the transformations. This is realized by the function REDUCE each of whose invocations performed transformations local to a fixed collection of set equations. The main loop in the main ....

N.C. Heintze and J. Jaffar, "A Decision Procedure for a Class of Herbrand Set Constraints", forthcoming CMU and IBM Research Report, 40 pages, October 1989.

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N. Heintze and J. Jaffar. A decision procedure for a class of Herbrand set constraints. In Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science (LICS), pages 42--51, June 1990.

No context found.

N. Heintze and J. Jaffar. A Decision Procedure for a Class of Herbrand Set Constraints. In IEEE Symp. on Logic in Computer Science, pages 42--51, 1990.

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