PROGRAM STRUCTURE TREES - Software Systems Lab

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One possibility is to analyze different parts of a program with different accuracy, such that only interesting regions are analyzed precisely. Other regions could be analyzed roughly and, if required, be refined later. Another possiblity is to hide the complexity of a program, by considering only the overall effect of a region on the program state, but not simulating every single change that the execution of a program region implies. As the complexity of a lot of algorithms is related to the number of analyzed program states, reducing the number of program states might improve runtime significantly. 5.1 The control flow automaton Static program analisis often uses a control flow automaton (CFA) to represent a program, in contrast to the CFGs that are more widespread in optimizing compilers. A control flow automaton is a graph G=(V, E) with a set of vertives V and a set of edges E. Every vertice represents a program state. Transitions in between program states are defined by the edges, that connect two states applying an operation. The operations can be either a set of calculations or a assume operation. 5.2 Convert an CFG to an CFA To convert an CFG to an CFA as seen in 5 it is necessary to find the program states and transitions in an CFG. In a CFG the program state is changed by the operations executed in the basic blocks. Before and after the operations in a basic block, there is a defined program state. Therefore we can create for every basic block BB two new program states c 1, c 2 one defining the state before and one after the execution of BB. The transition between these two program states can be defined as execution of the operations contained in the basic block. If a terminating branch statement exists in the basic block, the conditions can be applied as assume operations on the transitions from c 2 to the next program states. 8
a b a b c_1 i = 100 i=100 if (b == 80) T F c_2 b == 80 b != 80 d e d e (a) CFG (b) CFA Figure 5: Convert a CFG basic bock to CFA nodes and transitions references [1] Thomas Ball. What’s in a region?: or computing control dependence regions in near-linear time for reducible control flow. ACM Lett. Program. Lang. Syst., 2(1-4):1–16, 1993. [2] Carsten Gutwenger and Petra Mutzel. A linear time implementation of spqr-trees. In GD ’00: Proceedings of the 8th International Symposium on Graph Drawing, pages 77–90, London, UK, 2001. Springer-Verlag. [3] John E. Hopcroft and Robert Endre Tarjan. Dividing a graph into triconnected components. SIAM J. Comput., 2(3):135–158, 1973. [4] Richard Johnson, David Pearson, and Keshav Pingali. The program structure tree: Computing control regions in linear time. pages 171–185, 1994. [5] Jussi Vanhatalo, Hagen Völzer, and Jana Koehler. The refined process structure tree. In BPM ’08: Proceedings of the 6th International Conference on Business Process Management, pages 100–115, Berlin, Heidelberg, 2008. Springer-Verlag. 9
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