Characterizing minimal semantics-preserving slices of predicate-linear, free, liberal program schemas

This is a preprint version of the article - Copyright @ 2011 ElsevierA program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. A subschema of a schema is obtained from a schema by deleting some of its statements. We prove that given a schema S which is predicate-linear, free and liberal, such that the true and false parts of every if predicate satisfy a simple additional condition, and a slicing criterion defined by the final value of a given variable after execution of any program defined by S, the minimal subschema of S which respects this slicing criterion contains all the function and predicate symbols ‘needed’ by the variable according to the data dependence and control dependence relations used in program slicing, which is the symbol set given by Weiser’s static slicing algorithm. Thus this algorithm gives predicate-minimal slices for classes of programs represented by schemas satisfying our set of conditions. We also give an example to show that the corresponding result with respect to the slicing criterion defined by termination behaviour is incorrect. This complements a result by the authors in which S was required to be function-linear, instead of predicate-linear.This work was supported by a grant from the Engineering and Physical Sciences Research Council, Grant EP/E002919/1

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

Decidability of strong equivalence for subschemas of a class of linear, free, near-liberal program schemas

The article attached is a preprint version of the final published article which can be accessed at the link below. The article title has been changed. For referencing purposes please use the published details. Copyright © 2010 Elsevier B.V. All rights reserved.A program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. Two schemas are strongly equivalent if they always define the same function from initial states to final states for every interpretation. A subschema of a schema is obtained from a schema by deleting some of its statements. A schema S is liberal if there exists an initial state in the Herbrand domain such that the same term is not generated more than once along any executable path through S. In this paper, we introduce near-liberal schemas, in which this non-repeating condition applies only to terms not having the form g() for a constant function symbol g. Given a schema S that is linear (no function or predicate symbol occurs more than once in S) and a variable v, we compute a set of function and predicate symbols in S which is a subset of those defined by Weiser's slicing algorithm and prove that if for every while predicate q in S and every constant assignment w:=g(); lying in the body of q, no other assignment to w also lies in the body of q, our smaller symbol set defines a correct subschema of S with respect to the final value of v after execution. We also prove that if S is also free (every path through S is executable) and near-liberal, it is decidable which of its subschemas are strongly equivalent to S. For the class of pairs of schemas in which one schema is a subschema of the other, this generalises a recent result in which S was required to be linear, free and liberal.This work was supported by a grant from the Engineering and Physical Sciences Research Council, Grant EP/E002919/1

Program simplification as a means of approximating undecidable propositions

We describe an approach which mixes testing, slicing, transformation and formal verification to investigate speculative hypotheses concerning a program, formulated during program comprehension activity. Our philosophy is that such hypotheses (which are typically undecidable) can, in some sense, be `answered' by a partly automated system which returns neither `true' nor `false' but a program (the `test program') which computes the answer. The motivation for this philosophy is the way in which, as we demonstrate, static analysis and manipulation technology can be applied to ensure that the resulting test program is significantly simpler than the original program, thereby simplifying the process of investigating the original hypothesi

Pre/post conditioned slicing

Th paper shows how analysis of programs in terms of pre- and postconditions can be improved using a generalisation of conditioned program slicing called pre/post conditioned slicing. Such conditions play an important role in program comprehension, reuse, verification and reengineering. Fully automated analysis is impossible because of the inherent undecidability of pre- and post- conditions. The method presented reformulates the problem to circumvent this. The reformulation is constructed so that programs which respect the pre- and post-conditions applied to them have empty slices. For those which do not respect the conditions, the slice contains statements which could potentially break the conditions. This separates the automatable part of the analysis from the human analysis

Backward conditioning: A new program specialisation technique and its application to program comprehension

This paper introduces backward conditioning. Like forward conditioning (used in conditioned slicing), backward conditioning consists of specialising a program with respect to a condition inserted into the program. However, whereas forward conditioning deletes statements which are not executed when the initial state satisfies the condition, backward conditioning deletes statements which cannot cause execution to enter a state which satisfies the condition. The relationship between backward and forward conditioning is reminiscent of the relationship between backward and forward slicing. Forward conditioning addresses program comprehension questions of the form `what happens if the program starts in a state satisfying condition c?`, whereas backward conditioning addresses questions of the form `what parts of the program could potentially lead to the program arriving in a state satisfying condition c?' The paper illustrates the use of backward conditioning as a program comprehension assistant and presents an algorithm for constructing backward conditioned programs

Decidability of Strong Equivalence for Subschemas of a Class of Linear, Free, near-Liberal Program Schemas

In this paper we introduce near-liberal schemas, in which this non-repeating condition applies only to terms not having the form g() for a constant function symbol g. Given a schema S that is linear (no function or predicate symbol occurs more than once in S) and a variable v, we compute a set of function and predicate symbols in S which is a subset of those de�ned by Weiser's slicing algorithm and prove that if for every while predicate q in S and every constant assignment w := g(); lying in the body of q, no other assignment to w also lies in the body of q, our smaller symbol set de�nes a correct subschema of S with respect to the �nal value of v after execution. We also prove that if S is also free (every path through S is executable) and near-liberal, it is decidable which of its subschemas are strongly equivalent to S. For the class of pairs of schemas in which one schema is a subschema of the other, this generalises a recent result in which S was required to be linear, free and liberal.

VADA: A transformation-based system for variable dependence analysis

Variable dependence is an analysis problem in which the aim is to determine the set of input variables that can affect the values stored in a chosen set of intermediate program variables. This paper shows the relationship between the variable dependence analysis problem and slicing and describes VADA, a system that implements variable dependence analysis. In order to cover the full range of C constructs and features, a transformation to a core language is employed Thus, the full analysis is required only for the core language, which is relatively simple. This reduces the overall effort required for dependency analysis. The transformations used need preserve only the variable dependence relation, and therefore need not be meaning preserving in the traditional sense. The paper describes how this relaxed meaning further simplifies the transformation phase of the approach. Finally, the results of an empirical study into the performance of the system are presented