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65
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
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Cited by 696 (78 self)
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... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previous dependence representations to incorporate collections of procedures (with procedure calls) rather than just monolithic programs. Our main result is an algorithm for interprocedural slicing that uses the new representation. (It should be noted that our work concerns a somewhat restricted kind of slice: Rather than permitting a program to be sliced with respect to program point p and an arbitrary variable, a slice must be taken with respect to a variable that is defined or used at p.) The chief
Interprocedural Dataflow Analysis via Graph Reachability
, 1994
"... This paper shows howalarge class of interprocedural dataflowanalysis problems can be solved precisely in polynomial time. The only restrictions are that the set of dataflow facts is a finite set, and that the dataflow functions distribute overthe confluence operator (either union or intersection). ..."
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Cited by 373 (33 self)
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This paper shows howalarge class of interprocedural dataflowanalysis problems can be solved precisely in polynomial time. The only restrictions are that the set of dataflow facts is a finite set, and that the dataflow functions distribute overthe confluence operator (either union or intersection). This class of problems includesbut is not limited tothe classical separable problems (also known as "gen/kill" or "bitvector" problems)e.g.,reaching definitions, available expressions, and live variables. In addition, the class of problems that our techniques handle includes manynonseparable problems, including trulylive variables, copyconstant propagation, and possiblyuninitialized variables. Anovelaspect of our approach is that an interprocedural dataflowanalysis problem is transformed into a special kind of graphreachability problem (reachability along interprocedurally realizable paths). The paper presents three polynomialtime algorithms for the realizablepath reachability problem: an exhaustive version, a second exhaustive version that may be more appropriate in the incremental and/or interactive context, and a demand version. The first and third of these algorithms are asymptotically faster than the best previously known realizablepath reachability algorithm. An additional benefit of our techniques is that theylead to improved algorithms for twoother kinds of interprocedural analysis problems: interprocedural flowsensitive sideeffect problems (as studied by Callahan) and interprocedural program slicing (as studied by Horwitz, Reps, and Binkley).
Abstract interpretation frameworks
 Journal of Logic and Computation
, 1992
"... We introduce abstract interpretation frameworks which are variations on the archetypal framework using Galois connections between concrete and abstract semantics, widenings and narrowings and are obtained by relaxation of the original hypotheses. We consider various ways of establishing the correctn ..."
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Cited by 240 (23 self)
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We introduce abstract interpretation frameworks which are variations on the archetypal framework using Galois connections between concrete and abstract semantics, widenings and narrowings and are obtained by relaxation of the original hypotheses. We consider various ways of establishing the correctness of an abstract interpretation depending on how the relation between the concrete and abstract semantics is defined. We insist upon those correspondences allowing for the inducing of the approximate abstract semantics from the concrete one. Furthermore we study various notions interpretation.
Interprocedural MayAlias Analysis for Pointers: Beyond klimiting
, 1994
"... Existing methods for alias analysis of recursive pointer data structures are based on two approximation techniques: klimiting, which blurs distinction between subobjects below depth k; and storebased (or equivalently location or regionbased) approximations, which blur distinction between elements ..."
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Cited by 229 (0 self)
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Existing methods for alias analysis of recursive pointer data structures are based on two approximation techniques: klimiting, which blurs distinction between subobjects below depth k; and storebased (or equivalently location or regionbased) approximations, which blur distinction between elements of recursive data structures. Although notable progress in interprocedural alias analysis has been recently accomplished, very little progress in the precision of analysis of recursive pointer data structures has been seen since the inception of these approximation techniques by Jones and Muchnick a decade ago. As a result, optimizing, verifying and parallelizing programs with pointers has remained difficult. We present a new parametric framework for analyzing recursive pointer data structures which can express a new natural class of alias information not accessib...
Verification by abstract interpretation
 In Verification: Theory and Practice
, 2003
"... Dedicated to Zohar Manna, for his 2 6 th birthday. Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is ..."
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Cited by 192 (16 self)
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Dedicated to Zohar Manna, for his 2 6 th birthday. Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is illustrated on the particular cases of predicate abstraction, which is revisited to handle infinitary abstractions, and on the new parametric predicate abstraction. 1
Program Analysis via Graph Reachability
, 1997
"... This paper describes how a number of programanalysis problems can be solved by transforming them to graphreachability problems. Some of the programanalysis problems that are amenable to this treatment include program slicing, certain dataflowanalysis problems, and the problem of approximating th ..."
