Slicing Distributed Programs

– Instead of defining both Ctl formulas and least fixed point computation algorithms, program slicing can be described as a μ-calculus formula [11] only. This greatly simplifies the definition of existing classes of program slicing (backward/forward/chopping, static/dynamic/hybrid/conditioned, syntaxpreserving/amorphous) in a unified and concise framework. Due to its capability of defining both state and action predicates (instead of only state predicates in the case of Ctl formulas) together with fixed point operators, μ-calculus formulas can limit the scope of interest while inspecting the abstract state graph, thus allowing the definition of more precise slicing techniques. The μ-calculus logic presents additional advantages. On one hand, the different slicing methods can be mapped to property patterns that commonly occurs in the specification of concurrent and reactive systems. There exists such property pattern mappings for μ-calculus [12] that can be applied to the different slicing problems. On the other hand, μ-calculus acts as an assembly language with tool support adapted to the construction with rapid testing of new slicing techniques. In the case of alternation-free μ-calculus formulas, model checkers, like in the verification toolbox Cadp [6], can solve them with various linear time complexity algorithms, that generate minimal diagnostic examples representing the program slices. – Symbolic model checkers are not currently capable to find the set of states satisfying formulas using backward modalities, which are the overlined possibility (i.e., − 3) and necessity (i.e., − 2) operators used to define forward slicing techniques. One solution is to use explicit model checkers, like Gear [3], which can evaluate μ-calculus formulas with backward 2 and 3 operators. Another solution is to specify the slicing problem at a lower level, using Boolean equation systems (Bess) [2]. Forward data-flow analyses, represented as μ-calculus formulas with backward operators [13], can be trans-