Bagnara, R. A reactive implementation of pos using ROBDDs. In 8th International Symposium on Programming Languages, Implementation, Logic and Programs (September 1996), H. Kuchen and S. D. Swierstra, Eds., vol. 1140 of Lecture Notes in Computer Science, Springer-Verlag, pp. 107--121.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....were first introduced by Randal E. Bryant in [4] They turned out to be very useful in many areas where manipulation of boolean functions was needed. They allowed a real breakthrough of model checking [7] they have been used successfully in artificial intelligence [14] and in program analysis [8, 13, 2, 16]. One limitation of BDDs and its variants is that they can only represent finite functions. Indeed, it induces a well known and quite annoying restriction on model checking, and it restrains its use in program analysis. This paper explores the possibility of extending BDDs so that they can also ....

Bagnara, R. A reactive implementation of pos using ROBDDs. In 8th International Symposium on Programming Languages, Implementation, Logic and Programs (September 1996), H. Kuchen and S. D. Swierstra, Eds., vol. 1140 of Lecture Notes in Computer Science, Springer-Verlag, pp. 107--121.

....indicate the XSB table space requirements for the two goal independent analyses, as well as their ratio. The Pos domain is known to result in ecient analyses which derive modes with a high degree of precision [20, 44] Our times compare well with times in the literature (see for example also [44, 17, 22, 3]) For this simple domain, GI mgc does not have any relevant e ect on time, but as expected, improves the space requirements of the analysis. When times are not too small to measure (like in e.g. the goal dependent analysis of gabriel) we note an overhead of up to 100 when collecting ....

....case the designated paths are de ned to descend on the right branch of a . 2 node and down the second and third branches of a tree 3 node. Assuming the following mapping of constructors to type descriptions: 2 cons [ 0 nil tree=3 tree void=0 void the abstraction of the term [1,2,3] is fcons; nilg, the abstraction of [1,2,3 X] is fcons; Xg, the abstraction Michael Codish et al. Semantics Based Program Analysis for Logic Based Languages using XSB 9 of tree(1,tree(2,void,void) tree(3,void,void) is ftree; voidg and nally the abstraction of the ill typed term ....

R. Bagnara. A Reactive Implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Proceedings of the 8th International Symposium on PLILP, number 1140 in LNCS, pages 107-121, Aachen, Germany, Sept. 1996. Springer-Verlag.

.... the use of binary decision diagrams (BDD s) and their variants, such as reduced order binary decision diagrams (ROBDD s) 4] BDD s were originally used in the field of circuit design and have been shown to lead to fast and accurate analyses of logic programs for a wide range of benchmarks [1,2,5,12,7]. The number of iterations required in a groundness analysis based on BDD s is typically small (2 3) and very rarely more than 4 or 5 per predicate. Analysing the Aquarius Prolog compiler (a benchmark with over 3000 clauses) is reported to encounter a strongly connected component which ....

....clauses) is reported to encounter a strongly connected component which involves 10 12 iterations [7,9] The size of the BDD s encountered in an analysis is however often witnessed to become quite large. Recent work suggests several techniques to reduce the size of BDD s with no loss of accuracy [2,3]. Other work has indicated that widening techniques [6] can be applied to restrict the size of BDD s [7] Section 2 of this note illustrates that size is not the only problem facing P os based program analyses. A series of pathological inputs is described for which any (accurate) P os based ....

[Article contains additional citation context not shown here]

R. Bagnara. A reactive implementation of Pos using ROBDDs. In Programming Languages: Implementations, Logics and Programs, pages 107--121. Springer, 1996. LNCS 1140.

....last three columns of the table indicate the XSB table space requirements for the two goal independent analyses, as well as their ratio. The POS domain is known to result in optimal and very efficient analyses [17, 39] Our times compare well with times in the literature (see for example also [39, 14, 19, 3]) For this simple domain, GI mgc does not have any relevant effect on time, but as expected, improves the space requirements of the analysis. When times are not too small to measure (like in e.g. the Time Space Program GI GI mgc GD GD pp GI GI mgc GI=GI mgc cs o 0.21 0.40 0.00 0.00 ....

....with lists and binary trees. In this case the designated paths are defined to descend on the right branch of a . 2 node and down the second and third branches of a tree 3 node. Assuming the mapping of . 2 to cons, 0 to nil, tree 3 to tree, and void 0 to void, the abstraction of the term [1,2,3] is fcons; nilg, the abstraction of [1,2,3 X] is fcons; Xg, the abstraction of tree(1,tree(2,void,void) tree(3,void,void) is ftree; voidg and the abstraction of the ill typed term [1,2,3 tree(void,1,void) in which the list is terminated by a tree instead of by a nil constructor) is ....