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Cited by 119 (8 self)
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This paper describes how a number of programanalysis problems can be solved by transforming them to graphreachability problems. Some of the programanalysis problems that are amenable to this treatment include program slicing, certain dataflowanalysis problems, and the problem of approximating the possible "shapes" that heapallocated structures in a program can take on. Relationships between graph reachability and other approaches to program analysis are described. Some techniques that go beyond pure graph reachability are also discussed.
The Interprocedural Coincidence Theorem
 In Int. Conf. on Comp. Construct
, 1992
"... We present an interprocedural generalization of the wellknown (intraprocedural) Coincidence Theorem of Kam and Ullman, which provides a sufficient condition for the equivalence of the meet over all paths (MOP ) solution and the maximal fixed point (MFP ) solution to a data flow analysis problem. Th ..."
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Cited by 87 (11 self)
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We present an interprocedural generalization of the wellknown (intraprocedural) Coincidence Theorem of Kam and Ullman, which provides a sufficient condition for the equivalence of the meet over all paths (MOP ) solution and the maximal fixed point (MFP ) solution to a data flow analysis problem. This generalization covers arbitrary imperative programs with recursive procedures, global and local variables, and formal value parameters. In the absence of procedures, it reduces to the classical intraprocedural version. In particular, our stackbased approach generalizes the coincidence theorems of Barth and Sharir/Pnueli for the same setup, which do not properly deal with local variables of recursive procedures. 1 Motivation Data flow analysis is a classical method for the static analysis of programs that supports the generation of efficient object code by "optimizing" compilers (cf. [He, MJ]). For imperative languages, it provides information about the program states that may occur at s...
Cache Behavior Prediction by Abstract Interpretation
 Science of Computer Programming
, 1996
"... 1 Cache Memories and RealTime Applications Caches are used to improve the access times of fast microprocessors to relatively slow main memories. They can reduce the number of cycles a processor is waiting for data by providing faster access to recently referenced regions of memory1. Programs with h ..."
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Cited by 83 (11 self)
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1 Cache Memories and RealTime Applications Caches are used to improve the access times of fast microprocessors to relatively slow main memories. They can reduce the number of cycles a processor is waiting for data by providing faster access to recently referenced regions of memory1. Programs with hard real time constraints have to be subjected to a schedulability analysis by the compiler [17, 6]; it has to be determined whether all timing constraints can be satisfied. WCETs (Worst Case Execution Times) for processes have to be used for this. For hardware with caches, the appropriate worst case assumption is that all accesses miss the cache. This is an overly pessimistic assumption which leads to a waste of hardware resources. 1 Hennessy and Patterson [8] describe typical values for caches in 1990 workstations
Demanddriven Computation of Interprocedural Data Flow
, 1995
"... This paper presents a general framework for deriving demanddriven algorithms for interprocedural data flow analysis of imperative programs. The goal of demanddriven analysis is to reduce the time and/or space overhead of conventional exhaustive analysis by avoiding the collection of information tha ..."
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Cited by 78 (9 self)
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This paper presents a general framework for deriving demanddriven algorithms for interprocedural data flow analysis of imperative programs. The goal of demanddriven analysis is to reduce the time and/or space overhead of conventional exhaustive analysis by avoiding the collection of information that is not needed. In our framework, a demand for data flow information is modeled as a set of data flow queries. The derived demanddriven algorithms find responses to these queries through a partial reversal of the respective data flow analysis. Depending on whether minimizing time or space is of primary concern, result caching may be incorporated in the derived algorithm. Our framework is applicable to interprocedural data flow problems with a finite domain set. If the problem's flow functions are distributive, the derived demand algorithms provide as precise information as the corresponding exhaustive analysis. For problems with monotone but nondistributive flow functions the provided dat...
Proving Program Invariance and Termination by Parametric Abstraction, Lagrangian Relaxation and Semidefinite Programming
 IN VMCAIâ€™2005: VERIFICATION, MODEL CHECKING, AND ABSTRACT INTERPRETATION, VOLUME 3385 OF LNCS
, 2005
"... In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametr ..."
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Cited by 64 (1 self)
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In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstraction into numerical constraints by Lagrangian relaxation. The remaining universal quantification is handled by semidefinite programming relaxation. Finally the parameters are computed using semidefinite programming solvers. This new approach exploits the recent progress in the numerical resolution of linear or bilinear matrix inequalities by semidefinite programming using efficient polynomial primal/dual interior point methods generalizing those wellknown in linear programming to convex optimization. The framework is applied to invariance and termination proof of sequential, nondeterministic, concurrent, and fair parallel imperative polynomial programs and can easily be extended to other safety and liveness properties.