Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composing the transfer functions of the constituent instructions. However, precision can be improved by applying a single transfer function that captures the semantics of the block as a whole. Since blocks are program-dependent, this approach necessitates automation. There has thus been growing interest in computing transfer functions automatically, most notably using techniques based on quantifier elimination. Although conceptually elegant, quantifier elimination inevitably induces a computational bottleneck, which limits the applicability of these methods to small blocks. This paper contributes a method for calculating transfer functions that finesses quantifier elimination altogether, and can thus be seen as a response to this problem. The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.
Embedded software must meet conflicting requirements such as be-ing highly reliable, running on resource-constrained platforms, and being developed rapidly. Static program analysis can help meet all of these goals. People developing analyzers for embedded object code face a difficult problem: writing an abstract version of each instruction in the target architecture(s). This is currently done by hand, resulting in abstract operations that are both buggy and im-precise. We have developed Hoist: a novel system that solves these problems by automatically constructing abstract operations using a microprocessor (or simulator) as its own specification. With almost no input from a human, Hoist generates a collection of C func-tions that are ready to be linked into an abstract interpreter. We demonstrate that Hoist generates abstract operations that are cor-rect, having been extensively tested, sufficiently fast, and substan-tially more precise than manually written abstract operations. Hoist is currently limited to eight-bit machines due to costs exponential in the word size of the target architecture. It is essential to be able to analyze software running on these small processors: they are important and ubiquitous, with many embedded and safety-critical systems being based on them. In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.