R. Bagnara. A Reactive Implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Proceedings of the Eighth International Symposium on PLILP, number 1140 in LNCS, pages 107--121, Aachen, Germany, September 1996. Springer-Verlag.

.... formulae, denoted Pos and Def respectively [1] Numerous independent implementations have indicated that program analyses based on Pos and Def formulae are accurate and well suited to the analysis of logic programs, concurrent logic programs, constraint logic programs and deductive databases [1, 2, 5, 8, 9, 12, 13, 16, 21]. One of the best known applications of this type of analysis involves reasoning about groundness dependencies. For example, in this context the definite formula x (y z ) is interpreted to describe a program state in which x is definitely ground and there exists a grounding dependency such that ....

....does y . A variety of techniques have been devised to represent, maintain and manipulate various classes of propositional formulae for program analyses. Worth mentioning are: 1) the use of binary decision diagrams (BDD s) and their variants, like reduced order binary decision diagrams (ROBDD s) [2, 5, 9], which lead to fast Pos analyses for many benchmarks; 2) the use of dual Blake canonical form (DBCF) for Def [1] and (3) the use of a set of possibly non ground atoms over the alphabet ftrue; falseg to represent the truth table of a formula [8] The domain operations to support analyses with ....

[Article contains additional citation context not shown here]

R. Bagnara. A Reactive Implementation of Pos using ROBDDs. In Programming Languages: Implementations, Logics and Programs, pages 107--121. SpringerVerlag, 1996. LNCS 1140.

....must provide are thus more complicated in our approach. This is not a limitation, if one considers that in the actual implementation even more complex operations are used. For instance, all the abstract bindings arising from a bunch of uni cations are executed in one shot, instead of one at a time [3]. 2 Preliminaries Let S be a set. We will denote by S n the set of n tuples of elements drawn from S, whereas S denotes S n2N S n . Let Vars be a denumerable set of variable symbols. We will denote by TVars the set of terms with variables in Vars. We assume that Vars contains (among ....

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107-121, Aachen, Germany, 1996. Springer-Verlag, Berlin.

....arising in groundness analysis, and Reduced Ordered Binary Decision Diagrams (ROBDDs) are generally accepted to be the most efficient representation for Pos. Unfortunately, the size of an ROBDDs is, in the worst case, exponential in the number of variables it depends upon. Earlier work [2] has shown that a hybrid representation that separates the definite information from the dependency information is considerably more efficient than keeping the two together. The aim of the present paper is to push this idea further, also separating out certain dependency information, in ....

....Diagrams (ROBDDs) 6] to give the best performance. ROBDDs generated during program analysis often contain many variables that are definitely true. In the context of groundness analysis, this means that the corresponding program variable must be ground at that point in the program. It is shown in [2] that a hybrid representation for Boolean functions that keeps these definite variables separate is more efficient than ROBDDs alone. However, ROBDDs generated during program analysis also contain many pairs of variables that are equivalent. In terms of groundness, this means that either both ....

[Article contains additional citation context not shown here]

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107-- 121, Aachen, Germany, 1996. Springer-Verlag, Berlin.

....dependencies arising in groundness analysis, and Reduced Ordered Binary Decision Diagrams (ROBDDs) are generally accepted to be the most e#cient representation for Pos. Unfortunately, the size of an ROBDDs is, in the worst case, exponential in the number of variables it depends upon. Earlier work [2] has shown that a hybrid representation that separates the definite information from the dependency information is considerably more e#cient than keeping the two together. The aim of the present paper is to push this idea further, also separating out certain dependency information, in particular ....

....Diagrams (ROBDDs) 6] to give the best performance. ROBDDs generated during program analysis often contain many variables that are definitely true. In the context of groundness analysis, this means that the corresponding program variable must be ground at that point in the program. It is shown in [2] that a hybrid representation for Boolean functions that keeps these definite variables separate is more e#cient than ROBDDs alone. However, ROBDDs generated during program analysis also contain many pairs of variables that are equivalent. In terms of groundness, this means that either both ....

[Article contains additional citation context not shown here]

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107--121, Aachen, Germany, 1996. SpringerVerlag, Berlin.

