A New Method for Program Inversion

Abstract

Program inversion has been successfully applied to several areas such as optimistic parallel discrete event simulation (OPDES) and reverse debugging. This paper introduces a new program inversion algorithm for imperative languages, and focuses on handling arbitrary control flows and basic operations. By building a value search graph that represents recoverability relationships between variable values, we turn the problem of recovering previous values into a graph search one. Forward and reverse code is generated according to the search results. We have implemented our algorithm as part of a compiler framework named Backstroke, a C++ source-to-source translator based on ROSE compiler. Backstroke targets optimistic simulation codes and automatically generates a reverse function to recover values modified by a target function. Experimental results show that our method is effective and produces better performance than previously proposed methods.

Synthesizing Loops for Program Inversion

“…As noted previously, the framework comprises two novel intermediate program representations, which we refer to as value search graph and route graph [3]. This section summarizes the key ideas behind these representations, explaining how we use them to construct both forward and reverse programs.…”

“…This section summarizes the key ideas behind these representations, explaining how we use them to construct both forward and reverse programs. (Please see our earlier paper for all the formal details [3].) Section 3 describes our extensions for loops.…”

“…Given P , we first translate the program into a standard compiler intermediate program representation known as single static assignment (SSA) form [2]. From the SSA form, we construct a value search graph (VSG) [3]. The problem of finding a forward or reverse program becomes a combinatorial search problem on the VSG.…”

“…The problem of finding a forward or reverse program becomes a combinatorial search problem on the VSG. The result of this search is a subgraph of the VSG, which we call a route graph (RG) [3]. There may be many such search results, each of which is a particular forward or reverse program.…”

“…In this case, P + produces extra outputs, which we denote by S. Indeed, even if P is theoretically reversible without requiring extra output, we may nevertheless need to generate S due to fundamental technical limits on program analysis. This paper extends our prior compiler-based program inversion framework, called Backstroke [3], to handle the case of programs with loops. As a concrete introductory example, consider the following program on the left, which takes as input an integer n ≥ 0 and produces the output, s ← n i=0 i: s = 0; n = 0; while (n > 0) { while (s > 0) { s = s + n; n = n + 1; n = n -1; s = s -n; } }…”