A New Elimination-Based Data Flow Analysis Framework Using Annotated Decomposition Trees

Abstract

Abstract. We introduce a new framework for elimination-based data flow analysis. We present a simple algorithm and a delayed algorithm that exhibit a worstcase complexity of O(n 2 ) andÕ(m). The algorithms use a new compact data structure for representing reducible flow graphs called Annotated Decomposition Trees. This data structure extends a binary tree to represent flowgraph information, dominance relation of flowgraphs, and the topological order of nodes. The construction of the annotated decomposition trees runs in O(n + m). Experiments were conducted with reducible flowgraphs of the SPEC2000 benchmark suite.

Static Detection of Livelocks in Ada Multitasking Programs

“…In contrast, an algorithm [30] based on decomposition properties of reducible CFGs delivered only polynomial sizes for the SPEC2000 benchmark suite. This algorithm is known to produce exponential RE sizes only if the number of backedges (i.e., loops) is large compared to the overall number of edges in the CFG.…”

An Algebraic Framework for Compositional Program Analysis

“…The (single-source) path expression problem for a flow graph G = V, E, v entry , v exit is to compute for each vertex v ∈ V a path expression P[v entry , v] ∈ RegExp E representing the set of paths Paths[v entry , v]. An efficient algorithm for solving this problem was given in [37]; a more recent path expression algorithm appears in [35]. Understanding the specifics of these algorithms is not essential to our development, but the idea behind both is to divide G into subgraphs, use Gaussian elimination to solve the path expression problem within each subgraph, and then combine the solutions.…”

“…Understanding the specifics of these algorithms is not essential to our development, but the idea behind both is to divide G into subgraphs, use Gaussian elimination to solve the path expression problem within each subgraph, and then combine the solutions. Kleene's classical algorithm for converting a finite automaton to a regular expression [21] provides another way of solving path-expression problems that, while less efficient than [35,37], should provide adequate intuition for readers not familiar with these algorithms.…”

“…In the algebraic framework, an analysis designed by providing an abstract semantic domain K, an algebraic structure (called a Pre-Kleene algebra) defining the space of possible program properties which is equipped with sequencing, choice, and iteration operations; and a semantic function which interprets the meaning of a program action as an element of K. The correctness of an analysis (with respect to a given concrete semantics) is proved by establishing an soundness relation between the concrete semantic algebra and the abstract algebra. The result of the analysis is computed via a path expression algorithm [35,37], which re-interprets a regular expression (representing a set of program paths) using the operations of the semantic algebra.…”

“…This style of compositional loop analysis can yield interesting ways of computing loop invariants that cannot be defined iteratively. We identify a class of algorithms, the so-called path-expression algorithms [35,37], which can be used to efficiently implement analyses in our framework. Lastly, we develop a theory for proving the correctness of an analysis by establishing an approximation relationship between an algebra defining a concrete semantics and an algebra defining an analysis.…”