....provide are thus more complicated in our approach. This is not a limitation, if one considers that in the actual implementation even more complex operations are used. For instance, all the abstract bindings arising from a bunch of unifications are executed in one shot, instead of one at a time [3]. 2 Preliminaries Let S be a set. We will denote by S n the set of n tuples of elements drawn from S, whereas S # denotes S n#N S n . Let Vars be a denumerable set of variable symbols. We will denote by TVars the set of terms with variables in Vars . We assume that Vars contains (among ....

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107--121, Aachen, Germany, 1996. Springer-Verlag, Berlin.

....provide are thus more complicated in our approach. This is not a limitation, if one considers that in the actual implementation even more complex operations are used. For instance, all the abstract bindings arising from a bunch of unifications are executed in one shot, instead of one at a time [3]. 2 Preliminaries Let S be a set. We will denote by S n the set of n tuples of elements drawn from S, whereas S denotes S n2N S n . Let Vars be a denumerable set of variable symbols. We will denote by TVars the set of terms with variables in Vars. We assume that Vars contains (among ....

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107--121, Aachen, Germany, 1996. Springer-Verlag, Berlin.

....e#ciency (on both time and space) of groundness analysis. Due to extreme space limitations we just give a rough idea of how the hybrid representation and its operations look like. We also report on the experimental results we obtained with the China analyzer. The interested reader is referred to [3] for a complete account of this work. 2 A New, Hybrid Implementation for Pos The observation of many constraint logic programs shows that the percentage of variables which are found to be ground during the analysis, for typical invocations, is as high as 80 . This suggests that representing Pos ....

R. Bagnara. A reactive implementation of Pos using ROBDDs. Technical Report TR-96-19, Dipartimento di Informatica, Universita di Pisa, 1996.

....dependencies arising in groundness analysis, and Reduced Ordered Binary Decision Diagrams (ROBDDs) are generally accepted to be the most ecient representation for Pos. Unfortunately, the size of an ROBDDs is, in the worst case, exponential in the number of variables it depends upon. Earlier work [2] has shown that a hybrid representation that separates the de nite information from the dependency information is considerably more ecient than keeping the two together. The aim of the present paper is to push this idea further, also separating out certain dependency information, in particular all ....

....Diagrams (ROBDDs) 6] to give the best performance. ROBDDs generated during program analysis often contain many variables that are de nitely true. In the context of groundness analysis, this means that the corresponding program variable must be ground at that point in the program. It is shown in [2] that a hybrid representation for Boolean functions that keeps these de nite variables separate is more ecient than ROBDDs alone. However, ROBDDs generated during program analysis also contain many pairs of variables that are equivalent. In terms of groundness, this means that either both ....

[Article contains additional citation context not shown here]

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107-121, Aachen, Germany, 1996. SpringerVerlag, Berlin.

....dependencies arising in groundness analysis, and Reduced Ordered Binary Decision Diagrams (ROBDDs) are generally accepted to be the most e#cient representation for Pos. Unfortunately, the size of an ROBDDs is, in the worst case, exponential in the number of variables it depends upon. Earlier work [2] has shown that a hybrid representation that separates the definite information from the dependency information is considerably more e#cient than keeping the two together. The aim of the present paper is to push this idea further, also separating out certain dependency information, in particular ....

....Diagrams (ROBDDs) 6] to give the best performance. ROBDDs generated during program analysis often contain many variables that are definitely true. In the context of groundness analysis, this means that the corresponding program variable must be ground at that point in the program. It is shown in [2] that a hybrid representation for Boolean functions that keeps these definite variables separate is more e#cient than ROBDDs alone. However, ROBDDs generated during program analysis also contain many pairs of variables that are equivalent. In terms of groundness, this means that either both ....

[Article contains additional citation context not shown here]

R. Bagnara. A reactive implementation of Pos using ROBDDs. In H. Kuchen and S. D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, Proceedings of the Eighth International Symposium, volume 1140 of Lecture Notes in Computer Science, pages 107-- 121, Aachen, Germany, 1996. Springer-Verlag, Berlin.

....efficiency (on both time and space) of groundness analysis. Due to extreme space limitations we just give a rough idea of how the hybrid representation and its operations look like. We also report on the experimental results we obtained with the China analyzer. The interested reader is referred to [3] for a complete account of this work. 2 A New, Hybrid Implementation for Pos The observation of many constraint logic programs shows that the percentage of variables which are found to be ground during the analysis, for typical invocations, is as high as 80 . This suggests that representing Pos ....

R. Bagnara. A reactive implementation of Pos using ROBDDs. Technical Report TR-96-19, Dipartimento di Informatica, Universit`a di Pisa, 1996.

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