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The purpose of this paper is to show that indirect recursive procedures can be used for implementing real-time applications without harm, if a few conditions are met. These conditions ensure that upper bounds for space and time requirements can be derived at compile time. Moreover they are simple enough such that many important recursive algorithms can be implemented. In addition

Symbolic Evaluation is a technique aimed at determining dynamic properties of programs. We extend our intraprocedural dataflow framework introduced in [3] to support interprocedural symbolic evaluation. Our data-flow framework utilizes a novel approach based on an array algebra to handle aliases induced by procedure calls. It serves as as a basis for static program analysis (e.g. reaching definitions-, alias analysis, worst-case performance estimations, cache analysis). Examples for reaching definitions- as well as alias analysis are presented.

Caches impose a major problem for predicting execution times of real-time systems since the cache behavior depends on the history of previous memory references. Too pessimistic assumptions on cache hits can result in worst-case execution time estimates that are prohibitive for real-time systems.

A data-flow framework for symbolic reaching definitions analysis is presented. It produces a more accurate solution of the reaching definitions problem than can be achieved with "classic" data-flow analysis.

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) and Õ(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. 1

Abstract. Sreedhar et al. [SGL98, Sre95] have presented an eliminationbased algorithm to solve data flow problems. A thorough analysis of the algorithm shows that the worst-case performance is at least quadratic in the number of nodes of the underlying graph. In contrast, Sreedhar reports a linear time behavior based on some practical applications. In this paper we prove that for goto-free programs, the average case behavior is indeed linear. As a byproduct our result also applies to the average size of the so-called dominance frontier. A thorough average case analysis based on a graph grammar is performed by studying properties of the j-edges in DJ graphs. It appears that this is the first time that a graph grammar is used in order to analyze an algorithm. The average linear time of the algorithm is obtained by classic techniques in the analysis of algorithms and data structures such as singularity analysis of generating functions and transfer lemmas. 1.

Abstract. We present a generic symbolic analysis framework for imperative programming languages. Our framework is capable of computing all valid variable bindings of a program at given program points. This information is invaluable for domain-specific static program analyses such as memory leak detection, program parallelisation, and the detection of superfluous bound checks, variable aliases and task deadlocks. We employ path expression algebra to model the control flow information of programs. A homomorphism maps path expressions into the symbolic domain. At the center of the symbolic domain is a compact algebraic structure called supercontext. A supercontext contains the complete control and data flow analysis information valid at a given program point. Our approach to compute supercontexts is based purely on algebra and is fully automated. This novel representation of program semantics closes the gap between program analysis and computer algebra systems, which makes supercontexts an ideal intermediate representation for all domainspecific static program analyses. Our approach is more general than existing methods because it can derive solutions for arbitrary (even intra-loop) nodes of reducible and irreducible control flow graphs. We prove the correctness of our symbolic analysis method. Our experimental results show that the problem sizes arising from real-world applications such as the SPEC95 benchmark suite are tractable for our symbolic analysis framework. 1

Abstract. The average case of some elimination-based data-flow analysis algorithms is analyzed in a mathematical way. Besides this allows for comparing the timing behavior of the algorithms, it also provides insights into how relevant the underlying statistics are when compared to practical settings. 1.