... This paper concerns the problem of interprocedural slicing---generating 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

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We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a contextfree-language reachability problem whose answer gives a solution to the set-constraint problem. The interconvertibility of these two formalisms offers an conceptual advantage akin to the advantage gained from the interconvertibility of finite-state automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the "O(n³) bottleneck" for different types of program-analysis problems, and allows results previously obtained for context-free-language reachability problems to be applied to set-constraint problems.

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We show the interconvertibility of context-free-language reachability problems and a class of setconstraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gives a solution to the set-constraint problem. The interconvertibility of these two formalisms offers an conceptual advantage akin to the advantage gained from the interconvertibility of finite-state automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the "O(n ) bottleneck" for different types of program-analysis problems and allows results previously obtained for context-free-language reachability problems to be applied to set-constraint problems and vice versa.

Anumber of program-analysis problems can be tackled by transforming them into certain kinds of graph-reachability problems in labeled directed graphs. The edge labels can be used to filter out paths that are not of interest: A path P from vertex s to vertex t only counts as a “valid connection ” between s and t if the word spelled out by P is in a certain language. Often the languages used for such filtering purposes are languages of matching parentheses: • Insome cases, the matched-parenthesis condition is used to filter out paths with mismatched calls and returns. This leads to so-called “context-sensitive ” program analyses, such as context-sensitive interprocedural slicing and contextsensitive interprocedural dataflow analysis. • Inother cases, the matched-parenthesis condition is used to capture a graph-theoretic analog of McCarthy’s rules: “car(cons(x,y))=x ” and “cdr(cons(x,y))=y”. That is, in the code fragment c=cons(a,b); d=car(c); the fact that there is a “structure-transmitted data dependence ” from a to d, but not from b to d, iscaptured in a graph by using (i) avertex for each variable, (ii) an edge from vertex i to vertex j when i is used on the right-hand side of an assignment to j, (iii) parentheses that match as the labels on the edges that run fromatocandctod, and (iv) parentheses that do not match as the labels on the edges that run frombtocandctod.

this paper, we present a new approach to studying program-integration algorithms. In particular, we introduce

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