A Grammar-Based Approach to Invertible Programs

Abstract

Abstract. Program inversion has many applications such as in the implementation of serialization/deserialization and in providing support for redo/undo, and has been studied by many researchers. However, little attention has been paid to two problems: how to characterize programs that are easy or hard to invert and whether, for each class of programs, efficient inverses can be obtained. In this paper, we propose an inversion framework that we call grammar-based inversion, where a program is associated with an unambiguous grammar describing the range of the program. The complexity of the grammar indicates how hard it is to invert the program, while the complexity is related to how efficient an inverse can be obtained.

Polynomial-time inverse computation for accumulative functions with multiple data traversals

“…Since now an accumulative function can be viewed as non-accumulative context-generating functions, we hope that we can extend usual range-analysis-based program-inversion methods [16,19,24] to those functions, and hope that a program-inversion method developed in this way would be a good alternative to the existing approaches [15,26,27]. Another future direction is to develop an inverse computation method that can handle more kinds of copying.…”

“…Leftinverse computation [15-17, 19, 27] focuses on injective functions and tries to make an efficient inverse computation based on injectivity analysis, but it can only handle provably-injective functions. Right-inverse computation [1,24,32] including ours can handle more functions than left-inverse computation does-it works even for non-injective functions-but the yielded inverse-computation process is usually much slower than that of left-inverse computation. Another important difference is that left-inverse computation is compositional; if we have effective left-inverse computation methods for f and g, we have an effective left-inverse computation method for f • g. On the other hand, right-inverse computation may not be compositional; even if we have right-inverse computation methods for f and g, then right-inverse computation may happen to be undecidable for f • g. Left-inverse computation is suitable for applications in which efficiency is the biggest concern, such as in serialization/deserialization.…”

“…It is so far unclear how to perform tractable terminating inverse computation for func-tions with accumulations and multiple data traversals (Section 2). Some of the existing methods [1,16,24] do not terminate for functions with accumulations. Some approaches [15,26,27] can handle certain accumulative computations efficiently, but they do not work for non-injective functions such as eval .…”

Refactoring pattern matching

“…Matsuda et al [63] discussed right-inverse computation using grammar parsing. They construct a grammar from a program, so that the productions of the grammar abstract the evaluation of the program.…”

Polynomial-time inverse computation for accumulative functions with multiple data traversals

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