On the computational complexity of dynamic slicing problems for program schemas

This is the preprint version of the Article - Copyright @ 2011 Cambridge University PressGiven a program, a quotient can be obtained from it by deleting zero or more statements. The field of program slicing is concerned with computing a quotient of a program that preserves part of the behaviour of the original program. All program slicing algorithms take account of the structural properties of a program, such as control dependence and data dependence, rather than the semantics of its functions and predicates, and thus work, in effect, with program schemas. The dynamic slicing criterion of Korel and Laski requires only that program behaviour is preserved in cases where the original program follows a particular path, and that the slice/quotient follows this path. In this paper we formalise Korel and Laski's definition of a dynamic slice as applied to linear schemas, and also formulate a less restrictive definition in which the path through the original program need not be preserved by the slice. The less restrictive definition has the benefit of leading to smaller slices. For both definitions, we compute complexity bounds for the problems of establishing whether a given slice of a linear schema is a dynamic slice and whether a linear schema has a non-trivial dynamic slice, and prove that the latter problem is NP-hard in both cases. We also give an example to prove that minimal dynamic slices (whether or not they preserve the original path) need not be unique.This work was partly supported by the Engineering and Physical Sciences Research Council, UK, under grant EP/E002919/1

Unions of slices are not slices

Many approaches to slicing rely upon the 'fact' that the union of two static slices is a valid slice. It is known that static slices constructed using program dependence graph algorithms are valid slices (Reps and Yang, 1988). However, this is not true for other forms of slicing. For example, it has been established that the union of two dynamic slices is not necessarily a valid dynamic slice (Hall, 1995). In this paper this result is extended to show that the union of two static slices is not necessarily a valid slice, based on Weiser's definition of a (static) slice. We also analyse the properties that make the union of different forms of slices a valid slice

ConSIT: A conditioned program slicer

Conditioned slicing is a powerful generalisation of static and dynamic slicing which has applications to many problems in software maintenance and evolution, including reuse, reengineering and program comprehension. However there has been relatively little work on the implementation of conditioned slicing. Algorithms for implementing conditioned slicing necessarily involve reasoning about the values of program predicates in certain sets of states derived from the conditioned slicing criterion, making implementation particularly demanding. The paper introduces ConSIT, a conditioned slicing system which is based upon conventional static slicing, symbolic execution and theorem proving. ConSIT is the first fully automated implementation of conditioned slicing. An implementation of ConSIT is available for experimentation at &http://www.mcs.gold.ac.uk/tilde/~mas01sd/consit.htm